Detecting Suspicious Behavior in Surveillance Images
Contents
1. can be compared using Kullback Leibler divergence given by A ip tO D p1 p2 2 Pil l Sm Therefore using KL over histograms of two different ob jects one can compute the distance between the objects and therefore their similarity 3 The overall approach We have implemented two alternative methods of anomaly detection The difference between the methods re sides on the way the density estimation is performed In method 1 M1 the density estimation is done over the en tire image For that objects are clustered in similar groups and a probability density function is estimated per cluster This estimation is performed off line using the baseline data before images can be diagnosed Given an object in a new image its cluster membership is determined and the corresponding density function is used to compute its prob ability of being seen in the location where it is found In method 2 M2 the image is divided by using a grid When an object is found in a given block of the grid the probabil ity of the object being in the observed position is computed on the spot using a non parametric model that utilizes dis tances to objects that have been seen in the same block in the baseline data A more detailed explanation of the meth ods follows 3 1 Method 1 M1 The first step consists in clustering the objects extracted from the training set 1 e baseline data Clustering is per formed by means of a three level divisive2. and W Equitz Efficient and effective querying by image content Journal of Intelligent Information Sys tems 3 3 4 23 1 262 1994 4 A Gammerman and V Vovk Prediction algorithms and confidence measures based on algorithmic randomness the ory Theoretical Computer Science 287 1 209 217 2002 5 D Hawkins Identification of Outliers Chapman and Hall 1980 6 A K Jain and R C Dubes Algorithms for clustering data Prentice Hall Inc Upper Saddle River NJ USA 1988 7 E M Knorr and R T Ng Algorithms for mining distance based outliers in large datasets In VLDB 98 Proceedings of the 24rd International Conference on Very Large Data Bases pages 392 403 San Francisco CA USA 1998 Morgan Kaufmann Publishers Inc 8 9 10 11 S Ramaswamy R Rastogi and K Shim Efficient algo rithms for mining outliers from large data sets In SIGMOD 00 Proceedings of the 2000 ACM SIGMOD international conference on Management of data pages 427 438 New York NY USA 2000 ACM L Shapiro and G Stockman Computer Vision Prentice Hall 2001 B W Silverman Density Estimation for Statistics and Data Analysis Chapman amp Hall CRC April 1986 V N Vapnik Statistical Learning Theory Interscience September 1998 Wiley
3. as image segmentation can be used The result of this process is a a series of objects each characterized as a set of connected edges For each pixel in the edges of the object we use a standard computer vision 9 technique to compute the color image gradient of the pixel Without going into too many details we use finite differences to compute partial derivatives in the x and y directions for the red green and blue channels We form a Jacobian with the derivatives J rz Py Jx gy Ox by rz Ty is the first row gz gy is the second row and bz by is the third row We form S J J transposed J times J The larger eigenvalue of S is the edge strength squared and the corresponding eigenvector is the edge orientation The exact direction is determined by comparing the eigen vector and the rows of J The color gradient is the edge orientation vector times the edge strength square root of the larger eigenvalue With the color gradient values for each pixel computed we can sort the pixels and select the n pixels with largest gradient The n points are then placed in a histogram com posed of thirty six bins Each pixel belonging to an edge contributes to one of the bins according to the edge orien tation When the bin index is determined the bin count is incremented This histogram can be converted into a probability den sity function pdf by normalizing the sum of the histogram counts to unity Two pdfs p and p
4. baseline 4 2 2 Baseline set size Fig 8 shows false positive and true positive rates as a func tion of the size of the baseline For M1 as fewer baseline data is available clusters contain fewer objects and test ob jects are flagged as strange more often As a result we have more false positives and also an increased number of true detections The trend for true positives is less marked in dataset 2 since the detection rate is quite high to begin with For M2 as fewer data is available each grid block gets pop Figure 7 Images detected as outliers in dataset 3 a Three jaywalkers on the access road i e pedestrians in a location they have not been seen in the baseline set b Big truck on the access road that object was never present there in the baseline set c Lack of foreground objects d Jaywalker in the main road e Pedestrian on the right no sidewalk f Green truck on the sidewalk ajb Figure 3 Examples of outliers of dataset 1 one Figure 4 Example of a baseline image of dataset 2 ulated very sparsely Each object receives low probability even the training ones therefore the size of the codewords is larger As a result more objects are considered as normal Hence as the training set gets smaller we observe less false positives and less true positives The trend for false posi tives is not noticeable in dataset 2 since the rate is 0 from the start
5. by a series of frames shot over a controlled scene with ob jects following normal patterns of movement in the base line part of the set and being moved to anomalous spots in the test part Fig 4 shows a sample frame for training In the 82 baseline images the foreground objects the small chest and the grey remote control are seen in the middle part of the image In the test images we have 24 normal frames similar to the baseline frames and 22 outliers with foreground objects misplaced background objects moved or disappearing and new objects that have not been seen in the baseline The clustering of the objects in the baseline data was set at 9 clusters Fig 5 shows two examples Dataset 3 This data was obtained by placing a camera close to an office window in a building on campus The camera was pointing at a traffic intersection on campus and shooting a video of on going activities The camera used for this last set is an IQEye 511 The images were taken at 30 frames per second 704x480 all of the other features white balance etc where disabled A frame of the baseline data is shown in Fig 6 The original set has 7680 images The first 3680 are considered training and the remaining 4000 as test The number of clusters of objects for the baseline data is set at 45 4 2 Results 4 2 1 Basic results In this section we show the confusion matrices false pos itives and true positives for the best results obtained on da
6. clustering that uses a different distance function at each level The three distance functions are based on 1 dimension of the object pixel count 2 matching of the orientation and the size of the bounding box and 3 edge gradient At each level each cluster obtained in the previous level is split divisive clustering by re clustering its objects using an agglomera tive approach based on the Ward method 6 according to the distance function of that level First objects are clustered using the pixel count This allows early separation of objects having different sizes At the second level objects are grouped based on the orienta tion and the size of the bounding box This is useful for instance to separate pedestrians located close to the cam era from horizontally oriented cars positioned farther away from the camera Bounding boxes are normalized to have the same length of the longest edge and they are positioned so that their centers overlap The difference in orientation between two bounding boxes is captured by the smallest rotation angle alpha ranging from O to 90 degrees neces sary to align the two boxes see Fig 1 The distance be tween two bounding boxes is then defined as the maximum of the two distances d and d as shown in Fig 1 Finally at level three objects are clustered using the similarity be tween edge histograms Once the training objects are clustered it is possible to estimate the probability
7. scribe our anomaly detection approach how to obtain a fea tureless probabilistic description of images and the image processing techniques used for object detection In Sec tion 3 we describe how the individual components are in tegrated together in the overall approach Specifically we describe two different methods Experiments and results are discussed in Section 4 and conclusions are given in Section 5 2 Technical Description 2 1 Anomaly Detection In anomaly detection the goal is to find entities that are different from most other entities These entities called out liers are defined by Hawkins 5 as an observation that de viates so much from other observations that arouse the sus picion that it was generated by another mechanism This definition leaves the concept of deviation unexplained and therefore is general enough to apply to many different situa tions In our application we are looking for images that can be identified as outliers Using the definition above that means images that capture events generated by a mecha nism other than the one that generates the images we con sider normal Many anomaly detection algorithms see for example 7 8 find outliers by measuring the distance between entities where the entities are vectors of attributes However defin ing distances between two images is a difficult problem Some researchers have attempted to solve it by describing an image as a vector o
8. the base line images the representations of objects found in each block are saved To compute the codeword sizes for the baseline images we proceed as follows For every object in an image lo cated in block 6 we compute the probability of being in its current position using a non parametric model of the form Min o B i o d i o pi 1 maxi 06 B ixo d i o where o represents an object different from 2 seen in B in any of the baseline images The model computes the proba bility as the complement of the ratio between the minimum distance of the object in consideration from any object in B and the maximum distance of the object in consideration from any object in B Notice that the two extremes of this function are 0 when the minimum and maximum distances are the same and 1 when the minimum distance is 0 The first case corresponds to an object that has no close neigh bors the second to an object that has an identical copy in the block Using the probability so obtained it is simple to compute the contribution of the object to the codeword size and ul timately to compute the codeword size of the image In this way the distribution of strangeness for the baseline images can be obtained For a new image that needs to be diagnosed the pro cess is similar For every object of the image the non parametric model above allows to compute its probability The strangeness of the image is then computed Finally Str
9. Detecting Suspicious Behavior in Surveillance Images Daniel Barbara Carlotta Domeniconi Zoran Duri George Mason University Computer Science Department Fairfax VA 22030 Maurizio Filippone Richard Mansfield Edgard Lawson George Mason University Computer Science Department Fairfax VA 22030 E mail dbarbara cdomenic zduric rmansfi2 wlawson gmu edu Abstract We introduce a novel technique to detect anomalies in images The notion of normalcy is given by a baseline of im ages under the assumption that the majority of such images is normal The key of our approach is a featureless proba bilistic representation of images based on the length of the codeword necessary to represent each image Such code word s lengths are then used for anomaly detection based on Statistical testing Our techniques were tested on syn thetic and real data sets The results show that our ap proach can achieve high true positive and low false positive rates 1 Introduction Surveillance applications are becoming commonplace However having to browse through a large number of frames in search of worthy images is a labor intensive and error prone task A technique that could highlight which images are worth a deeper and closer look would be of outmost importance Additionally such a technique could highlight crucial information that is otherwise missed Al though video and image surveillance have received a lot of attention in the computer vis
10. Figure 6 Example of a baseline image of dataset 3 4 2 3 Scale of the objects We tested the effect of changing the scale of the images on TP and FP rates The objective was to test the sensitivity of our approach to the quality of the images smaller frames corresponds to less quality Fig 9 summarize the results For both methods decreasing the size of the image reduces the number of true positives In M1 this is due to the fact Se a 1 1 20 30 40 50 60 70 30 frames in training set FP and TP dependency on training size 100 T T T Figure 8 False positive and true positive rates as a function of the size of the baseline set Upper dataset 1 Lower dataset 2 that all objects start appearing more similar to each other This results in less clusters and an estimation of density functions closer to uniform distributions that cover the en tire image Thus objects that should be detected as out of place or never seen are not identified as such In M2 the effect in individual blocks is the same Objects appear simi lar to each other and therefore do not get flagged as strange The trend is less marked in dataset 2 because there are less foreground objects in that set 4 2 4 Grid Size The grid size affects the two methods differently In M1 the grid size has an impact on the density estimation In M2 however the impact is on the objects that we will find i
11. OUD provides a diagnosis of the image 4 Empirical Evaluation 4 1 Data We conducted experiments with three datasets Two were synthetically created by taking digital photographs of a controlled scene consisting of a few objects on a table We moved the objects in certain restricted patterns first to Normal ss Outlier 34 Table 1 Confusion matrix for dataset 1 Detected Detected as Normal as oer SS Normal 24 ere eae ot Outlier 22 Table 2 Confusion matrix for dataset 2 create a baseline of normal images Later we moved the objects to areas in the image where they had never been be fore in the baseline set and introduced new objects to the scene We also made objects including background objects that had never moved before disappear and background ob jects change their positions to create anomalies These two datasets were designed to have a proper account of normal and outlier frames so we could do a quantitative evaluation of the techniques These two sets were shot with a Sigma SD9 SLR digital camera with the FOVEON X3 image sensor that has three layers of Pixel Sensors each pixel cap tures 3 colors as opposed to the standard 1 color pixel us ing high resolution 2263x1512 pixels Details are pro vided below In each of the experiments the results are reported for the best selection of parameters The value of y is kept to 1 variations over this parameter did not exhibit a significan
12. ako aes nxn Hens Figure 10 M1 s TP and FP rates for differ ent grid sizes in Upper dataset 1 Lower dataset 2 5 60 we a p T n i j 50 h ae oe p ka a i GH ca 40 i f a iF E a o O 10 a en Bee ns as o ash 1 fi 1 fi 1 o 10 20 0 40 50 60 70 50 90 100 block size n means nxn pixels per block 100 T T T T T T T T E 5A A A APE a gob Baa ET tg TG G E Hb 4 amp 60 7OF 60 f ss 50F 40 30 20 F 10H Jom D ese at ttt L 1 1 1 gt o 10 0 0 40 0 60 70 80 90 100 block n means nxn pixels per block Figure 11 M2 s TP and FP rates for vary ing grid sizes for Upper dataset 1 Lower dataset 2 The numbers in the x axis mean the number of pixels per block n means nxn pixels thermore we plan to improve the process of discovering anomalies by using additional information such as sound and to deal with situations where images are poorly regis tered References 1 D Barbara C Domeniconi and J P Rogers Detecting outliers using transduction and statistical testing In KDD 06 Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining pages 55 64 New York NY USA 2006 ACM Press 2 T M Cover and J A Thomas Elements of Information Theory Wiley Interscience August 1991 3 C Faloutsos R Barber M Flickner J Hafner W Niblack D Petkovic
13. density for a specific cluster To do so we divide the image with a grid and have each ob Figure 1 Bounding boxes and the second distance function ject found in the baseline image set contribute with a Gaus sian distribution to the density The standard deviation of the Gaussian for each object t is estimated as y SS ves where c is the pixel count of object 1 and n is the number of objects in the same cluster as object 7 The user can set y to let the density estimation have the desired sparseness For more than three standard deviations the contribution is set to zero Each training object is assigned to the element of the grid where it belongs The contribution is computed only for the centers of the blocks of the grid At the end of this process each cluster at the lowest level has a density function associated with it which will permit the calcula tion of the likelihood of seeing an object belonging to that cluster in a particular block of the grid The objects extracted from test images are assigned to the clusters of training objects as follows For each distance level StrOUD is first used against all the clusters If the object does not fit any cluster for at least one distance level it is declared an outlier otherwise we determine its clus ter by using majority voting among the k closest clusters members Cluster refinements are performed at each level This means that a test object is first assigned to one cl
14. es as The image is drawn from the same distribution that generated the images we use as a baseline With the help of a confi dence level we can use the p value to accept or reject this hypothesis If the p value is less than 1 0 the null hypoth esis is rejected Otherwise the alternative hypothesis H1 The entity is an outlier is accepted For the problem under consideration the entities are images and we need to define a suitable function for a As mentioned before functions that measure the distance between two images typically do not capture meaningful anomalies To avoid this problem we rely on the length of the description of the image in probabilistic terms to mea sure its strangeness The principle is deeply rooted in infor mation theory and code design 2 Optimal codes are built p value in such a way that the most common words receive shorter descriptions A similar concept can be applied to images replacing words with the objects in the image In the next section we explain how to achieve this 2 2 Probabilistic Description of Images In this section we explain our choice of strangeness func tion and its relationship with information theory and code design An image can be considered to be composed of a series of geometrical objects later on we will explain how we recover these objects in practice One can argue that over all the possible normal images of a given area each ob ject follows a spa
15. f features e g 3 This approach detects anomalies based on the extracted features for in stance an image with predominantly blue color where color is one of the features would be an outlier among im ages that do not have a lot of blue in them Clearly these are not the kinds of anomalies we are interested in Instead we utilize an anomaly detection technique we have recently developed presented in 1 The approach called StrOUD for Strangeness based Outlier Detection algorithm com pares the entity that we wish to diagnose to a sample of entities and uses statistical testing to decide if the entity in question is an outlier The comparison is made by us ing a measure called strangeness qa that represents how strange the entity is Strangeness is defined as a function and can take many forms a characteristic that makes the method adaptable to many different scenarios Once a strangeness function has been chosen the next step is to compute the strangeness for a sample of data This sample of data called baseline will represent what normalcy is Notice that since anomalies are strange it is reasonable to assume that most of the data in that sam ple will be normal and therefore the strangeness values of that data will approximate what the normal distribution of strangeness would look like If an abnormal data ob servation would occur too often it would cease to be an anomaly Following the paradigm of tra
16. h of the codeword used to represent that image Such code words lengths become the key information for anomaly de tection based on statistical testing Our approach to the problem has many desirable prop erties The methodology does not employ a model to de fine normalcy or abnormal behavior This characteristic is highly desirable since techniques that utilize models either learned through data or manually built tend to be brittle and produce a large number of false positives We assume that baseline images against which anomalies will be flagged are available The size of the baseline sample is related to the confidence level at which one wishes to operate As a rule of thumb if the sample has N images the maximum confidence at which we can operate is 1 for instance with 20 images one can utilize a confidence of 95 The baseline set itself provides the definition of normality as we shall explain later Furthermore our approach does not re quire the recognition of specific objects e g cars people Rather we represent objects as geometric shapes that can be compared without attempting to recognize them This as sumption increases the robustness of the overall technique as object recognition is a difficult task prone to misclassi fications As a result our methodology can be applied in dependently of the image context of which we make no assumptions The paper is organized as follows In Section 2 we de
17. ion community the issue of de tecting anomalous images is largely ignored In this paper we introduce the design of a novel tech nique that achieves this goal The method is capable of flagging anomalous images where anomalies are defined as situations that are not encountered in a baseline of images used to train the technique Our implementation uses stan dard techniques for foreground and background object de CS Dept University of Sheffield UK filippone dcs shef ac uk tection in images which can be substituted for other meth ods but its novelty resides in the way it compares images to find those that contain anomalies A common approach for anomaly detection is to repre sent entities as vectors in a given feature space and com pute distances therein However defining a meaningful set of features and a proper distance measure between images is a challenging problem Inevitably the selected features will bias the kind of anomalies we are able to detect To address this issue we introduce an anomaly detection ap proach based on a featureless probabilistic representation of images The underlying principle is rooted in information theory and code design Optimal codes are built so that the most common words receive shorter descriptions We ap ply a similar concept to images where words are replaced by the detected objects The collection of objects in an im age along with their probabilities contributes to the lengt
18. n a particular block and therefore on the probability given by the non parametric model For this reason we decided to conduct separate experiments for the two methods and report them in separate figures Fig 10 shows the effect of the grid size on M1 The x axis reports the number of divi sions made in each dimension of the image e g the value three corresponds to nine blocks In general the method is quite robust with respect to grid sizes maintaining sim ilar values of TP and FP rates throughout the tested range Fig 11 shows the effect of the grid size on M2 The x axis in this case represents the size in pixels of one block the smaller the size the larger the number of blocks in the im age The trend in dataset 1 is a decrease of the true positive TP and FP for M1 and M2 vs scale of objects T T T T 3 all n 20 a amr 4 Te eae O Erna Ore 10 pes J xp Oe 20 o 40 50 60 70 80 90 100 scal TP and FP rates for M1 and M2 scale of objects 1 oo T T T B rt 90 Saras th E B E 80 70 4 60 4 e 50 al 40 F 4 30 4 20 lr 4 10 F o a p mem o 4 1 1 20 o 40 50 60 70 80 30 100 Figure 9 TP and FP rates for different scales of the frames in a dataset 1 b dataset 2 rate as the blocks get very small This is due to the fact that at those sizes only partial objects are included in the blocks and they all look similar The trends of TP and FP f
19. nsduction 11 4 the computation of the a for each of the observations in the baseline data is done by taking out that observation from the sample and computing the function that defines its strangeness This mechanism is called transduction in the literature 11 4 After this step a sample distribution of a values becomes available and we are ready to diagnose new entities To diagnose an entity using the available distribution of qa values we make use of a test of randomness The most widely applied test is called hypothesis testing and it in volves the calculation of the p value A p value is the small est level at which we can reject the null hypothesis Infor mally is the measure of evidence against the hypothesis the smaller the p value the greater the evidence against the null hypothesis In our case the p value is calculated as fol lows If the entity we are trying to diagnose has strangeness M and the distribution of values in the baseline data is Q1 02 Q y 1 the p value can be calculated as FES Masel Oy Oa n 1 The symbol in Eq 1 indicates the cardinality of the set of a values that are greater than or equal to the value of the test entity In other words the p value is calculated as the fraction of entities that exhibit strangeness at least as large as the strangeness of the test entity The null hypothesis is Hg The entity is not an outlier For the application we are describing it translat
20. or a large range of grid sizes are quite stable 5 Conclusions and future work We have introduced a technique that flags anomalies in images with high true positive and low false positive de tection rates Two methods were investigated M1 makes use of clustering and density estimation to define compact and probabilistic representations of images In this context clustering can be interpreted as a compression technique useful to handling noise M2 avoids clustering by storing the objects observed in the baseline organized by grid cell Local comparisons are carried out between new objects and the baseline where locality is defined by the cell of the grid M2 resembles lazy learning paradigms where no training is carried on off line all the computation is performed once a test image is presented to the technique Since objects are stored by grid cell position their retrieval and compar isons with test objects can be carried out quite efficiently On average the on line computational complexity of M2 1s similar to that of M1 Nevertheless M2 has larger memory requirements as it needs to store the objects of the baseline M1 discards them after performing clustering and density estimation In the future we plan to aid the computation of density functions with the use of domain knowledge Fur 90 Oy eren yo hes Ea Ce 0 a ap N Q oa 100 i a 0 fates gal
21. t change of the results The confidence utilized is 95 In method M1 a value of k 1 neighbors is used to determine the best cluster fit Dataset 1 A sample frame is shown in Fig 2 Most of the pictures contain five objects two toy cars a toy plane a toy train and a small chest that serves as part of the back ground The cars plane and train move in specific patterns throughout the baseline set of frames as shown in the same figure Fig 2 Lower the plane moves on a strip on the up per left corner of the image the cars on a strip in the middle part of the image the train on a strip in the right side of the image The baseline part of the set is composed by 90 images each with the foreground objects located in their normal positions somewhere along the strips indicated in Fig 2 Lower The test part of the set consists of 68 images 34 of them are normal similar to those in the baseline and 34 of the images contain at least one anomaly Anomalies consist of foreground objects placed in parts of the image where they have never been before e g a car in the plane s strip background objects 1 e the chest disappearing or being moved to other places in the image or new objects e g a remote control device appearing in the image Ex amples of the outliers can be seen in Fig 3 The clustering of the objects in the baseline set was set at 30 clusters Dataset 2 This set is similar to the first It is composed
22. tasets 1 and 2 using the two methods described in Sec tion 2 along with examples of outliers found for dataset 3 we do not have the ground truth for that set so quantita tive analysis of the results are not available The results reported in this section are obtained using the best settings for the two methods The confidence level used in the ex periments is 95 Table 1 shows the results obtained for dataset 1 using 90 images as baseline and with a test set composed of 34 normal images and 34 outliers Table 2 shows the results on dataset 2 with a test set of 24 normal images and 22 out liers M1 performs well on both datasets with high true positive and low false positive rates M2 does specially well Figure 2 Upper A frame from dataset 1 Lower Normal patterns of movement for foreground objects in dataset 1 on dataset 2 with 0 false positives and a high 95 46 true positive rate For dataset 3 Fig 7 shows examples of images that were flagged as outliers by our techniques In all these images foreground objects or people were detected in unlikely po sitions and therefore caused a large increase in codeword sizes Image c is an exception it contains no foreground objects It is flagged as an outlier because our statistical testing procedure considers both tails of the distribution of the a values In this case the strangeness or p value see eq 1 of the image is too small smaller than the values for the
23. tial distribution which is unknown This spatial distribution indicates the probability of the object be ing located at a specific location x y within the image It is easy to represent the whole set of possible objects as a dictionary of words A particular arrangement of objects constitutes an image and it is akin to a code composed of symbols in a given dictionary In the field of Information Theory 2 it is well known that data compression can be achieved by the assignment of short descriptions to the most frequent symbols in the vo cabulary In the Morse code for instance the most frequent symbol is represented by a single dot One can prove that a lower bound for optimal codes assigns a codeword of length log p to the symbol 7 if its probability of occurrence is p Similarly we could describe each image as a codeword composed of symbols one for each object in the image The length assigned to a symbol representing an object in a par ticular position would be a function log p of the like lihood of the object being in that location This likelihood is given by the unknown spatial probability density of the object While the spatial density of all the objects over all the possible normal images is unknown we can estimate it from the baseline sample of images The problem becomes a density estimation problem 10 Equipped with estimates of the spatial density functions for the objects we observe in an image
24. uster based on its size At the second level the test object is com pared only with the training objects within the same cluster and so on Finally once the final cluster of a test object is determined we estimate the probability associated to their position using the density function previously calculated for the cluster In the grid method a test object takes the probability associated to the grid element it belongs to If the probability is zero it is set to 107189 since the proba bility of outlier objects is set to 10 19 For each image we compute the size of the codeword de scribing the image as log p i where the summation is over objects 2 detected in an image This also represents the strangeness of an image Running StrOUD using the size of the codeword as strangeness it is possible to flag each image as normal or outlier with different confidence levels Detected Detected as Normal as Outlier ee ee 3 2 Method 2 M2 Method 2 partitions a given image into blocks It then estimates the probability for an object to appear in a given position of a specific block by utilizing only objects seen within the same block in the baseline data Thus this ap proach performs local estimations of probabilities where locality is defined by the size of the blocks without cluster ing objects into groups A grid of fixed size for the entire process is used and every image is divided according to such grid For
25. we can compute the length of the image by adding the contributions log p for each of the objects The quantity log p which we call the size of the image codeword is what we use as strangeness measure for the image Notice that if an object is located in an unlikely position in the image its contribu tion to the codeword size is going to be large potentially making the image abnormal This is precisely what we are trying to achieve images with objects in unlikely positions or with objects that have rarely or never been seen in the baseline collection are going to have large strangeness and most likely will be diagnosed as outliers There are many methods available for density estima tion from parametric methods that assume that the data is drawn from a known parametric family of distributions e g Gaussian to non parametric methods such as his tograms We will later describe the density estimation meth ods we used 2 3 Image processing and object detection 2 3 1 Background Subtraction We assume that the camera observes a scene in which the background changes slowly relative to the motion of the people and the objects in the scene The resulting pictures are registered This allows to utilize background subtrac tion to identify foreground and background objects These techniques have been successfully employed before see 9 Alternatively other techniques to obtain object de scriptions from images such
Download Pdf Manuals
Related Search