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part 2, 7.4 MB - School of Electrical and Computer Engineering

1. vfov double scalar Vertical field of view hfov double scalar Horizontal field of view position double array Three element array of sensor x y 2 coordinates lookAt double array Three element array of look at x y z coordinates upv double scalar Three element array representing the up direction clipping double array Two element array consisting of the minimum and maximum ranges dataDim uint32 array Row x Column dimension of the result image in pixels the vertical and horizontal sampling 5 1 4 Configuration File Format Figure 5 1 shows the structure of a configuration file Configuration files can be loaded and saved with the load configuration and save configuration functions respectively 5 2 Model Libraries Model libraries are a collection of model geometries and associated parameters for rendering It is important to note that it is best not to have model libraries that contain too many highly detailed models because all model information is stored in main memory If a user were to create a model library with 20 models and each model file was larger than 20 megabytes when loaded then MATLAB would need over 400 megabytes of memory to store the model library at bare minimum Keep your system s memory requirements in mind when creating model libraries 5 2 1 Model Library Structure Model library structures never need to be manipulated directly so this section may b
2. 5 3 2 Point Clouds Point clouds are created by taking the two dimensional points in a range image and convert ing them to their corresponding three dimensional coordinates The resulting point cloud consisting of L points is constructed as a 3 x L matrix If an image is rendered with a N x M data dimension then there will be at most NM coordinates in the resulting point 27 cloud The number of coordinates L is less than NM when there is sky present in the scene when a ground plane is not rendered or when pixels are set at the minimum or maximum range values A typical point cloud is shown in Figure 5 4 It is worth noting that if you desire to create a single point cloud from multiple views this can be easily accomplished by appending the new point clouds to the previous ones For example if you have a 3 x 15000 point cloud and a 3 x 20000 point cloud from two different views of the same scene they can be combined into a single 3 x 35000 point cloud Figure 5 4 A typical point cloud 5 3 3 Depth Buffer If desired the user can also create images that consist of the raw values pulled from the OpenGL depth buffering system after rendering the scene This type of image is similar to the range image in that each pixel represents some notion of range but the values will be arbitrary double precision floating point values This tends to be useful for visualizing data sets since depth is treated linearly without converting to true ran
3. a number of information theoretic tools were used to determine bounds on target detection performance in images with noise and clutter The bounds noted in that study included Kullback Leibler and Chernoff distances The study considered the cases without nuisance parameters and with the nuisance parameter of orientation Our work focuses on standard deviation bounds on estimating pose parameters although most ATR algorithms consider them to be nuisance parameters We are considering the pose parameters directly because of their importance in aim point selection or other scenarios where it is important to identify specific points on a target We investigate how the bounds change as we vary the distance position and orientation of the targets A similar study using CRLBs was performed by Gerwe et al to determine bounds on orientation when viewing satellites from ground based optical sensors All imagery required in our CRLB study is synthetic by nature so we are not bound to using one specific collection of laser radar data sets We can generate scenes with any viewing parameters and any combination of targets This allows us to see how the CRLBs change as the scene parameters change Tel 404 385 2548 Fax 404 894 8363 E mail jdixonQece gatech edu lantermaQece gatech edu This paper begins with a discussion of our LADAR statistical model in Section 1 1 We then consider the CRLB and its derivation for our LADAR signal model in Section 1 2
4. amx30 stl bmpl1f Files of type Al Files y Cancel Figure 3 5 Dialog box for selecting CAD model files to add to the model library 13 Create New Model Library Model List ambwe54 amx13 bmplf brdm1 brdm1w Type Geometry File amx30 stl Intensity File amx30 stl Figure 3 6 Model library creation GUI after adding CAD model files Please note When a model file is read all geometry files referenced therein will be loaded into main memory If you have too many large geometry files referenced in a model library your computer may not be capable of loading the model library Please consider the memory capabilities of your computer and the size of your model geometry files when creating model libraries 3 4 Model Editor GUI Model geometry files are created in many different ways The units used to define the models and the orientation in which a model rests can vary greatly from file to file In addition to organizing a collection of model files model libraries hold information about resizing rescaling and reorienting the models themselves These adjustments allow you to redefine the default units and orientation of a model without permanently altering the geometry file The Model Editor GUI can be launched by pressing the Model Editor button in the main LADAR Simulator GUI see Figure 3 7 14 Model Editor X Axis View Y Axis View Test Angle o Rotation Axis E Z Y C
5. 0 0 500 1000 1500 2000 0 500 1000 1500 2000 Distance from Target meters Distance from Target meters a b 1 8 Boung gt Angle ene Number of Pixels on Target Vs Distance w 4000 7 7 1 S 1 6 Number of Pixels o 3500 o 3 1 4 J o 2 3000 1 21 2 J 3 lt gt 2500 4 s ot E 5 2000 E 0 8 r 7 a o m x 1500 7 gt 0 6 a 1000 1 z 0 4 4 Z m 0 2 500 4 gt 3 0 0 0 500 1000 1500 2000 0 500 1000 1500 2000 Distance from Target meters Distance from Target meters e d Figure 2 Cramer Rao lower bounds on estimating a x position b y position and c orientation angle for a single M60 tank with respect to distance between the LADAR sensor and the tank and d pixels on target versus distance when the M60 is at an orientation angle of 0 degrees pointing to the right that the decrease in visible tank surface area makes it more difficult to estimate the target s depth parameter Considering that ATR algorithms are typically designed to be invariant to pose these results suggest that they are indeed affected by it to some degree It is interesting to note how the bound changes if parameters are coupled or decoupled We see as expected that the bounds are higher when the parameters must be jointly estimated In some cases the bounds are extremely close as seen with the bounds on y position and angle estimation in Figures 3 b and 3 c respectively In the case of estimating z position in Fig
6. 2 quantifies the relationship between the data and all possible hypothesized scenes and is thus a function of several pose type and thermal state parameters with a dimension that changes with the number of targets in the hypothesized scene As shown in the previous section we can easily estimate the thermal state parameters given a particular pose To estimate the parameters of interest we need a way to sample from this posterior distribution that can also adjust the number of targets since we do not know this information in advance We follow the jump diffusion framework presented by Lanterman et al Miller et al and Srivastava et al The algorithm is designed around a reversible jump Markov process that accounts for the continuous and discrete aspects of the ATR problem The discrete components are handled by jumping from one inference task to another deciding whether to add a target remove a target or changing a target s type These choices will henceforth be called birth death and metamorph respectively The continuous aspects namely the inference of the pose parameters are refined via a diffusion process The decision process used when determining whether or not to accept a jump involves random sampling and Metropolis Hastings acceptance rejection For birth and metamorph jumps a representative set of candidate locations and orientation angles are chosen respectively For death jumps candidates are chosen
7. 4 5 6 Several passive radar systems have been developed in recent years with Lockheed Martins Silent Sentry and John Sahr s Manastash Ridge Radar 7 8 serving as notable examples B Coupling Passive Radar RCS Based Target Recognition with a Coordinated Flight Model The goal of this research is to enhance existing passive radar systems which are al ready capable of detecting and tracking aircraft with target recognition capabilities In particular the proposed approach to target recognition which falls into the second school of thought on ATR uses the covertly obtained RCS from a passive radar source as the primary parameter for identification More precisely target recognition is conducted by comparing the covertly collected RCS of the aircraft under track to the simulated RCS of a variety of aircraft comprising the target library To make the simulated RCS as accurate as possible the received signal model accounts for aircraft position and orientation propagation losses and antenna gain patterns A coordinated flight model uses the target state vector produced by the passive radar tracker to approximate aircraft orientation Coupling the aircraft orientation and state with the known antenna locations renders computation of the incident and observed azimuth and elevation angles possible The Fast Illinois Solver Code FISC simulates the RCS of potential target classes as a function of these angles Thus the approximated i
8. Next we proceed into the implementation and the experimental discussion in Sections 1 3 and 2 respectively Then we discuss some of the results and what information we gain from performing this CRLB analysis in Sections 3 3 4 Finally we will conclude and offer some suggestions for future work in this area in Section 4 1 1 LADAR statistical model For LADAR images we employ a coherent detection likelihood function that incorporates single pixel noise statistics developed by Shapiro and Green and used in a multi target ATR study for LADAR data If d is an image of measured range values and p is an image of uncorrupted true range values then the loglikelihood function is given by 1 1 td n u r Pralm 2ro n 20 n Ram LLs d u Y log 1 Pra n exp where o n is the local range accuracy for pixel n given by Rres CNR n and Pra n is the probability of anomalous measurement for pixel y given by o n log N 0 557 Pra n A Ramp is the range ambiguity interval and N is the number of range resolution bins given by Ramb N Rres Rres is the range resolution and CNR is the carrier to noise ratio taken to be Pr roA 2ap n CNR n By Chea 5 where a is the atmospheric extinction coefficient Epp is the receiver s optical efficiency Ehe is the receiver s heterodyne efficiency 7 is the detector s quantum efficiency hv is the photon energy p is the ta
9. Collection Time Bank Turn Trajectory 4 Pe F 157 38 EW CE PEN 077 _ m _EF 15 Falcon 20 E F 15 Falcon 100 80 aiz PE T 38 Falcon 20 z E T 38 Falcon 100 1 1 E Falcon 20 Falcon 100 Probability of Error 5 10 15 20 25 Length of Collection Time s Fig 8 Probability of Error Vs Time Banked Turn Trajectory Noise Figure 40 dB June 11 2006 DRAFT 19 100 90 80 Probability of Error Fig 9 Probability of Error Vs Time Banked Turn Trajectory Noise Figure 45 dB June 11 2006 Probability of Error Vs Length of Collection Time Bank Turn Trajectory 20 T T T T I I AN 21 PE F 15 T 38 LL A O Pe F 15 Falcon 20 a 3 FE F 15 Falcon 100 a gt Z PE T 38 Falcon 20 pa Pe T 38 Falcon 100 4 Z LLK P 3 A E Falcon 20 Falcon 100 10 15 20 25 Length of Collection Time s 30 35 40 DRAFT Appendix E L M Ehrman and A D Lanterman A Laplace Approximation of the Kullback Leibler Distance Between Ricean Distributions IEEE Trans on Informa tion Theory to be submitted A Laplace Approximation of the Kullback Leibler Distance between Ricean Distributions Lisa M Ehrman Member IEEE and A D Lanterman Member IEEE Abstract An approximation of the Kullback Leibler distance between Ricean distributions is derived using Laplace s method It is found to be more accurate th
10. al In practice we must add a criterion to determine when the algorithm has converged Assuming that the data can be represented by a hidden set of configuration parameters there is nothing to tell the algorithm that the current set of estimated configuration parameters are close to these hidden ones Two more issues arise when computing the Langevin SDE during a diffusion the choice of stepsizes for the derivative computation and the choice of stepsizes for the diffusions themselves In the previously discussed experiments both of these were determined empirically through a trial and error approach that yielded the best adjustments to the configuration parameters In practice these need to be determined in an automated fashion because they depend on the types of targets in the scene and the scene s viewing parameters We consider alternative algorithms that facilitate local parameter search via Metropolis Hastings or Gibbs style sampling in a small region around the current parameter estimate Using these schemes we can adjust the configuration parameters so that they adjust the targets by individual pixel values leading to faster convergence rates With the additional variability that we can now model with the eigentank expansion incorporated into the jump diffusion process there is a need to restrict that variability to actual target types As shown in Section 6 2 matching a target against a portion of background with similar thermal s
11. by removing a single target from the hypothesized configuration The posterior probabilities are computed at each of these candidates and one candidate is randomly chosen with a probability proportional to its posterior probability In practice one candidate posterior probability typically swamps the others so it often appears as though the candidate with maximum probability is automatically chosen The Metropolis Hastings algorithm accepts the chosen candidate with probability CEE an 1 14 Teel esas Cprop where Cprop is the proposed state of the configuration while cprig is the current state The functions r Cprop Corig and T Corig Cprop are the transition probabilities see Lanterman et al 3 for details The function r c is the probability of being in state c which in this case is derived from the logposterior H c d for that state The choice of which type of jump to perform is determined probabilistically by a prior distribution based on the number of hypothesized targets in the configuration As typical with continuous time Markov processes the time between jumps is exponentially distributed During these intervals between jumps the diffusion process takes over and perturbs the continuous pose parameters by small amounts to better align the hypothesized targets with the data Diffusions are accomplished using the Langevin stochastic differential equation dC y t Voy H Cy r djdr V2dWy 15 where Wy is a Wiener proc
12. changes of the pose parameters This technique was originally used to compute derivatives of forward looking infrared FLIR loglikelihood functions as part of a diffusion process in an ATR study in Ref 9 2 EXPERIMENTS For the experiments that follow we assume the laser radar parameters found in Table 1 which were taken from the coherent detection forward looking laser radar discussed by Bounds We assume the laser radar points toward a single M60 tank with a vertical field of view of 12 mrad The tank parameter space O has variables z y and 0 where z and y are horizontal and depth coordinates on the ground while 9 is an angular orientation in degrees all referenced to some known initial position and orientation The size of the image obtained from the laser radar is assumed to be 125 x 60 pixels Images of the tank viewed from the maximum and minimum ranges studied are shown in Figure 1 Optical Efficiency opt 0 5 Heterodyne Efficiency Ehet 0 5 Detector Quantum Efficiency n 0 25 Receiver Aperture Dimension Dr 13 cm Atmospheric Extinction Coefficient a 1 dB km Average Transmitted Power Ps 5 W IF Filter Bandwidth B 80 MHz Photon Energy hv 1 87 x 107 J Range Resolution Rres 6m Target Reflectivity p 0 25 Table 1 Parameter values for the coherent detection LADAR statistical model In the first experiment we estimated CRLBs for the orientation horizontal position and depth position for a target of interest whil
13. define the elements within a FLIR image The patterns that we are interested in are built from templates These templates may undergo transformations Tel 404 385 2548 Fax 404 894 8363 E mail jdixonQece gatech edu lantermaQece gatech edu such as translations rotations changes of scale or any other action that can be represented mathematically To determine the transformations present in the imagery acquired from the FLIR sensor we must be able to synthetically create similar imagery thus the tasks of pattern synthesis and pattern recognition are linked in this framework Continuing with this pattern theoretic terminology we will refer the objects of interest within the imagery as generators A configuration will denote the set of generators that make up the scene 1 2 Representation of complex scenes In this study the set of generators in a scene configuration will consist of an unknown number of vehicles This is the image seen by the FLIR sensor Each generator will contain knowledge about the object it represents which in this case includes position orientation type and thermal profile A single generator g representing a ground based target in the set of generators G will be part of the configuration space C R x 0 27 x Axa which defines a ground based position and orientation a generator class representing the type of target e g A M2 M60 T62 and a set of thermal parameters a A scene with N targets lives
14. direction and you know that the vehicle is supposed to me 4 meters long in that direction then you can type 4 into the z field All other Model Dimensions will adjust accordingly as will the scale factor The camera positions in the three windows will also be adjusted to provide the same view of the object after they have been resized Note that when adjusting the Translation or Rotation Axis Adjustment fields the units are in the native model units and not the scaled ones When using the Model Editor GUI some trial and error is usually involved in order to obtain desired model adjustments 17 3 5 Ground Plane GUI The Ground Plane GUI provides users access to the geometric description of the ground plane see Figure 3 10 The ground plane is a flat rectangular surface A corner is defined by setting the x y z coordinates of the Origin field The lengths in the z and y directions are specified using the next two text fields If negative values are supplied in these fields then the ground plane extends along the axes in the negative direction An arbitrary intensity value is specified in the last text field The value itself is arbitrary and may be set to any positive integer Ground Plane Settings SIE Ground Plane Origin 10 410 X Length Y Length 20 Intensity 1776 Ground Plane Parameters successfully Read Figure 3 10 GUI for changing ground plane settings When changing fields the GUI will perform a general
15. in a space CN Since the number of targets is not known in advance the full parameter space is a union C U Cy 2 FLIR STATISTICS Our analysis of FLIR data sets for ATR purposes is based on a Bayesian framework We start with a likelihood function that models FLIR sensor statistics and use it to compare scenes synthesized from hypothesized config urations with the collected data The likelihood is combined with prior information to form a Bayesian posterior distribution We consider uniform priors over position and orientation In practice we implicitly introduce the prior information that two targets may not occupy the same space by not considering such scenes 2 1 Gaussian likelihood model Our earlier FLIR ATR studies assumed a likelihood function based on Poisson statistics The FLIR sensor was taken to be a CCD detector producing Poisson distributed data with means proportional to the radiant intensities of the objects in the sensor s field of view Using such a model assumes the sensor is calibrated to give specific photon counts While this is often true in astronomical imaging it is usually not the case for operational FLIR sensors Hence we switch to a Gaussian model similar to the one discussed by Koskal et al This model assumes the measured temperature is related to the true temperature of the objects present in the scene by Gaussian distributed noise consisting of a combination of thermal noise and shot noise We treat the
16. loglikelihood function with respect to the parameter vector To make the calculation simpler we will compute o n for a given and approximate it as being constant with respect to small changes in With this approximation the first term in 6 may be dropped and the derivative can now be computed as follows 2D n p n 0 u n A Lrr D p y SE a ee 8 n D n u n 5 n n O gt o2 n i 9 n Our sensor model treats the data scene D n as a Gaussian random variable with a mean given by the uncorrupted range u n O and variance o n for pixel n Therefore E D n u n Using this relationship the FIM becomes D n u n 2 y n D n p n 2 R El D n es My D SE 2 10 ely Pee A 11 I u n O 77 n n 12 E D n u n D n n 0 gt 2 o n a 00 The expectation in this last equation appears in the form of a covariance between the random variables D n and D We assume that pixels in the LADAR image are independent so the covariance is zero when n Therefore each element in the FIM can be reduced to n Taking the inverse of this matrix leaves us with a lower bound on the covariance matrix for the parameters of interest By saying that the covariance matrix is bounded by the inverse FIM we mean that Cov gt F i e the matrix Cov O F is nonnega
17. probability of error in a binary hypothesis testing problem can be approximated as a function of the Chernoff information between two den sities In the case of this ATR algorithm the densities representing the magnitude of the RCS of two aircraft being compared are best modeled as Rician For this reason Section III B derives a closed form approximation for the Chernoff information between two Ri cian densities Section IV then compares the ATR performance predicted by the Chernoff information approach with that obtained using Monte Carlo trials Having shown that the two approaches provide similar results Section V then uses the Chernoff information to determine how long an aircraft must be tracked in order for the probability of error in the ATR algorithm to drop below a desired threshold This application demonstrates the advantage of using the Chernoff information to approximate the performance of the ATR algorithm Since the Chernoff information is a function of the number of measurements collected its application to this problem is quite natural Monte Carlo trials in contrast would make for a particularly cumbersome approach to the problem A Approximating the Probability of Error Via the Chernoff Information It is widely known that the probability of error in a binary hypothesis test conducted in the Bayesian framework can be approximated in terms of the Chernoff information 12 In particular the probability of error is approxi
18. specified x y z coordinates and rotated by some angle around the three axes Targets may be rescaled if the units used to define the target s CAD model are undesirable Chapter 3 Graphical User Interfaces This chapter reviews the different graphical user interfaces GUls used in the LADAR Simulator 3 1 Main LADAR Simulator GUI To run the LADAR Simulator GUI type ladar_sim in the MATLAB prompt The GUI will prompt the user for a configuration file to load This file contains information for setting up a scene An example configuration file can be found in ladar_simulator config sample config If you wish to load default configuration settings just press the Cancel button in the dialog box Next another dialog box will appear This box asks the user to load a model library file This file contains structural information about the models referenced in the configuration file If a configuration file was selected a predetermined model filename will be chosen and the user must locate that file If no configuration file was selected the user is free to specify any available model library file The default model library file is ladar_simulator sample ml If no model libraries are available the user may create one by pressing the Cancel button and using the Model Library Creation GUI For instructions on how to use this GUI see Section 3 3 For the LADAR Simulator GUI to run a model library must be selected or created Once the model lib
19. temperature measurements at each pixel to be independent of all other pixels so the loglikelihood function becomes Lan dla SU 108 vane CA i n where ju is an ideal noiseless image d is the measured data and NEAT is the FLIR s noise equivalent tem perature difference The summation is computed over all pixels n in a given data image In this study we are only concerned with how the loglikelihood changes with different scene configurations so we can ignore terms that do not depend on yp and simply reduce the loglikelihood function per pixel to the squared error between the measured data and a hypothetical uncorrupted image p 2 2 Gibbs posterior distribution Given an estimated configuration state c the likelihood and the prior combine to form a Gibbs posterior distri bution of the form r c d x exp H e d 2 where H c d L d c P c is the logposterior created by summing the loglikelihood L d c and the logprior P c L d c Lrn d render c where render c is the process of obtaining an uncorrupted image m from a scene configuration c through perspective projection and obscuration This distribution will represent how closely related the hypothesized configuration is to the data image This distribution is sampled by a type of reversible jump Markov chain Monte Carlo routine called a jump diffusion process described in Section 4 3 REPRESENTING VARIABILITY IN INFRARED IMAGERY 3 1 Eigentanks We approach the modelin
20. the sensor scans over the field of view angles Square images are created by setting the two field of view angles to the same value while rectangular images result from one field of view angle being larger than the other regardless of the pixel dimensions The sensor s position can be specified in world or spherical coordinates To use world coordinates simply set the x y z parameter vector For spherical set the p 6 coordinates representing range azimuth and elevation An illustration of the view and coordinate system can be seen in Figure 2 1 Range is taken to be the distance between the sensor and the look at coordinate also specified as a x y z parameter vector The minimum and maximum viewable ranges must also be set using the appropriate parameters When viewing point clouds the data dimension and field of view angles are used to defined the scene from which the points will be extracted a b Figure 2 1 A Standard a and overhead b view of a scene s layout The sensor location is represented by the white circle 2 3 Adding Targets Scenes may contain any number of objects in a variety of positions and orientations These objects may be referred to as targets throughout this document Target geometries are 4 obtained by reading in CAD model descriptions The CAD model formats that this soft ware supports are PRISM Stereolithography 3D Studio and Princeton Shape Benchmark Targets are placed at
21. to be resting on a ground plane with unknown position x y unknown orientation angle 6 unknown type a A M60 T62 and unknown thermal state represented by the expansion coefficients for each eigentank a ay To determine the N and D terms required when computing the expansion coefficients we used a paint by numbers technique Each target in a configuration is rendered with a set of increasing yet disjoint region numbers so that each intensity region is colored by a different number One can easily compute the N by counting the pixels of a common region number and D by summing the corresponding data pixels After computing the expansion coefficients the inferred intensities can be used to color in the image of region numbers We consider the background to be of constant intensity equal to the average background intensity of the data This final image is considered the hypothesized true scene and is compared to the data set through the loglikelihood function The Gibbs form posterior distribution is explored by sampling the space of possible configurations with respect to the parameters of interest which involves rendering hypothesized scenes during any birth death or metamorph move In determining the acceptance probability for any move we obtained good results by assuming that the forward and reverse transition probabilities are equal and simply comparing the proposal and original posterior probabilities of the hypoth
22. validity check for the most recently used parameter and revert to the original value if the current value is found to be invalid Pressing the Reload button will reset to the GUI to its original state after it was first launched Pressing the OK button will save the ground plane settings close the Ground Plane GUI and redraw the scene using the new ground plane Pressing the Apply button will save the current ground plane settings and redraw the scene Pressing the Cancel button will close the Ground Plane GUI and discard all changes since the last time the Apply button was pressed Pressing the Enter Return key after editing a text field simulates pressing the Apply button 18 Chapter 4 Library Interface The functions used to read in models create manipulate scene configurations and draw display scenes are all available to call directly from a user defined MATLAB script or function This capability was included to allow users to run their own simulations using synthetic data generated on the fly Some of the functions and their descriptions are described here e Loading and Saving Files load_configuration Load configuration file into structures load data Retrieve image or point cloud from data file load_model_library Read model library file into a structure save_configuration Save configuration to a text files save_data Save a range image or point cloud to a data file save model library Save model
23. Appendix A J H Dixon LADAR Simulator User Manual LADAR Simulator User Manual Jason H Dixon Email jdixon at ece dot gatech dot edu Version 0 7 January 16 2007 Copyright 02006 Jason H Dixon This program is free software you can redistribute it and or modify it under the terms of the GNU General Public License as published by the Free Software Foundation either version 2 of the License or at your option any later version This program is distributed in the hope that it will be useful but WITHOUT ANY WAR RANTY without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE See the GNU General Public License for more details A copy of the GNU General Public License has been included with this program in the file gpl txt It can viewed by visiting the website http www gnu org copyleft gpl html and obtained by writing to the Free Software Foundation Inc 51 Franklin Street Fifth Floor Boston MA 02110 1301 USA This software includes other software and files that are subject to different copyright reg istrictions e gl h is from the Mesa 3 D graphics library Copyright 1999 2001 Brian Paul All Rights Reserved It is subject to the MIT Licesne The official MESA 3 D website is http www mesa3d org e glext h and glu h are Copyright 1991 2000 Silicon Graphics Inc and are subject to the SGI Free Software License B Version 1 1 See http oss sgi com projects FreeB e T
24. E 20 5 3 A Se PER ee AES 27 Pol Range MALE TA ROT e 27 A A IN Ra a ole Ma a aie POK TOBA 27 5 3 3 Depth Buffer riire Wa ere a e M O y Sag WO WA AE 28 Abstract This document describes a simulation tool used to created synthetic range imagery and three dimensional point cloud datasets within MATLAB Created scenes consist of multiple faceted models at user specified coordinates orientation angles and sizes The tool consists of a graphical user interface GUI and a simple library interface The GUI aids scene creation by facilitating object placement specifying the ground plane defining the viewing perspective and adjusting model parameters The library interface allows the use of the scene generation code to write MATLAB scripts that create and analyze customized data sets The tool currently supports faceted models in PRISM 3D Studio stereolithography and Princeton Shape Benchmark object file formats Chapter 1 Getting Started 1 1 System Requirements System requirements for running the LADAR Simulator are e MATLAB Version 7 0 or above with the LCC compiler e Installed OpenGL libraries e Operating System Windows XP Mac OS X There is no recommended requirement for RAM CPU speed or hard disk space except for what is required for MATLAB Please keep in mind that rendering three dimensional graphics is a resource intensive process The software has been tested on 2 0 GHz Pentium 4 system with 512MB of RAM producing sa
25. Left x 6 2 y 7 9 2 0 022 1 24 1 Little Endian Row Major O Lower Left SEREM Phase Redrawing Complete C Colormap Figure 3 1 Main LADAR Simulator GUI window The Target List listbox shows targets that have been added to the current configuration The text fields below the list box are used to set target parameters Targets may be added removed or updated by pressing the corresponding buttons next to the Target List list box Targets may also be added with the mouse by left clicking on the desired location in the scene When you select an item in the listbox the corresponding target parameters will appear in the text fields Users may also update existing targets by pressing the Enter key after changing one of the text field values Scene configurations may be loaded from configuration files by pressing the Load button The Save button will save a configuration to a file The adjustable target parameters are as follows e Position the location of the target in the scene x and y are ground coordinates while z is the coordinate above or below the ground plane In most situations z will be set to zero e Rotation Angle an angle rotation in degrees starting from the positive z axis and moving counter clockwise e Rotation Axis axis about which to perform rotations To perform rotations about z axis this should be set to 0 0 1 e Scale stretches or shrinks a target by multiplying the scale by the coordinat
26. Section IV demonstrates that the approximation of the algorithm s performance using the Chernoff information is very similar to that which is obtained using Monte Carlo trials As such the Chernoff information approach can confidently be used to address questions that would be cumbersome to address via Monte Carlo trials For example a useful piece of information is the length of time that the aircraft must be tracked in order to identify it with a desired probability of error The number of Monte Carlo trials required to address this question is staggering as a complete set of trials would be required for each period of time tested However this problem is easily addressed using the Chernoff information Figures 4 and 5 show the probability of error as a function of the length of time that the target is tracked using noise figures of 40 and 45 dB for the first straight and level trajectory Similar results are given in Figures 6 through 9 for the second straight and level trajectory and the banked turn trajectory respectively Several points are worth stating Consider the first straight and level trajectory Whether the noise figure is 40 or 45 dB the most difficult comparisons for the ATR algorithm are the between the F 15 and T 38 and the Falcon 20 and Falcon 100 This corroborates fairly well with the results presented in Figure VII and makes intuitive sense since the June 11 2006 DRAFT 8 F 15 and T 38 are both fighter style aircra
27. a function of the noise figure computed by both approaches Two points are worth making First both methods agree that the probability of error is near zero The noise figure is a unitless quantity that increases proportionately to the noise power It should not be confused with SNR For more information see the papers listed in the bibliography by Ehrman and Lanterman June 11 2006 DRAFT 7 until the noise figure reaches 50 dB This noise level is higher than the maximum noise level anticipated in any real system thus the algorithm is expected to perform very well at realistic noise levels Second the results obtained using the Chernoff information corroborate those obtained using Monte Carlo trials Although there is slight disagreement during the transition period with noise figures between 50 and 60 dB the results obtained using the Chernoff information generally agree with those obtained from Monte Carlo trials Figure 2 shows the probability of error curves for the second straight and level trajec tory Although the algorithm s performance has improved now that a wider range of aspects are presented to the receiver the results obtained using the Chernoff information still corroborate those obtained using Monte Carlo trials The trend continues using the banked turn trajectory whose probability of error curves are given in Figure 3 V USING THE CHERNOFF INFORMATION TO EFFICIENTLY ANALYZE PERFORMANCE OF AN ATR ALGORITHM
28. able or gFile vertex Table single matrix N x 8 matrix of model vertices vertex TableLength uint32 N as used in vertexTable facetIndexLists cell array M x l array of uint32 arrays of indices into vertexTable facetIndexListSizes uint32 array M x 1 array containing the sizes of each array in facetIndexLists numberOfFacets uint32 scalar the M as referenced above number of facets in model intensity Region uint32 array the intensity index of each facet max Vertex single array three element z y z for the largest bounding box coordinate min Vertex single array three element z y z for the smallest bounding box coordinate intensityList uint32 array K x 1 array of intensity or arbitrary values intensityListLength uint32 scalar K as referenced above number of intensities 5 2 3 Model Library File Format The model library file format is designed to keep a record of CAD models common to a certain scene and the adjustable parameters for each of those models To load or save model library files use the load model library or save model library functions respectively The first line in the file contains the term number_of models followed by a single space and an integer 25 representing the number of models in the file Each model is listed on consecutive lines and the model parameters on a single line are separated by a single space The parameters are as follows 1 10 A unique nonnegative integer model iden
29. als in 3 Begin with the second integral To apply Laplace s method we first write q ez TSp LSq a A SH ae f exp hpg x da 0 where hpg is defined as l zz m o G2 tn 120 2 9 7 as 8 2 2 c Sp 20 Taking the Taylor Series expansion of h g x around the value of z that maximizes hpg 1 results in hala hpal Ehi 8 a0 Mg 10 Thus 8 is approximated by exp hpa 2 EOG dx 11 Taking an additional approximation of changing the lower limit in the integral from 0 to infty 11 may be rearranged into a form containing the integral of a Gaus sian density over its full range which lets us approximate 11 as explhpg y form approximation of the third integral in 3 Simi larly the second integral in 3 may be approximated as explhpp 2 27 hy 7 where the definition of hpp fol low naturally from the definition of hpq simply substitute Sp for sq in the last term of 9 Our Laplace approximation for the relative en tropy between Rician distributions is then given by D p z q 2 2r hga This provides a closed s s m 2 exp hpp 21 ex hp 2 20 hu 12 All that remains to finish this closed form approximation is to find expressions for and Rig 2 The first derivative of hp z is nate 3 oa hn in o 52 a Setting this equal to zero and using the
30. amera Location 19 1022 X Camera Location 19 1022 A A Render Z Axis View Model Native Dimensions 6367 39 3122 7 2943 86 E Y 2 Translation x y z 3700 0 0 Rotation angle x y z 0 0 0 0 Rotation Axis Adjustment 500 0 0 x y 2 Scale Factor Y OSA 6 3674 3 1227 2 9439 X Camera Location 19 1022 RA Model Library Successfully Loaded Figure 3 7 GUI for changing model library parameters The GUI has three windows where each window faces the origin from one of the three coordinate axes The GUI attempts to automatically adjust the viewing distance in each window so that the model is completely visible If a different view is desired you can change the value underneath the window This value represents the distance between the camera and the origin along the specified axis To zoom in on the object in the window simply decrease the magnitude of this value To zoom out increase the magnitude of this value The Model pop up menu allows you to choose the model to be adjusted The Translation text fields are used to define a default movement to occur in each direction before an object 15 is placed in a scene Typically model files are defined in such a way that the origin is considered to be one of the bottom corners of the object It may be convenient to place the origin on the bottom center of the model so that if a target is placed at 0 0 0 then the target will
31. an a simple Gaussian approximation Keywords relative entropy Stein s lemma I INTRODUCTION The Rician density may be expressed as x r s TS g2 P 20 lo z i 1 The Ricean density which reduces to a Rayleigh density if b 0 arises in a number of engineering problems from fad ing multipath channels in communications to modeling the radar cross section of aircraft observed with low frequency radar 1 2 3 The Kullback Leibler distance also called the relative entropy is a natural information theoretic discrepancy measure between two distributions For instance Stein s lemma 5 uses relative entropy to describes asymptotic be havior in detection problems p x Computing the relative entropy between two Rician dis tributions involves some intractible integrals This corre spondence presents closed form approximations to the rel ative entropy between Ricean distributions 3 7 A Derivation of the Relative Entropy Between Two Rician Densities We will consider two Rician densities p x and q x that have the same o parameters but differing s parameters which will be denoted as s and s The relative entropy between two densities is given by Dolata Pro a Substituting 1 into 2 reveals that the relative entropy between two Rician densities with the same o parameter This work was supported by the NATO Consultation Command and Control Agency NC3A the U S Air Force O
32. andard deviation of pose parameters change with orientation angle or distance from target We note that the absolute values of these bounds are not as significant as the relative trends The LADAR model that we employ does not account for all possible sources of noise and image corruption so the bounds are much lower than one would expect them to be in practice 3 1 CRLBs versus range from LADAR The Cramer Rao lower bounds on pose estimation as a function of range from the target of interest behave as one would expect bounds tend to increase as range increases This can be attributed to the decrease in target information provided by the sensor i e fewer pixels on target because as the sensor moves further away the target becomes smaller within the limits of the field of view The equations for the LADAR statistics also tell us that the local range accuracy increases with range thus increasing the CRLB even further This result is consistent for all parameters as can be seen in Figure 2 Figure 2 d shows the number of target pixels present in the image at the given ranges from the LADAR For larger range values the curve is not monotonically increasing since small dips appear sporadically along the curve This may be due to a number of factors including limitations of the rendering process Within a small range interval it is possible that different features of the object being viewed will appear on the final image and the pixels containing
33. anding Teacher Award as voted on by the senior class of the School of Electrical and Computer Engineering at Georgia Tech June 11 2006 DRAFT 100 Probability of Error Vs Noise Figure Straight a 90 F 80 70 60 50 40 Probability of Error P 30 20 10 June 11 2006 m T T T p nd Level Trajectory 1 B O x MC Runs PE F 15 T 38 MC Runs Pe p_5 Falcon 20 MC Runs Pe p_5 Falcon 100 MC Runs Pe 88 Falcon 20 MC Runs Pe 38 Falcon 100 MC Runs Pe pajcon 20 Falcon 100 Bound P E F 15 T 38 Bound Pe p_5 Falcon 20 Bound Pz p_5 Falcon 100 Bound Pe _38 Falcon 20 Bound Pe r_g Falcon 100 Bound P Falcon 20 Falcon 100 12 60 70 Noise Figure dB 80 90 Fig 1 Probability of Error Vs Noise Figure Straight and Level Trajectory 1 100 DRAFT 100 Probability of Error Vs Noise Figure Straight and Level Trajectory 2 90 F 60 50 40 Probability of Error Pe 30 20 10 June 11 2006 80 MC Runs P 70 O E F 15 T 38 I T M I MC Runs P A MC Runs P MC Runs P _g_5 Falcon 100 e MC Runs Pe 1 38 Falcon 20 z E T 38 Falcon 100 5 E Falcon 20 Falcon 100 gt E F 15 T 38 E F 15 Falcon 20 MC Runs P Bound P Bound P Bound P 9 gt Bound P lt X E F 15 Falcon 20 E F 15 Falcon 100 E T 38 Falcon 20 Boun
34. approximation I z z results in plhp 2 0 Sp A o 14 eget 250 14 which yields a feasible solution CE 2 80 15 tm 5 8p 4 53 8a E 15 Taking the derivative of 13 produces the unweildy but straightforwardly implemented expression 7 m mik 1 Ey I SP hp ae o A I gt 3 s R 3 O esate Sg R 2 O GEE Ip Gt 5 ey ESEE 16 for the second derivative In summary the closed form approximation of the relative entropy is obtained by sub stituting 15 and 16 into 12 II COMPARISONS To compare the Gaussian approximation with the Laplace approximation the sg parameter is swept over a range of values while the s and o parameters are held constant Figure 1 shows the resulting relative en tropy and approximate probability of a Type II error Bplla exp D pllq as suggested by Stein s lemma when Sp 10 0 4 and sy is swept from 0 to 20 The approx imation derived using the Laplace method produces results that are nearly identical to the numerically approximated results The Gaussian approximation is not as accurate as the Laplace approximation for the smaller values of sq The difference becomes even more apparent if we reduce Sp to 5 and sweep s from 0 to 10 as shown in Figure 2 Relative Entropy for s 10 00 s 0 05 0 05 20 00 t 0 00 0 50 100 00 sigma2 4 0 T T T T T T T T T s D pllq Normal Ap
35. ar Data with Application to Passive Radar Opti cal Engineering letter of acceptance subject to minor revision received Feb 2 2006 revision submitted Feb 2007 Chernoft Based Prediction of ATR Performance from Rician Radar Data with Application to Passive Radar Lisa M Ehrman and Aaron D Lanterman Center for Signal and Image Processing School of Electrical and Computer Engineering Georgia Institute of Technology Atlanta GA 30332 USA Telephone 770 528 7079 404 385 2548 I ABSTRACT This paper develops a method for quickly assessing the performance of an ATR algorithm without using computationally expensive Monte Carlo trials To do so it exploits the relationship between the probability of error in a binary hypothesis test under the Bayesian framework to the Chernoff information Since it has been demonstrated in prior work that the RCS profiles being used to identify the targets are well modeled as Rician we begin by deriving a closed form approximation for the Chernoff information between two Rician densities This leads to an approximation for the probability of error in the ATR algorithm that is a function of the number of measurements available We conclude the paper with an application that would be particularly cumbersome to accomplish via Monte Carlo trials but that can be quickly addressed using the Chernoff information approach This application evaluates the length of time that an aircraft must be tracked before t
36. ations will occur about the z axis so the z y portion of this field should be set to 0 0 1 In the future more intuitive rotations like Euler angles will be supported The scale field scales the dimensions of the current target by a total value of s It then scales the corresponding dimensions as defined in the CAD model by an additional z y or z in each of those directions By default this array should be set to 1 1 1 1 for no additional scaling The visible field is either set to zero or one and controls the visibility of the target in the configuration for visible targets leave this set to one The library function that manipulates the target structure is set_target_param Table 5 2 Target structure fields Field Name Data Type Description class uint32 scalar Unique target class ID position single array Three element array of target x y 2 coordinates orientation single array Four element array of target 0 x y 2 orientation scale single array Four element array of target s z y 2 scale visible uint32 scalar O or 1 specifying whether to render a target 5 1 3 View Settings Structure The view settings are stored in a separate structure with parameters defined in Table 5 3 The library functions that manipulate the view structure are new view settings and set_view_ param 22 Table 5 3 View settings structure fields Field Name Data Type Description
37. d Pe T 38 Falcon 100 Bound Pz calcon 20 Falcon 100 y 13 Noise Figure dB Fig 2 Probability of Error Vs Noise Figure Straight and Level Trajectory 2 100 DRAFT 14 Probability of Error Vs Noise Figure Bank Turn Trajector 100 U 90 F 80 70t LLI a 60 e ui gt 50 MC Runs Pe e 151 08 E MC Runs PE F 15 Falcon 20 P MC Runs PE F 15 Falcon 100 MC Runs Pe T 38 Falcon 20 MC Runs Pe 38 Falcon 100 de MC Runs PE Falcon 20 Falcon 100 Bound Pe E is 1 38 gt Y Bound Pe F_45 Falcon 20 Bound Pe F_45 Falcon 100 i Bound PE T 38 Falcon 20 Bound P E T 38 Falcon 100 E Falcon 20 Falcon 100 I I I 70 80 90 100 Noise Figure dB e Bound P Fig 3 Probability of Error Vs Noise Figure Banked Turn Trajectory June 11 2006 DRAFT Probability of Error Fig 4 Probability of Error Vs Time Straight and Level Trajectory 1 Noise Figure 40 dB June 11 2006 100 90 80 70 60 50 10 15 20 25 30 35 Length of Collection Time s 40 Probability of Error Vs Length of Collection Time Straight and Level Trajectory 1 T T T T T T T I I ae F 15 T 38 SC EE INNE OZ gt E F 15 Falcon 20 _E F 15 Falcon 100 E T 38 Falcon 20 E T 38 Falcon 100 FE Pe Falcon 20 Falcon 100 45 DRAFT 15 16 Probability of Error Vs Le
38. d Image Science and Vision 20 5 pp 817 826 2003 D R Gerwe and P S Idell Cramer Rao analysis of orientation estimation Viewing geometry influences on the information conveyed by target features Journal of the Optical Society of America A Optics and Image Science and Vision 20 5 pp 797 816 2003 J Green T J and J H Shapiro Maximum likelihood laser radar range profiling with the expectation maximization algorithm Optical Engineering 31 11 pp 2343 54 1992 J Green T J and J H Shapiro Detecting objects in three dimensional laser radar range images Optical Engineering 33 3 pp 865 74 1994 A D Lanterman Jump diffusion algorithm for multiple target recognition using laser radar range data Optical Engineering 40 8 pp 1724 1728 2001 A D Lanterman M I Miller and D L Snyder General Metropolis Hastings jump diffusions for automatic target recognition in infrared scenes Optical Engineering 36 4 pp 1123 37 1997 J K Bounds The infrared airborne radar sensor suite Tech Rep RLE Technical Report No 610 Massachusetts Institute of Technology December 1996 U Grenander A Srivastava and M I Miller Asymptotic performance analysis of Bayesian target recog nition IEEE Transactions on Information Theory 46 4 pp 1658 65 2000 Appendix D L M Ehrman and A D Lanterman Chernoff Based Prediction of ATR Per formance from Rician Rad
39. der Miller and Srivastava is that recognition performance is inherently linked to the ability to estimate nuisance parameters such as the orientation and location of a target Even if a particular algorithm is designed to be invariant to pose and does not explicitly estimate pose parameters the issue percolates under the surface affecting how well the algorithm can perform ACKNOWLEDGMENTS This work was sponsored by the Air Force Office of Scientific Research AFOSR grant F49620 03 1 0340 10 11 REFERENCES A E Koksal J H Shapiro and M I Miller Performance analysis for ground based target orientation estimation FLIR LADAR sensor fusion Conference Record of the Thirty Third Asilomar Conference on Signals Systems and Computers vol 2 pp 1240 4 Pacific Grove CA 1999 U Grenander M I Miller and A Srivastava Hilbert Schmidt lower bounds for estimators on matrix lie groups for ATR IEEE Transactions on Pattern Analysis and Machine Intelligence 20 8 pp 790 802 1998 A Jain P Moulin M I Miller and K Ramchandran Information theoretic bounds on target recogni tion performance based on degraded image data IEEE Transactions on Pattern Analysis and Machine Intelligence 24 9 pp 1153 66 2002 D R Gerwe J L Hill and P S Idell Cramer Rao analysis of orientation estimation Influence of target model uncertainties Journal of the Optical Society of America A Optics an
40. djust the axis about which the rotation occurs In the case of the long gun the center of the bounding box may be closer to the front of the tank and a rotation would appear awkward An example of this effect is shown in Figure 3 9 16 a b Figure 3 9 Images showing how adjusting the rotation axis affects the final rotation Both images show two T62 tanks one at the default orientation and another at the same location but rotated by 90deg There is no rotation axis adjustment in a so the rotation axis is further from the center of the tank body This gives the rotated tank the appearance that it was displaced slightly In image b the rotation axis is moved so that it is in the center of the tank body This results in a rotation as we would intuitively think about one The Native Dimensions field shows the extent of the current model along the x y z axes Think of this as the dimensions of the bounding box along each of these axes The values in this field are determined by the native geometries of the model file meaning that they are the same as in defined in the CAD model geometry file The Model Dimensions text field shows how the extents change after applying the value in the Scale Factor field The scaling can also be adjusted by entering a new value directly in the x y or z Model Dimensions field For example a model s native dimensions are defined in a such a way that you have a vehicle that is 5000 units long in the x
41. e skipped if desired The Model Editor and New Model Library GUls are currently the only means by which model libraries may be changed Model library structures contain two fields numModels and models numModels is a field of type uin32 that stores the number of models in the library structure models is an array of model structures defined in Section 5 2 2 5 2 2 Model Structure Model structures never need to be manipulated directly so this section may be skipped if desired 23 model_library lt filename gt v_field_of_view lt degrees gt h_field_of_view lt degrees gt camera_position lt x position gt lt y position gt lt z position gt object_position lt x position gt lt y position gt lt z position gt up_vector lt x position gt lt y position gt lt z position gt clip_distance lt min range gt lt max range gt data_dims lt vertical pixels gt lt horizontal pixels gt number_of_targets lt nonnegative integer gt target 1 class_of_target lt nonnegative integer ID gt position lt x position gt lt y position gt lt z position gt orientation lt degrees gt lt x axis gt lt y axis gt lt z axis gt scale lt global value gt lt x position gt lt y position gt lt z position gt target lt final target number gt class_of_target lt nonnegative integer ID gt position lt x position gt lt y position gt lt z position gt orientation lt degrees gt lt x axis gt lt y axis gt lt
42. e same file and path as in the Geometry File field unless working with PRISM models In that case use the radiance filename For more information about the meaning of these fields see Section 5 2 3 12 To add model files to the library press the Add button A file dialog like the one shown in Figure 3 5 will appear Navigate to the subfolder with the geometry files and select the one s you wish to add to the model library Once you click Open the Model List listbox will populate with the chosen models and you can see the corresponding text fields by clicking on a model in the list see Figure 3 6 By default the classes are numbered sequentially in the same order in which the files were selected The types are determined by the extension of the geometry file The names are determined by the filename Any of the fields may be changed from the their default values The Remove button will remove the currently selected model from the library When finished press the Done button and the model library creation GUI will close the new model library will be loaded and you will be returned to the main LADAR Simulator GUI Select Model File s Look in B stl_models e GF EJ brdm3 stl cv35ren stl gaz67b stl browni stl B dump stl gme stl bt5 stl emt stl hemtt stl btr7d stl Flackp stl LS howitzer stl EB cargotru stl 3 fordgpa stl hummer stl challmgr stl g gaskin stl j122 stl File name ambwc54 stl amx13 stl
43. e varying the distance from the laser radar sensor to the target Each data set was assumed to have a single target sitting on a ground plane with a fixed horizontal position centered on the line of sight of the LADAR sensor When computing the Cramer Rao lower bounds we considered the cases where the parameters are coupled parameters are estimated jointly or decoupled each parameter is estimated individually assuming the other parameters are known To present bounds for the x and y parameters we compute the CRLB for TWarning tildes are used to indicate the three dimensional world coordinates used when rendering scenes in OpenGL while primes indicate image pixel coordinates a b Figure 1 Views of the M60 tank at a a position close to the laser radar sensor and b a position far from the laser radar sensor a set of equally spaced angles through a full 360 degree rotation and present the average of the CRLBs One could also present similar results for specific rotations of interest In the second experiment we fix the laser radar sensor and the target at a single location Bounds on the pose parameters are computed at each orientation angle at fixed intervals between 0 and 360 degrees to determine how our estimation ability changes as we view the target from different angles This experiment only considers the location closest to the LADAR 3 RESULTS In the following sections we present charts showing how the bounds on the st
44. els It is interesting to note how the bounds are affected by changes to image resolution We repeated the experiment defined in the previous section where we determined the bound on y position estimation with respect to orientation angle except this time we used an image resolution of 500x240 pixels Sample images from this study are shown in Figure 4 Plots from the experiment can be seen in Figure 5 The general trends in both plots remain unchanged since there are still strong peaks at the orientation angles where the target is facing directly towards or away from the LADAR sensor The values of the standard deviations however differ by an order of magnitude greater than three Another major difference between the charts can be seen in the ripples in the CRLB curve for the lower resolution images a b Figure 4 Images of M60 tanks at different resolutions Image a is 125x60 pixels and image b is 500x240 pixels 3 Bound on Y Position Estimation 4 Bound on Y Position Estimation 1 8X 10 x10 Coupled T 4 4 Coupled O sae O GG 5 1 7 Uncoupled 42 Uncoupled E E s 1 6 c 4 4 2 2 215 338 7 7 T 3 6 gt 1 4 4 gt 6 6 3 4 J 31 3 4 2 5 S 3 2 o o m 1 2 m 3 gt gt 2 8 z tt aed Noe 3 i FT 2 Z 0 2 67 J 1 L L L L L L 0 100 200 300 400 0 100 200 300 400 Orientation Angle degrees Orientation Angle degrees a b Figure 5 Cramer Rao bound
45. entification using modeled radar cross sections and a coordinated flight model in Proceedings from the Third Multi National Conference on Passive and Covert Radar Seattle WA October 2003 11 L Ehrman and A Lanterman A robust algorithm for automated target recognition using passive radar in Proceedings from the IEEE Southeastern Sympostum on System Theory Atlanta GA March 2004 12 T M Cover and J A Thomas Elements of Information Theory John Wiley amp Sons Inc 1991 June 11 2006 DRAFT 11 VII BIOGRAPHIES Lisa M Ehrman received a B S in electrical engineering from the University of Dayton in May of 2000 She worked for the following two years for MacAulay Brown Inc supporting the Suite of Integrated Infrared Countermeasures SIIRCM program lead by the United States Army Her main role was in the Test and Evaluation group but she also supported the Modeling and Simulation side of the program In pursuit of a research oriented career Lisa left MacAulay Brown in 2002 and began attending the Georgia Institute of Technol ogy She received her M S in electrical and computer engineering in May 2004 and her Ph D in electrical and computer engineering in December 2005 Her Ph D dissertation focused on automatic target recognition via passive radar and an EKF for estimating air craft orientation She has been a full time research engineer at the Georgia Tech Research Institute GTRI since May 2004 Her work a
46. es used to define the target From within the main LADAR Simulator GUI other GUls may be launched To change the viewing perspective and associated parameters press the View Settings button see Section 3 2 To adjust CAD model parameters press the Model Editor button see Section 3 4 To create new model libraries press the New Model Library button see Section 3 3 To change the current model library press the Change Models button To save range images or point clouds users can use the corresponding button and radio toggles When saving data sets it s best to remember the format used because it will be necessary information for correctly reloading datasets By default data is saved in the native machine format column major with the upper left corner of the image set as the origin 3 2 View Settings GUI The View Settings GUI facilitates the adjustment of scene viewing parameters see Figure 3 2 The text fields of the GUI are as follows e Field of View two fields representing the vertical and horizontal scanning angles used to determine the viewing area The angles are interpreted as or fov 2 from the current look at position in either direction e Position cartesian x y z coordinates representing the sensor location When the cartesian coordinates are changed the spherical coordinates are adjusted automatically e Position spherical p 0 coordinates representing the range azimuth and elevation from t
47. ese coordinates An array of four numbers in the form 0 x y z including the brackets and commas Similar to the previous field this one represents a default rotation to take place for rendering a model By default this can be set to 0 0 1 0 An array of three numbers in the form x y z including the brackets and commas This represents a translation to take place before a rotation occurs By default this may be set to 0 0 0 A scalar value that represents a scaling of the coordinates in the model file By default this may be set to 1 For an example model library file see Figure 5 2 26 number_of_models 3 O OFF mod shapel off mod shapel off O shapei 0 0 0 0 0 0 0 0 0 0 1 1 OFF mod shape2 off mod shape2 off O shape2 0 0 0 0 0 0 0 0 0 0 1 2 OFF mod shape3 off mod shape3 off O shape3 0 0 0 0 0 0 0 0 0 0 1 Figure 5 2 Example of a model library file 5 3 Data Sets The LADAR Simulator can create data sets in two forms range images and point clouds Data sets can be saved or loaded with the functions save_data and load data respectively Data is displayed in MATLAB with the function display_data 5 3 1 Range Imagery Range images are rectangular grids where each element represents the range from the sensor to world coordinate captured by that element In MATLAB these images are stored in matrix form See Figure 5 3 for a typical range image Figure 5 3 A typical range image
48. esized configuration scenes For a more intuitive sense of the implementation of the jump diffusion process see Figure 1 The derivative needed in solving the Langevin SDE 15 was computed with a finite difference approximation 0H cid H c 0 d H cp 0 d n I l 16 OCp 26 where c is an element of the configuration c 6 is some small deviation of the parameter cp and the ellipses indicate the remaining parameters are held fixed We use tildes earlier to indicate that the coordinate system is transformed according to the camera position and orientation Exponential Wait Time Over Diffuse Accept Reject Hypothesis with Metropolis Hastings Data Matches Hypothesis Choose Birth Death or Metamorph by Prior on Number of Targets Proposed State Original State No Jump Birth Ye Metamorph Determine Proposal Configuration State Probabilistically Sample Candidate Locations On Ground Plane Remove Individual Targets Sample Candidate Orientation Angles Estimate Expansion Coefficients and Compute Thermal Intensities Render Hypothesis Scenes at Candidate States Compute Likelinoods and Posterior Probabilities Figure 1 Simple block diagram for implementing the jump diffusion process for ATR in infrared data 6 RESULTS 6 1 Jump diffusion experiments Results from a jump difusio
49. ess and H Cy 7 d is the logposterior associated with the configuration parameter vector Cy which contains the configuration parameters for N targets of fixed classes The time index 7 refers to a unit of time within the diffusion interval Once 15 is discretized it can simply be thought of as a discrete time index such that a finite number of diffusions will occur between jumps and that number is an exponential random variable For a more detailed analysis of theory behind jump diffusions in general please refer to the aforementioned works by Lanterman et al Miller et al and Srivastava et al 1 5 IMPLEMENTATION This analysis was performed on an Apple Macintosh G4 computer running MATLAB 7 Objects were rendered from faceted tank models using the OpenGL three dimensional graphics application programming interface API OpenGL performs the transformation 2 4 2 1 y taking a three dimensional hypothesized scene and turning it into a two dimensional image through perspective projection and obscuration Our example configurations consist of a combination of M60 and T62 faceted tank models placed over an infrared background image The background image was included to give a sense of what a true infrared scene would look like but no effort was made to relate the viewing parameters of the background to the viewing parameters of the rendered images The rendered image was corrupted by Gaussian noise and bad pixels Targets are assumed
50. fected by them Keywords automatic target recognition ATR Cramer Rao bounds laser radar information theory 1 INTRODUCTION As the number of target recognition algorithms increases so does the need for accurate ways to compare the performance of one algorithm with another Without a measure for performance users of target recognition systems will have no way of identifying the superiority of one algorithm compared to another or determining if the sensor in use needs to be improved to achieve better target recognition results It is also useful to know if there is a fundamental limit on the ability to estimate a target s parameter of interest from data from a sensor In this study we consider targets imaged through laser radars By reformulating the target recognition problem as a deterministic parameter estimation problem we can apply the Cramer Rao lower bound CRLB to determine this measure of performance and these fundamental limits A number of studies have used information theoretic bounds for the purposes of performance estimation or the accuracy in estimating parameters of interest One such study performed by Koskal et al used performance bounds to determine pose estimation accuracy from forward looking infrared FLIR and laser radar LADAR In these experiments Cramer Rao bounds were compared to Hilbert Schmidt bounds on the mean squared error of estimating orientation as a function of noise In a study performed by Jain et al
51. ffice of Scien tific Research grant F49620 03 1 0340 and start up funds from the School of Electrical and Computer Engineering at the Georgia Insti tute of Technology L M Ehrman is with the Georgia Tech Research Institute e mail lisa ehrman Qgtri gatech edu A D Lanterman is with the School of Electrical and Computer En gineering Georgia Institute of Technology Mail Code 0250 Atlanta GA 30332 e mail lanterma ece gatech edu is oe LSq J p x In Zo dz The approximations presented in Sections I B and I C are suggested as a means of evaluating the integrals in 3 B A Gaussian Approximation for the Relative Entropy Between Rician Densities The relative entropy between two Gaussian distributions p x and q x is given by 4 D oola u 2 lo r 1 0 q where p x is a Gaussian density with mean uy and variance Up and q x pg and vq are defined similarly The mean of a Rician random variable X is given by E X 22 exp lt x 1 dex Gz e 1 x and its variance is 5 Var X s 20 E X 6 If the Gaussian means and variances in 4 are set to match the Rician means and variances given in 5 and 6 then 4 approximates the relative entropy between two Rician distributions C A Laplace Approximation for the Relative Entropy Be tween Two Rician Densities Our proposed closed form approximation uses Laplace s method 6 to evaluate the integr
52. ficients will either include matching the hypothesized target s intensity regions with the wrong regions of targets in the data or matching intensity regions with background If the background includes clutter that contains thermal characteristics similar to those of known targets then algorithm may choose a thermal profile that blends into the background If this happens during a birth move in the jump diffusion process a phantom target can appear in the hypothesized scene Since the likelihoods tend to increase with the existence of these phantom targets it becomes more difficult for the jump diffusion algorithm to remove them later on through a death movement An example of this can be seen in Figure 3 Here we simply computed expansion coefficients at four different positions over an infrared image that contained no targets The purpose was to see which facets of the resulting targets had thermal characteristics similar to the background data As seen in the image some target features appear as they would on a typical data set while other features blend into the background to the point where the tank almost disappears Figure 3 Tanks with radiance profiles derived from background emissions 7 CONCLUSIONS AND FUTURE AREAS OF RESEARCH We have discussed the unification of two pattern theoretic concepts in the realm of ATR for infrared data Combining the jump diffusion ATR algorithm with thermal state estimation we can perform ATR task
53. ft while the Falcon 20 and Falcon 100 are both commercial Another noteworthy point is that the probability of a correct identification when considering the Falcon 20 and Falcon 100 never exceeds 70 if the noise figure is 45 dB and the maximum time spent collecting data is 50 seconds This is largely attributed to the scenario Since the aircraft fly directly away from the receiver the range of aspects presented to the receiver is very narrow Better performance is expected using the second straight and level maneuver in which the aircraft fly broadside to the receiver This is indeed the case Using the second straight and level trajectory with a noise figure of 40 dB the ATR algorithm can correctly distinguish between all pairs of aircraft with a probability of error below 5 within 12 seconds instead of nearly 50 Similarly when the noise figure increases to 45 dB the algorithm correctly identify all pairs of aircraft within 14 seconds When using the first straight and level maneuver the algorithm was never able to reach this level of certainty Clearly the ATR algorithm s performance improves as a broader range of aspect angles are presented to the receiver The ATR algorithm performs even better against aircraft executing the banked turn maneuver This is probably caused by the same trend just described The more aspects of the aircraft presented to the receiver the better the ATR algorithm performs Using the second straight and level maneu
54. g of the thermal variations of targets from the mindset of empirical statistics and construct prior distributions on the radiant intensities of target facets 5 By simulating a large number of radiance measurements taken while varying environmental and internal heating parameters over reasonable ranges we generate a population of radiance profiles to which we apply principal component analysis For simulating radiances we employ the PRISM software originally developed by the Keweenaw Research Center at Michigan Technological University Assuming a Gaussian model the first few eigenvectors here called cigentanks provide a parsimonious representation of the covariance Suppose the surface of the CAD model of the tank is divided into I regions with the intensity assumed constant across each region and that we are employing J basis functions Let A denote the surface area of region i and A represent the intensity of region i We employ representations of the form A gt gt Y Pij Ma where m is the mean of region is eigentank j at region i and 4 is the eigenvalue associated with eigentank j The a s are expansion coefficients To generate the eigentank models we first synthesize a large database of N radiance maps written as a vectors A n APP n APP n 7 RIX for n 1 N The radiance maps are simulated under a wide range of conditions both meteorological solar irradiance wind speed relative
55. ge value The effect of this is that the default colormap will not obscure certain image features if the minimum and maximum ranges are set too far apart Rendering is also faster since there is no conversion to range values allowing the GUls to be more responsive to changes and simulations to run faster It is beneficial to work in this mode when setting up a scene Figure 5 5 shows a side by side comparison of a range image and a depth buffer image with larger then necessary minimum and maximum range difference 28 a b Figure 5 5 Comparison of a range image and depth buffer image when minimum and max imum ranges are set at 0 1 and 100 respectively 29 Appendix B J A Dixon and A D Lanterman Toward Practical Pattern Theoretic ATR Algorithms for Infrared Imagery Automatic Target Recognition XVI SPIE Vol 6234 Ed F A Sadjadi April 2006 pp 212 220 Toward practical pattern theoretic ATR algorithms for infrared imagery Jason H Dixon and Aaron D Lanterman Center for Signal and Image Processing School of Electrical and Computer Engineering Georgia Institute of Technology Atlanta GA 30332 USA ABSTRACT Techniques for automatic target recognition ATR in forward looking infrared FLIR data based on Grenan der s pattern theory are revisited The goal of this work is to unify two techniques one for multi target detection and recognition of pose and target type and another for structured inference of for
56. he look at point in the scene When the spherical coordinates are changed the cartesian coordinates are adjusted automatically e Look At cartesian coordinates representing the point to which the sensor is pointing When the look at point is changed the spherical coordinates are adjusted automat ically It is assumed that changing the look at point does not reflect a change to the sensor position e Min Max Range two fields representing the placement of the clipping planes relative to the sensor location Targets or part of the ground plane placed beyond these range limits will not appear in the rendered scene Pixel values in range images that represent scene elements beyond the range limits will be clipped to the minimum and maximum range values e Dimensions two fields representing the vertical and horizontal number of rows versus number of columns pixels in range images For point clouds these fields represent the number of samples used to extract point cloud information in the event that all samples are valid points then the product of these two fields is the number of points in the point cloud When combined with the field of view angles these fields can be thought of as the angular scanning sampling in the vertical and horizontal directions e Up Vector supplies the rendering system with a vector orientation for up In most cases these may be set to 0 0 1 representing the positive z axis as the up directio
57. he probability of error in the ATR algorithm drops below a desired threshold II RCS BASED TARGET IDENTIFICATION A Past Approaches to ATR The literature surrounding the recognition of fast moving fixed wing aircraft is typically divided into two schools of thought On one side of the debate are researchers who propose the creation of target images to accomplish identification Advocates of this approach suggest everything from two dimensional inverse synthetic aperture radar ISAR images to a sequence of one dimensional range profiles 1 The alternate approach bypasses the creation of images and attempts recognition directly on the data Herman 2 3 takes this second approach to automatic target recognition ATR using data obtained from a passive radar system Although ATR has been a subject of much research Herman s application of passive radar was innovative Unlike traditional radar systems passive radar systems bypass the need for dedicated transmitters by exploiting illuminators of opportunity such as commercial television and FM radio signals In doing so they are able to reap a number of benefits Most notably the fact that passive radar systems do not emit energy renders them covert An additional benefit is that the illuminators of opportunity often operate at June 11 2006 DRAFT much lower frequencies than their traditional counterparts It has long been proposed that low frequency signals are well suited for ATR
58. he 3D Studio File Format Library is Copyright 1996 2001 J E Hoffmann ALL Rights Reserved It is subject to the GNU Lesser General Public License The official website is http 1ib3ds sourceforge net Contents 1 Getting Started 1 1 1 System Requirements Ls loeb RA A A BA 6 Pia 1 E ASA ma Say as e da W E A 1 1 ales Vand Poleras a EA MAAAC So eee be he 2 2 Scene Creation Overview 3 2 1 Parts of a CONG U 4 zo ud aa WE LWA EE EL 3 22 DEt e the View A o pire sae A ME geod O Foki 4 23r Adding LAP ECU Pai ST So age RR 4 3 Graphical User Interfaces 6 3 amp 1 Mam LADAR Sim lator GUI ese PR ER ORG EA A rd 6 32 View Settings GUL aele sirasi pora Bod ewe OE ee eR ee 8 3 3 New Model Library GUI bs ok a Oho Ae So oe ooo ee RE A 10 3 4 Model Editor GUI usa a6 82 ale 26 SERA SRS AT AW on BER 14 3 5 Ground Plane GUL a 2a ob Rts els Rk Gack Be aa wo A ee 18 4 Library Interface 19 5 File and Structure Formats 21 Goole a O c a at pe ir RL GO ane Bee ee ee 0 21 5 1 1 Configuration Structure le Ne Lp ta te Blew lee te Z panel A WATA ce 21 S2 Atrea TUGRUITES sa e Bo 4G RS AAA a e i 21 5 1 3 View Settings Structure 46 W aa AE OO a eg 22 5 1 4 Configuration File Format rd stw we A gii A 23 5 2 Model Libraries a Sul tt ad da eee AS AW WE AA 23 5 2 1 Model Library Structure als A a A A WTA tied 23 5 22 Model St ctur n 4 atesty ia eG woli R A AW 23 5 2 3 Model Library File Formats a rsa ow eee ee SC
59. humidity etc and operational vehicle speed engine speed gun fired or not etc to yield a wide variety of sample thermal states SE _ 1 N DB We compute the empirical mean m J p 1 A n and covariance L K 30771 m A 7 n m 3 n l We seek the eigenvalues y and the eigentanks that satisfy Wig y Ki O15 A 4 l Notice the weighting by the surface measure Writing the A s as a diagonal matrix A and the eigentanks as P y 6 7 RY we can express 4 as 7 KA The cigentanks and eigenvalues y can be readily found via standard numerical routines 3 2 Logposterior for rigid targets This discussion will follow the derivation found in Lanterman et al but will employ our Gaussian data likelihood instead of a Poisson likelihood Consider a collected data set d Let N denote the number of pixels in region i as seen by the detector and Dj zen d k be the sum of data pixels in region i Conditioned on the ay s d k Gaussian A NEAT for k Ri In accordance with the principal component analysis discussed in the preceding section a Gaussian prior is placed on the a s with variances given by the eigenvalues found from the analysis Dropping terms independent of a the logposterior for the pixels on target in terms of the expansion coefficients is HD N Y odl E 5 i kER j e ats Af aj sa aa nd i kERi J Sn 7 ay PRISM was sold and maintained by Therm
60. ignatures becomes even more likely In the future we plan to examine different types of penalties that can be used with the likelihood function to reduce these false alarms Finally it should be noted that these algorithms have not been tested with real infrared data Before we can do so we need to solve the problem of calibration between our models and real infrared images ACKNOWLEDGMENTS This work was sponsored by the Air Force Office of Scientific Research AFOSR grant F49620 03 1 0340 REFERENCES 1 U Grenander and M I Miller Representations of knowledge in complex systems Journal of the Royal Statistical Society Series B Methodological 56 4 pp 549 603 1994 2 U Grenander Elements of Pattern Theory Johns Hopkins University Press Baltimore MD 1996 3 A D Lanterman M I Miller and D L Snyder General Metropolis Hastings jump diffusions for automatic target recognition in infrared scenes Optical Engineering 36 4 pp 1123 37 1997 4 A E Koksal J H Shapiro and M I Miller Performance analysis for ground based target orientation estimation FLIR LADAR sensor fusion Conference Record of the Thirty Third Asilomar Conference on Signals Systems and Computers vol 2 pp 1240 4 Pacific Grove CA 1999 5 M L Cooper A D Lanterman S Joshi and M I Miller Representing the variation of thermodynamic state via principle component analysis in Proc of the Third Workshop o
61. l University They were designed for the infrared simulation code PRISM but suffice well for our laser radar study API Using OpenGL we perform the transformation y 2 9 Z taking a three dimensional scene and turning it into a two dimensional image through perspective projection We simulated ideal LADAR data sets by exploiting the depth buffering system employed by OpenGL The first step is to read the values that OpenGL stores in its depth buffer Next these values and the z y two dimensional pixel coordinates for the corresponding points in the image can used to undo the perspective projection and obtain the original y Z vectors of three dimensional world coordinates for the scene The uncorrupted range values are determined by computing the distance from the camera location to those particular coordinates producing a range image To compute the derivatives necessary for determining the CRLBs a finite difference approximation is em ployed Remembering that m is a complicated nonlinear function of the parameter vector obtained from render we can apply the following equation Ou _ Orender _ render 0 render 0 8875 66 6 25 2 where is some small deviation of the parameter which is a component of and the ellipses indicate that the remaining parameters are held fixed The derivative provides us with a representation of how the image changes with small
62. library structure to a text file e Manipulating Configuration Structures add_target Add target with given parameters to configuration new config Create an empty configuration structure remove target Removes a target from a configuration set_ground_param Update the ground plane in a configuration set_target_param Update a single target in a configuration e Manipulating View Structures new_view_settings Create a view settings structure set_view_param Update a view setting parameter e Working with Scene Data 19 add_noise Adds noise to range imagery or point cloud data display_data Display a scene in a given figure or axes e Scene Creation render_scene Create a range image or point cloud data set Customized simulations typically start out with loading a model library and a configu ration file use load model_library and load_configuration If no configuration file is available then a configuration is created from scratch with the new_config function with some ground plane information Targets are added with the add target function The view is created and modified with the new view settings and set_view_param functions respectively and so on The ladar_simulator folder contains a subfolder called scripts with an example simu lation file named make multiview ptc m It creates a single point cloud from multiple views of the same scene consisting of an object positioned in the
63. lled outside the integral le the Laplace Method to essentially just rewrites the remaining terms from 8 in e 0 form or MOA u fee Pet SEE an ro SE 4AM 1o SP Baz 0 This is equivalent to A s5 s2 00 p A ln e 207 nda y 10 0 where hen in E SFP A Vin o FP in ta Es z an 20 Thus u X reduces to A s7 s X e BO acer 4 an 12 where is the value of z found by setting the derivative of h x A equal to zero To make the math tractable the zeroth order and first order Bessel functions are approximated as Loly exp y and 1 y exp y This works best if the Bessel function arguments are large as is likely to be the case in practice This approximation results in two solutions However it is trivial to show that given the limits of integration of the Rician density the only valid solution is 1 1 1 Asa Sp Soy zy s sz 2SpSq 2 SpSq 2455 57 407 13 2 The second derivative of h x A is given by le 3 0 z ES E G gen sr June 11 2006 DRAFT 0 5 2 20 lo 52 Thus the probability of error in a binary Bayesian hypothesis test is approximated by a a Avs RR 15 ACB 44 mino lt a lt a Poet th amp A 4 zn razy Pg ze 16 IV COMPARISON OF CHERNOFF INFORMATION PREDICTIONS WITH MONTE CARLO RESULTS To demonstrate that the Chernoff information can be used to appro
64. mated with Pp z e Cel 1 where C p x q x is the Chernoff information The Chernoff information between two densities p x and q x is typically found using June 11 2006 DRAFT C p z q 1 mino lt x lt TUX 2 where u X is given by wr arto e 3 x To approximate the probability of error in the proposed ATR algorithm between two aircraft p x and q x are set to the Rician densities 3 z Cts 2S E a and aC LN rq ae Se A 5 where Ip is the zeroth order modified Bessel function of the first kind Note that x is the magnitude of the covertly collected RCS of the aircraft being tracked s and s are the magnitudes of the simulated RCS for both aircraft and o is the noise power Substituting 4 and 5 into 3 results in OT ras Ta e pas u X In sza 202 Lo Bee 20 Lo dz p 6 Rearranging 6 results in a d 2 2 oo e z gt ze 22 82 LQ n BR o 32 Z e mr ZA F dz k 7 o Lacan eH i which is further reduced to 00 Msi s2 22492 ee Te 24 A MOGA a E A dzy 8 0 p 072 Io FE June 11 2006 DRAFT B Deriving a Closed Form Approximation for the Chernoff Information The presence of Bessel functions in 8 render computation of an analytical solution quite difficult However this can be accomplished by applying the Laplace Method to the integral The first exponential term is not a function of z so it is pu
65. middle of a ground plane The sensor takes frames at 120 deg increments and merges the point clouds from the individual frames into a single point cloud It then saves the point cloud and configuration structure to files using the save_data and save_configuration functions respectively Each range im age is displayed along the way as was well as the final point cloud using the display_data function This script may be used as a guide for creating other customized simulations 20 Chapter 5 File and Structure Formats Although the GUls and library interfaces should be sufficient for most users it may be desirable for users to directly manipulate the configuration files model libraries or the various structures This chapter includes descriptions of these formats If the tools provided for manipulating the structures and files are sufficient for your needs then this chapter may be skipped When manipulating the structures directly it is important to remember data types By default MATLAB stores everything as a double precision floating point value Since these structures are passed to C functions that utilize external libraries many of the fields in these structures are not double precision floating point Therefore it is important to use the appropriate data type when assigning values to the structure fields referenced in this chapter 5 1 Configurations The configuration file and structure format includes fields for organizing diffe
66. n If the camera is pointed straight down then a new up direction must be chosen so that the vector has a projection along the zy plane View Settings View Parameters Field of view vertical horizontal Position x y z 11 25 6 4952 7 5 Pasition dist az elev 15 30 30 Look At O MiniMax Range 0 1 Dimensions Row x Columns Up vector x y z 256 View Settings Successfully Loaded Figure 3 2 View settings GUI window When changing fields the GUI will perform a general validity check for the most recently used parameter and revert to the original value if the current value is found to be invalid Pressing the Reload button will reset to the GUI to its original state after it was first launched Pressing the OK button will save the view settings close the View Settings GUI and redraw the scene using the new settings Pressing the Apply button will save the current view settings and redraw the scene Pressing the Cancel button will close the View Settings GUI and discard all changes since the last time the Apply button was pressed Pressing the Enter Return key after editing a text field simulates pressing the Apply button 3 3 New Model Library GUI The LADAR Simulator GUI allows users to create their own model library files consisting of references to CAD models in supported model file formats and a set of adjustable parameters When the New Model Library button in LADAR Simulator GUI windo
67. n Conventional Weapon ATR pp 479 490 U S Army Missile Command 1996 6 M L Cooper U Grenander M I Miller and A Srivastava Accommodating geometric and thermo dynamic variability for forward looking infrared sensors in Algorithms for Snythetic Aperture Radar IV E Zelnio ed SPIE Proc 3070 pp 162 172 Orlando FL 1997 7 M L Cooper and M I Miller Information measures for object recognition in Algorithms for Synthetic Aperture Radar Imagery V E Zelnio ed SPIE Proc 3370 pp 637 645 SPIE Orlando FL 1998 8 A D Lanterman Bayesian inference of thermodynamic state incorporating Schwarz Rissanen complexity for infrared target recognition Optical Engineering 39 5 pp 1282 1292 2000 9 M I Miller U Grenander J A O Sullivan and D L Snyder Automatic target recognition organized via jump diffusion algorithms IEEE Transactions on Image Processing 6 1 pp 157 74 1997 10 A Srivastava U Grenander G R Jensen and M I Miller Jump diffusion Markov processes on orthogonal groups for object pose estimation Journal of Statistical Planning and Inference 103 1 2 pp 15 37 2002 11 A D Lanterman M I Miller and D L Snyder Representations of shape for structural inference in infrared scenes in Automatic Object Recognition VII F A Sadjadi ed Proc SPTE 3069 pp 257 268 Orlando FL 1997 12 A D Lanterman Schwarz Wallace and Ris
68. n simulation are shown in Figure 2 Figure 2 a shows the initial FLIR dataset used in this simulation which consists of four tanks The top most and bottom most tanks are both M60s and the remaining two are T62s Each was initialized with a different position orientation and thermal state We assume the camera viewing parameters are known The algorithm begins by searching over the configuration space for the best set of parameters for a single new target In the subsequent images the white tanks represent the estimated configuration at that point in the simulation Figure 2 b shows that the first tank located is the M60 that is positioned closest to the FLIR sensor Since this tank has the greatest number of pixels on target it makes sense that the algorithm would choose that position for a tank to achieve the greatest gain in likelihood The next few images shown in Figures 2 c 2 e show how the algorithm subsequently detects and places new targets over the existing targets in the data set Between the birth death and metamorph moves the algorithm diffuses over the existing targets in an attempt to refine their pose parameters The estimated thermal emission profiles of the hypothesized targets change as the diffusions take place due to the adjustments of pose changing the overlap with the corresponding target in the data image Figures 2 f and 2 g are interesting because they demonstrate the flexibility of the jump diffusion process A metamor
69. ncident and observed angles allow the appropriate RCS to be extracted from a database of FISC results Using this process the RCS of each aircraft in the target class is simulated as though each is executing the same maneuver as the target detected by the system Two additional scaling processes are required to transform the RCS into a power profile simulating the signal arriving at the receiver First the RCS is scaled by the Advanced Refractive Effects Prediction System AREPS code to account for propagation losses that occur as functions of altitude and range Then the Numerical Electromagnetic Code NEC2 computes the antenna gain pattern further scaling the RCS A Rician likelihood model compares the scaled RCS of the illuminated aircraft with those of the potential targets resulting in identification The result is an algorithm for covertly identifying aircraft with a low cost passive radar system June 11 2006 DRAFT 3 III ASSESSING THE PERFORMANCE OF THE ATR ALGORITHM VIA THE CHERNOFF INFORMATION Prior work 9 10 11 has shown that the proposed ATR algorithm has merit How ever to more fully test the algorithm against aircraft in a variety of locations executing a variety of maneuvers a staggering number of Monte Carlo trials are required To combat this dilemma a more efficient approach for assessing the ATR algorithm s capabilities is desired This paper describes one such approach Under the Bayesian framework the
70. ng Passive Radar and an EKF for Estimating Aircraft Orien tation Atlanta GA PhD Dissertation School of Electrical and Computer Engineering Georgia Institute of Technology Fall 2005 S Kullback Information Theory and Statistics John Wiley amp Sons 1959 T M Cover and J A Thomas Elements of Information Theory John Wiley amp Sons 1991 N DeBruijn Asymptotic Methods in Analysis Dover Publica tions Inc 1981 L M Ehrman and A D Lanterman Assessing the Performance of a Covert Automatic Target Recognition Algorithm in Auto matic Target Recognition XV SPIE Proc 5807 Ed F A Sadjadi Orlando FL April 2005 pp 77 78
71. ngth of Collection Time Straight and Level Trajectory 1 100 90 F 80 Probability of Error 15 20 Length of Collection Time s 25 30 P E F 15 T 38 Pe F 15 Falcon 20 Pe F 15 Falcon 100 PE T 38 Falcon 20 PE T 38 Falcon 100 Pe Falcon 20 Falcon 100 40 45 50 Fig 5 Probability of Error Vs Time Straight and Level Trajectory 1 Noise Figure 45 dB June 11 2006 DRAFT 17 Probability of Error Vs Length of Collection Time Straight and Level Trajectory 2 100 T T T T T Sax FE F 15 T 38 90 Pi F 15 Falcon 20 gt PE F 15 Falcon 100 Gia PE T 38 Falcon 20 80 Pe T 38 Falcon 100 aaa PE Falcon 20 Falcon 100 70 4 Q i 60h 1 5 L i a 50 4 i 3 e 407 8 Length of Collection Time s Fig 6 Probability of Error Vs Time Straight and Level Trajectory 2 Noise Figure 40 dB June 11 2006 DRAFT 100 90 80 Probability of Error Probability of Error Vs Length of Collection Time Straight and Level Trajectory 2 18 4 6 8 10 12 Length of Collection Time s P E F 15 T 38 Pe F 15 Falcon 20 PE F 15 Falcon 100 PE T 38 Falcon 20 PE T 38 Falcon 100 PE Falcon 20 Falcon 100 16 18 20 Fig 7 Probability of Error Vs Time Straight and Level Trajectory 2 Noise Figure 45 dB June 11 2006 DRAFT Probability of Error Vs Length of
72. oAnalytics Inc P O Box 66 Calumet MI 49913 web www thermoanalytics com It has been replaced by the MuSES infrared signature prediction software The PRISM databases and resulting principle component models employed in the experiments discussed here were created by Dr Matthew Cooper 7 Incorporating A gt gt j Ag m and taking the derivative with respect to each aj we obtain equations of the form 2NiAi gaz Ni 232A Dreri Uk a a N 2 NEAT 1 8 Nic Or Dir Mi Bij taD a Qj 9 7 NEAT Yj To maximize the logposterior we must satisfy these J necessary conditions Ni d i Piz Oi Di j A 5 3 0 W 10 NEAT 7 N Pik Pij N m DD Qj z W OOE ON 11 oe gt NEAT NEAT gt NEAT m A an NEAT k i i J Fortunately these are linear equations conveniently expressed in matrix form NEAT gt N83 NL MA 01 NP Di Nami diag 13 gt Nida By gt N iB y NEAT AJ gt Bu D Nimi YJ For a given target pose these equations allow us to compute approximate MAP estimates for the aj s in closed form which we denote as j Note that changes with different poses as the MAP estimate adjusts to best match the data under the constraint of the eigentank model For a multiple target scene we perform a similar calculation for each target 4 INFERENCE BY METROPOLIS HASTINGS JUMP DIFFUSIONS The full posterior distribution represented by
73. ph move occurs before the rightmost T62 fully diffuses over the T62 in the data set and the best orientation angle turns out to be in the opposite direction the estimated tank no longer points away from the FLIR sensor as shown in the data Once the diffusion allows the estimated T62 to noticeably cover the T62 in the data image another metamorph move brings it into the appropriate alignment as shown in Figure 2 g The final estimate is shown in Figure 2 h All of the targets are aligned with the corresponding targets in the data image The estimated thermal emissive profiles also match those found in the data Figure 2 Screen captures from iterations of a jump diffusion process for FLIR ATR 6 2 Phantom targets With the incorporation of the inference of target thermal signatures in a given configuration our jump diffusion algorithm suffers from a potential increase in false alarms when initially detecting targets This can be attributed to the amount variability that our current eigentank model is capable of capturing which includes thermal states that are generally not attainable by actual targets If we are rendering a target model over a segment of the data image that contains a target of the same type and if pose parameters match up correctly then the inferred thermal states will also match the true values since intensity regions will overlap properly If any of these conditions are not met then the computation of the expansion coef
74. prox to D pllq d Closed Form Solution for D pllq 2 4 6 8 10 12 14 16 18 20 s 1 0 8 Normal Approx to B y Closed Form Solution for B 0 6 a 0 4 0 2 0 Fig 1 sp 10 0 4 and sg sweeps from 0 to 20 top D pllg bottom Bpl q REFERENCES 1 L M Ehrman and A D Lanterman Automated Target Recogn tion using Passive Radar and Coordinated Flight Models in Auto matic Target Recognition XIII SPIE Proc 5094 Ed F A Sadjadi Orlando FL April 2003 pp 196 207 Relative Entropy for s 5 00 s 0 05 0 05 10 00 t 0 00 0 50 100 00 sigma2 4 0 i T T T T T T T T aponta Dplq J PA Normal Approx to D pllq 251 i Closed Form Solution for D pllq J D plla q Probability of misidentifying q x as p x s 5 00 s 0 05 0 05 10 00 t 0 00 0 50 100 00 sigma2 4 0 1 T T T T T 7 i Tv ost Normal Approx to B Ke Closed Form Solution for B 0 6 y 4 a ES 0 4 N 4 Y 0 25 ot Pi O per i i i i i i i i 1 2 3 4 5 6 7 8 9 10 Fig 2 sp 5 0 4 and sg sweeps from 0 to 10 top D p q bottom plig L M Ehrman and A D Lanterman A Robust Algorithm for Au tomated Target Recognition using Passive Radar in Proc IEEE Southeastern Symposium on System Theory Atlanta GA March 2004 pp 102 106 L M Ehrman An Algorithm for Automatic Target Recognition Usi
75. r contains the MATLAB functions scripts and C files for creating simulated range scenes and point clouds Other files in the directory include e sample models ml model library of simple models There are a number of sub folders containing example files e config scene configurations e models simple faceted models e scenes range images and point clouds The rest of the folders contain program related libraries Chapter 2 Scene Creation Overview This chapter provides a high level overview of the simulator and using it to define and render scenery 2 1 Parts of a Scene The LADAR Simulator tools allow users to create synthetic LADAR data sets range images and point clouds from predefined three dimensional scenes The tool starts by setting up a three dimensional world view of a particular scene in a space with axes z y and z zx and y represent coordinates along the ground or any plane at some given height as in the standard three dimensional coordinate system used in computer graphics The z coordinate represents the height at particular z and y values If we consider the ground then all values will be zero A viewing sensor is usually positioned at some point above the z 0 plane pointing at some predefined point in the world The position of the sensor may be defined in rectangular x y and z coordinates or in terms of range azimuth and elevation spherical coordinates based on the look at point A flat rec
76. rary has been chosen the LADAR Simulator GUI will appear see Figure 3 1 The GUI contains all components necessary to create a scene The axes on the right side of the window displays the rendered configuration or point cloud The type of scene is selected from three possible choices using the pop up menu below the scene axes Full Range Point Cloud Depth Buffer For a detailed description of these scene types see Section 5 3 By default the color mapping used for two dimensional data sets is determined automatically by the minimum and maximum values in the scene This can be overridden by marking the Colormap check box and selecting the minimum and maximum values values for color map scaling The user can add or remove a ground plane to the scene by selecting the Ground Plane check box The dimensions of the ground plane can be defined by pressing the adjacent Options button For details about setting up a ground plane see section 3 5 Gaussian distributed noise of a chosen variance may be added to the scene by selecting the Noise check box The noise is centered on the range values or coordinates in the case of point cloud data LADAR Simulator Target List Simulated Scene Ada A Save v Load Class 162 Position x y 2 Rotation Angle Rotation Axis x y 2 Scale fall x y z 0 1 1 1 Endian Data Order Origin winx 51 02 winy 30 02 Scene Type Full Range E Big Endian Column Major Upper
77. rational and environmental conditions This is analogous to the challenges posed by varying illumination in visual band imagery In the mid 1990s an effort was initiated at Washington University in St Louis to develop pattern theoretic algorithms for ATR in infrared imagery The fruits of that work included a process for detecting and classifying multi target scenes consisting of known target types estimating the thermal signature characteristics of targets of interest and ideas for the inference of targets of unknown type or shape depending on how you view the problem Most of these techniques remained disjoint and were never fused into a unified ATR framework In this work we seek to unify two of these methods multi target detection recognition and thermal state estimation 1 1 Pattern theory Ulf Grenander s work in pattern theory is the motivating force behind our framework for automatic target recognition While most computer vision and object recognition techniques focus on the separate stages of recognition feature extraction segmentation classification etc the pattern theoretic framework seeks to unify these separate concepts into a single process such that all steps are performed jointly The detection recognition process is performed directly on the data itself in the hopes that the information loss that may arise from traditional preprocessing schemes may be avoided In following the pattern theory philosophy we must first
78. rent components of a scene These components include target parameters view settings and the ground plane description All arrays are stored row wise 5 1 1 Configuration Structure The configuration structure description is shown in Table 5 1 It holds information on the targets and the ground plane in the scene 5 1 2 Target Structure The target structure description is shown in Table 5 2 The class field holds a nonnegative integer that identifies a unique model in the corresponding model library The position field represents the target s x y z coordinate position The orientation is stored in angle axis notation so that rotations occur by rotating the target 0 degrees along the x y z axis In 21 Table 5 1 Configuration structure fields Field Name Data Type Description num Targets uint32 scalar Number of targets in the scene targets structure array Array of target structures 1 Do not include a ground plane O Use default ground plane sA oma MAPA 1 Use ma a plane defined in the configuration structure groundlntensity uint32 scalar ground intensity any nonnegative integer groundOrigin double array Three element x y 2 array representing the origin of the ground plane groundXLength double scalar Length of the ground plane in the positive x direction groundY Length double scalar Length of the ground plane in the positive y direction most cases rot
79. rget reflectivity B is the IF filter bandwidth Pr is the peak transmitting power and Ak is the receiver s aperture area We will only consider the case with no anomalous measurements i e Pra 0 so the last term drops out of the loglikelihood function It can now be reduced to d n n n Lrr d u 5 log 270 n 20 n n 6 1 2 Derivation of the Cramer Rao bound The matrix Cramer Rao bound for a vector of unbiased estimators is defined as the inverse of the Fisher infor mation matrix FIM for that estimator vector where each element of the FIM is defined as Fl E zz 1ento 0 zg bosp D 0 7 where p d O is the data loglikelihood which is a function of the target parameters z y 0 7 We use D in 7 to indicate that we would plug in a random variable for d The coordinates x and y denote the target location on the ground plane which is assumed to be flat and 0 is the orientation angle with respect to the axis that points out of the ground plane We treat the loglikelihood as a complicated nonlinear function of that can be observed through the uncorrupted range image u It is best to think of u n as u n O render O at pixel n in the resulting two dimensional image created through obscuration and perspective projection of the three dimensional scene consisting of a target with parameter vector O To derive the Cramer Rao lower bound we begin by determining the derivative of the
80. rivatives needed by the Fisher information matrix artifacts introduced when rendering laser radar imagery and the effects caused by the finite spatial resolution of the images may be necessary to make this technique more practical Ideally an ATR system designer should be able to input sensor parameters and target modes and determine the bounds on the standard deviation of parameter estimators The CRLBs can give target recognition algorithm developers a goal to shoot for If performance is already near the bound then there may be little point in spending more resources to further improving the algorithm In particular if the performance does not match the needs of the user the bounds may tell us that further effort on algorithm development will be wasted a better namely a more informative sensor is needed If the performance matches the needs of the user but is not near the bound then that suggests that similar performance might be achieved using a more sophisticated algorithm in conjunction with a less expensive sensor Such trade offs are important to analyze particularly since the cost of computing hardware tends to follow Moore s law while the cost of sensors remains relatively fixed This paper has solely considered the bounds on estimating pose parameters assuming the target type is known Our future work will also consider bounds on the performance of target recognition algorithms One important result arising from the work of Grenan
81. s on estimating y position for a single M60 tank with respect to the current orientation angle of the tank Graph a was computed using a resolution of 125x60 pixels and graph b was computed using a resolution of 500x240 pixels 3 4 Choosing derivative stepsizes One significant problem encountered in this study is the choice of stepsize for the derivatives used to compute the Fisher information matrix The computation of these derivatives is tricky in that there is no clear analytic means to do so The plots shown in Figure 6 provide an illustrative example The stepsizes chosen for the CRLB computations in 6 b are one quarter the size of those chosen for the computations in 6 a One noteworthy difference is seen in the absolute magnitudes of the bounds themselves The bounds computed using the smaller derivative stepsizes are on average slightly lower than those computed with the larger derivative stepsizes A second difference between the two plots is seen in the subtle difference between the coupled and uncoupled curves specifically that the bounds computed with the larger stepsizes appear to have larger gaps between the curves Intuitively it makes sense that the smaller stepsizes should offer the more precise derivative computation but given the nature of the rendering process and the discretization of resulting images this may not be so Further study is needed to determine if ideal stepsizes can be chosen if a better approximation
82. s with data sets having a great deal of variability One can visualize the usefulness of estimating the thermal characteristics of a target of interest Knowing these values and the corresponding radiance regions can allow ATR systems to predict the state of the target of interest i e if it is moving if it has just fired etc There are however a number of challenges to resolve before this ATR procedure can be viewed as practical These include how the algorithm detects new targets the need for stopping conditions so the algorithm knows when to terminate a better method of determining the Langevin SDE 15 numerically and a likelihood penalization strategy to avoid detecting a target over background information Even though targets can be found over time via our current birth strategy if the viewing grid is sampled finely enough this process does not make intelligent use of the available information Guessing locations to search and then rendering fully detailed CAD models at those locations is computationally expensive and does not guarantee that all targets will be detected The algorithm must also deal with partial false alarms which occur when a new target only partially overlaps with one that exists in the data set In theory the diffusion process should account for these situations but in practice it can sometimes have difficultly when refining the pose parameters A few potential rapid detection schemes were investigated by Lanterman et
83. sanen Intertwining themes in theories of model order estima tion International Statistical Review Vol 69 No 2 pp 185 212 2001 Appendix C J A Dixon and A D Lanterman Information Theoretic Bounds on Target Recognition erformance from Laser Radar Data Automatic Target Recog nition XVI SPIE Vol 6234 Ed F A Sadjadi April 2006 pp 394 403 Information theoretic bounds on target recognition performance from laser radar data Jason H Dixon and Aaron D Lanterman Center for Signal and Image Processing School of Electrical and Computer Engineering Georgia Institute of Technology Atlanta GA 30332 USA ABSTRACT Laser radar systems historically offer rich data sets for automatic target recognition ATR ATR algorithm development for laser radar has focused on achieving real time performance with current hardware Our work addresses the issue of understanding how much information can be obtain from the data independent of any particular algorithm We present Cramer Rao lower bounds on target pose estimation based on a statistical model for laser radar data Specifically we employ a model based on the underlying physics of a coherent detection laser radar Most ATR algorithms for laser radar data are designed to be invariant with respect to position and orientation Our information theoretic perspective illustrates that even algorithms that do not explicitly involve the estimation of such nuisance parameters are still af
84. straddle the center point Using the same units as the geometry file you can specify desired translations along the z y or z axes An example is shown in Figure 3 8 Y Axis View Y Axis View Fa X Camera Location 20 2549 X Camera Location 20 2549 a b Figure 3 8 Images showing a tank before a and after b a translation adjustment along the z axis After the adjustment tanks placed in a scene will not be halfway in the ground plane The Rotation text fields are used to define a default rotation to occur before an object is placed in a scene Sometimes model files are defined in such a way that leaves them in an unnatural orientation when used in a scene For example a car model may be sitting on its bumper by default These text fields allow you to define a rotation along any of the axes that will occur before a model is placed In the case of the car you can define a rotation that places the car on its wheels The rotations are specified in the angle axis notation where you specify a rotation angle and the vector form of an axis about which to rotate The Rotation Axis Adjustment text fields allow you to adjust the position of a model before a rotation occurs By default rotations occur on an axis that in the center of the model s bounding box For symmetric models this works out well When there are features that take away from this symmetry such as an extra long gun extending from a tank it may be desirable to a
85. t GTRI has included comparing and devel oping tracking algoirthms for ballistic missile defense feature assisted tracking tracking unresolved separating targets using monopulse radar and the development of launch point estimation and impact point prediction algorithms for small ballistic targets Aaron D Lanterman is an Assistant Professor of Electrical and Computer Engineering at the Georgia Institute of Technology which he joined in the fall of 2001 In 2004 he was chosen to hold the Demetrius T Paris Professorship a special chaired position for the development of young faculty He finished a triple major consisting of a B A in Music B S in Computer Science and B S in Electrical Engineering at Washington University in St Louis in 1993 He stayed on for graduate school receiving an M S 1995 and D Sc 1998 in Electrical Engineering His graduate work focused on target recognition for infrared imagery as part of the multi university U S Army Center for Imaging Science After graduation he joined the Coordinated Science Laboratory at the University of Illinois at Urbana Champaign as a postdoctoral research associate and then as a visiting assi stant professor where he managed a large project on covert radar systems exploiting illuminators of opportunity such as television and FM radio signals His other research interests include target tracking image reconstruction and music synthesis In 2006 he received the Richard M Bass Outst
86. tangular ground plane of any desired size can be placed at the coordinates where z 0 to give the appearance that objects in the scene are resting on a surface The units of the world coordinates are not explicitly set and may represent anything For example let us say that you want to view a tank from 50 meters away but the faceted model of the tank is defined in millimeters with dimensions 6367 x 3122 x 2943 Specifying 50 as the range will result in an appearance that may be interpreted in two different ways 1 the tank is 6367mm x3122mm x2943mm and the sensor is 55mm away or 2 the tank is 6367m x3122m x2943m and the sensor is 50m away Without scaling the values the distance from the target and the dimensions of the tank are considered to be the same units To have all objects in the scene drawn appropriately the units of the tank must be converted to meters by scaling by 1 1000 or the units for the sensor s range from the target must be specified in millimeters 2 2 Setting the View The viewing area and resolution of the resulting imagery are set via the field of view and data dimension parameters Field of view is defined in the horizontal and vertical directions relative to the position of the sensor in units of degrees In essence the sensor scans fov 2 and fov 2 in both directions The number of pixels in the image is determined by the data dimension parameters think of this parameter as the angular sampling that is occurring as
87. tering Approach to Joint Passive Radar Tracking and Target Classification Doctoral Dissertation Department of Electrical and Computer Engineering Univ of Illinois at Urbana Champaign Urbana IL 2002 3 S Herman and P Moulin A particle filtering approach to joint radar tracking and automatic target recog nition in Proc IEEE Aerospace Conference Big Sky Montana March 10 15 2002 4 Y Lin and A Ksienski Identification of complex geomtrical shapes by means of low frequency radar returns The Radio and Electronic Engineer 46 pp 472 486 Oct 1976 5 H Lin and A Ksienski Optimum frequencies for aircraft classification IEEE Trans on Aerospace and Electronic Systems 17 pp 656 665 Sept 1981 6 J Chen and E Walton Comparison of two target classification techniques IEEE Trans on Aerospace and Electronic Systems 22 pp 15 21 Jan 1986 7 J Sahr and F Lind The Manastash ridge radar A passive bistatic radar for upper atmospheric radio science Radio Science pp 2345 2358 Nov Dec 1997 8 J Sahr and F Lind Passive radio remote sensing of the atmosphere using transmitters of opportunity Radio Science pp 4 7 March 1998 9 L Ehrman and A Lanterman Automated target recogntion using passive radar and coordinated flight models in Automatic Target Recognition XIII SPIE Proc 5094 Orlando FL April 2003 10 L Ehrman and A Lanterman Target id
88. than the first difference may be found 3 Bound on Y Position Estimation 4 Bound on Y Position Estimation 1 3X 10 11 x 10 _ Coupled Coupled 1 7 Uncoupled Uncoupled o o T mb al N mb b T y Y lt i Std Dev Bound on Y Position meters R Std Dev Bound on Y Position meters 0 100 200 300 400 0 100 200 300 400 Orientation Angle degrees Orientation Angle degrees a b Figure 6 Cramer Rao bounds on estimating y position for a single M60 tank with respect to the current orientation angle of the tank Graph a was computed using a derivative stepsize four times the size of that used for the computations in graph b 4 CONCLUSION This paper presented preliminary results on quantifying fundamental limits on target pose estimation perfor mance for laser radar imagery We considered Cramer Rao lower bounds on the variance of unbiased estimators of pose parameters of interest We have shown that the ability to estimate pose parameters appears to depend heavily on true pose in that different features can be seen from the laser radar when viewing targets from dif ferent positions and orientations A good feature of this procedure is that it can be performed for any type of sensor as long as the sensor data likelihood function is known and the CRLB can be derived A more theoretical analysis on computing the numerical de
89. these features may contain different amounts of information A more theoretical analysis of spatial resolution and sampling may be necessary to determine the exact cause These non monotonic qualities of the CRLB curve may also be related to derivative approximations that were necessary when computing the Fisher information matrix It is clear that the bounds may change when adjusting the derivative stepsizes but the overall effect of those changes is not entirely clear at present Some of these issues also arise in work by Gerwe et al 3 2 CRLBs versus orientation angle The results of this experiment can be seen in Figure 3 When estimating the bounds on z position and angle orientation we see that the CRLBs vary with changes to these parameters although the variation is difficult to intuitively explain When estimating y position we see noticeable peaks around 90 degrees and 270 degrees In those instances the M60 is either pointing toward the LADAR sensor or away from it This may suggest Bound on X Position Estimation Bound on Y Position Estimation 00 12 T 0 18 2 Coupled 2 Coupled E dd Uncoupled E 0 16 Uncoupled 5 IN 5 0 14 pl ry e 9 0 08 HB 0 12 i i x gt 0 17 J 6 0 06 fw 6 gt he fs 7 0 08 A 7 lt 4 5 fo 3 h 8 0 04 i fa 0 06 cl J gt gt a e 0 04 i z 0 02 3 z 2 m 0 02 J o o gt gt lt 0 lt
90. tifier in the configuration structure file this integer is the same as the class Type of CAD model STL for ASCII or binary stereolithography files 3DS for binary 3D studio files PRISM for files in the Prism file format from Thermoanalytics and OFF for Princeton shape benchmark files Relative path starting from the location of the model library file and filename of the CAD model A repeat the previous path and filename for non Prism files For Prism files this field contains the corresponding radiance file The number O not used but left in for code legacy purposes A unique text string ID for the model This will be displayed in the pop up menus of the GUIs that allow that users to switch model types when creating a scene An array of three numbers in the form x y z including the brackets and commas This represents a coordinate translation from the model s origin as defined in the units that the model was created in By default this field is set to 0 0 0 When changed this field allows users to define another point in the model space as the origin As an example imagine rendering a model at the point 0 0 0 in the scene coordinates In many instances this has the effect of rendering a lower corner of the model at that point If the user would like for all models to be centered at the point of placement then one could adjust the x and y parameters of this vector to first translate the model by th
91. tisfactory results 1 2 Installation Follow these steps to set up the LADAR Simulator 1 Extract the contents of the archive ladar_simulator zip 2 Move the folder named ladar_simulator to a desired location 3 Start MATLAB and navigate to that same ladar_simulator directory 4 The MATLAB compiler needs to be set to LCC Run the command mex setup MATLAB will ask you if you want to locate installed compilers Type y and press the Enter key One of the resulting choices should begin with Lec C followed by a version number and directory Type in the number corresponding to that choice and press the Enter key MATLAB will ask you to verify your choice 1GUI layouts may not look right or be fully functional in MATLAB 7 0 for Mac This issue was resolved with version 7 3 R2006b 5 In the MATLAB prompt run the command install _ladar_sim This will compile the relevant C files and add the folder to the MATLAB path You are now ready to start using the LADAR Simulator It can be run from any working directory you choose To uninstall the LADAR Simulator simply remove the directory from the MATLAB path and delete the folder If you do not wish to install the LADAR Simulator you may choose to run all GUIs and programs from within the ladar simulator folder itself but you must first run the command make_ladar_sim to compile the necessary source files 1 3 Files and Folders AII files are located in the folder ladar_simulator This folde
92. tive definite This implies that the diagonal elements of the covariance matrix are greater than or equal to the diagonal elements of the inverse FIM The diagonal elements of the inverse FIM are known as the Cramer Rao lower bounds for the corresponding variances in the covariance matrix A number of studies have noted that Cramer Rao lower bounds are theoretically only defined for flat Euclidean spaces The study performed by Gerwe et al notes that in practice CRLBs can be applied to curved spaces if the bound is relatively small compared to the possible range of values in the space Since we are concerned with orientation angles of targets we only have to consider cases where the angle bound is much less than 180 degrees Note that the maximum error one can have in orientation is 180 degrees Another benefit of using Cramer Rao lower bounds in this manner is that we can adapt them for any type of sensor assuming that the sensor likelihood function between the uncorrupted data values and the measured data values is known Sensor fusion is naturally incorporated by simply adding the loglikelihoods of the individual sensors 1 3 Implementation This analysis was performed on an Apple Macintosh G4 computer running MATLAB 7 Objects were rendered from faceted tank models using the OpenGL three dimensional graphics application programming interface The models were provided by Dr Al Curran of the Keeweenaw Research Center Michigan Technologica
93. ure 3 a there are many noticeable gains if the other parameters are known ahead of time Of course this will rarely be the case in practice 4 x10 Bound on X Position Estimation 9 9 00 u Std Dev Bound on X Position meters N al Coupled Uncoupled _ Bound on Y Position Estimation a o N Std Dev Bound on Y Position meters R Coupled Uncoupled 1 3 7 1 2 J 6 5 y 1 1 bere wz J 6 i L i 1 L L L 0 100 200 300 400 0 100 200 300 400 Orientation Angle degrees Orientation Angle degrees a b Bound on Angle Estimation Pixels on Target Vs Orientation 0 016 r r 3800 r r Coupled Number of Pixels a Uncoupled 3600 7 0 015 Ej E 3400 014 4 o 5 m gt 3200 7 c lt FR 5 0 013 63000 J ke v 5 2800 4 8 0 012 J a 3 2600 7 0 011 J v y 5 y AG 2400 0 01 i i 2200 i i i 0 100 200 300 400 0 100 200 300 400 Orientation Angle degrees Orientation Angle in degrees c d Figure 3 Cramer Rao bounds on estimating a x position b y position and c orientation angle for a single M60 tank with respect to the current orientation angle of the tank Figure d shows how the number of pixels on target changes with orientation angle 3 3 Image resolution effects The employed LADAR model acquires range imagery with a resolution of 125x60 pix
94. ver it takes 12 14 seconds for noise figures of 40 45 dB for enough aspects to be presented to the receiver that the probability of error drops below 5 Since aircraft are constantly presenting new aspects to the receiver when executing the banked turn maneuver the probability of error decreases even more rapidly with the exception of the Falcon 20 and Falcon 100 pair In this case the aircraft look very similar to each other at the aspects angles initially presented to the receiver VI CONCLUSIONS Through the development of the closed form approximation of the Chernoff information between two Rician densities and its application to the probability of error in a binary hypothesis testing problem under the Bayesian framework this paper develops a means for rapidly assessing the performance of a covert target recognition algorithm Monte Carlo trials have already suggested that the ATR algorithm will be successful at the anticipated noise levels The new approach for assessing the algorithm s performance allows it to be June 11 2006 DRAFT 9 more thoroughly tested Evaluating the ATR algorithm using real rather than simulated data is reserved for future work June 11 2006 DRAFT 10 REFERENCES 1 S Jacobs and J O Sullivan Automatic target recognition using sequences of high resolution radar range profiles IEEE Trans on Aerospace and Electronic Systems 36 2 pp 364 382 2000 2 S Herman A Particle Fil
95. w is pressed a dialog box will appear that allows the user to select the name and path of the model library 10 file to be created see Figure 3 3 The file must be saved to a directory in or above where the CAD model files are stored Once the file has been specified the New Model Library GUI will appear as shown in Figure 3 4 Make a New Model Library Choose Filename Save in temp eH ej Ej File name temp ml Save astpo NN Carcel Figure 3 3 Choose the filename and path for the model library file The New Model Library GUI is an interface used to create a model library file with chosen model CAD files see Figure 3 4 11 Create New Model Library IE Model List Fields Class Type 0 PRISM Geometry File None Intensity File None Figure 3 4 Empty model library creation GUI The listboxes and fields are defined as follows Model List listbox that displays the model files currently in the library When a model is selected the corresponding parameters will be shown in the GUI text fields Class a unique nonnegative integer used to identify a model in the library Type a pop up menu that allows you to choose among CAD file types These include STL PRISM 3DS and OFF Name a text string identifier for the model Geometry File path and location of the geometry CAD model file relative to the location of the model library file Intensity File th
96. ward looking in frared FLIR thermal states of complex objects The multi target detection recognition task is accomplished through a Metropolis Hastings jump diffusion process that iteratively samples a Bayesian posterior distribution representing the desired parameters of interest in the FLIR imagery The inference of the targets thermal states is accomplished through an expansion in terms of eigentanks derived from a principle component analysis over target surfaces These two techniques help capture much of the variability inherent in FLIR data Coupled with future work on rapid detection and penalization strategies to reduce false alarms we strive for a unified technique for FLIR ATR following the pattern theoretic philosophy that may be implemented for practical applications Keywords automatic target recognition ATR infrared FLIR pattern theory 1 INTRODUCTION The problem of detecting and classifying objects of interest in images has been extensively studied producing many viable techniques Many ATR systems that are in use today tend to divide the process of recognition into separate stages These include target detection feature extraction clutter rejection classification and possibly other stages depending on the nature of the algorithm Infrared imagery is challenging because in addition to geometric variability we must also deal with the thermal variability related to target heat signatures changing under different ope
97. ximate the proba bility of error of the ATR algorithm with a reasonable degree of success its predictions for the probability of error are compared to those obtained through Monte Carlo trials Three trajectories are used in the comparison The first two trajectories involve aircraft flying in straight and level paths with velocities of 200 m s and altitudes of 8000 m In the first straight and level trajectory the aircraft fly directly away from the receiver while in the second they fly broadside to it Because a much broader range of aspect angles are visible to the receiver in the second flight path the probability of error is expected to be lower than in the first Finally the third trajectory is a constant altitude banked turn in which the aircraft velocity is 100 m s and the altitude is 8000 m To thoroughly compare the probability of error predicted using Chernoff information and that computed using Monte Carlo trials each is computed for a number of noise figures In particular the simulations are conducted with the noise figure varying from 30 to 100 dB in increments of 5 dB Note that this extends to noise figures much larger than would ever be expected in a real system simply so that the breaking point of the algorithm is visible Prior work demonstrates that the maximum noise figure ever anticipated in the proposed system is 45 dB Figure VII shows the probability of error obtained using the first straight and level flight path as
98. z axis gt scale lt global value gt lt x position gt lt y position gt lt z position gt use_ground lt 1 0 or 1 gt intensity lt nonnegative integer gt origin lt x position gt lt y position gt lt z position gt x_length lt value gt y_length lt value gt Figure 5 1 Configuration file format 24 The fields of a model structure are defined in Table 5 4 Section 5 2 3 goes into more detail about the purpose of some of these fields In the case of gFile and rFile these will most likely be the same unless the CAD model is defined in the PRISM format For CAD models that have no intensity information the relevant fields are populated with arbitrary values when the models are first read from the files Table 5 4 Model structure fields and descriptions Field Name Data Type Description class uint32 scalar numerical identifier for the model type char array text description of the model type name char array text identifier for the model translate single array three element z y z translation from the model s origin rotate single array four element 0 y z default model rotation rotateAdjust single array three element x y z translation of the model rotation axis scale single scalar global scaling of model units gFile char array file and path of geometry file rFile char array file and path of radiance file if avail

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