Motion2D User Manual
Contents
1. y WA pi the flow vector modeled at point p B is a matrix the form of wich depends on the chosen model but the coefficients of which depend only on the point coordinates 1 3 1 Constant motion models MDL_TX 2D translation motion model along the x axis with 1 parameter cy wa pi up a MDL_TY 2D translation motion model along the y axis with 1 parameter ca wa pi up c MDL_TR 2D translation motion model with 2 parameters c1 c2 gt Au u pi u C1 BAT v pi u C2 1 3 2 Affine motion models MDL_AFF TX DIV 2D affine motion model with 2 parameters c a tak ing into account the translation along the x axis and the 2D divergence auto 4 0 a 8 CHAPTER 1 ABOUT MOTION2D MDL_AFF_TR_DIV 2D affine motion model with 3 parameters c1 Ca a1 taking into account the 2D translation and the 2D divergence a MDL_AFF_TR_ROT 2D affine motion model with 3 parameters c1 c2 a taking into account the 2D translation and the 2D rotation _ u pi C1 0 ay Ti i ale lalo MDL_AFF_TX_NULL 2D affine motion model with 5 parameters ca a1 42 43 04 with a E If we express the parameter vector A in another basis of elementary mo tion sub fields dt cy ca div rot hyp1 hyp2 with div 5 a1 a4 rot a3 a2 hypl a1 a4 and hyp2 5 a2 as this motion model has the particularity to consider the translation along the x axis as n2. 18 CHAPTER 2 USAGE b fs back warped image path Specify the path and the generic name of the files contain ing the back warped images built using the estimated motion model We support only PNG PNM PGM P5 PPM P6 and RAW RAW8 RAW16 image file formats The format is selected by analysing the filename extension Example b tmp B 04 png j d back warped image nrows Set the number of rows of the back warped image By default the back warped image has the same rows number than the images to proceed This option is taken into account only when option b is used k d back warped image ncols Set the number of columns of the back warped image By default the back warped image has the same rows number than the images to proceed This option is taken into account only when option b is used t d back warped image row origin This option makes it possible to fix the co ordinates of the row origin of the back warped image compared to the origin of the images to treat This option is taken into account only when option b is used u d back warped image col origin This option makes it possible to fix the co ordinates of the column origin of the back warped image compared to the origin of the images to treat This option is taken into account only when option b is used w Zs weights image path Specify the path and the generic name of the files contain ing the M estimator weights These weights in 0 1 are re
3. the parameter vector A in another basis of elementary mo tion sub fields 8 c1 c2 div rot hyp hyp2 with div a1 as rot a3 a2 hypl 5 a1 a4 and hyp2 4 a2 as this motion model has the particularity to consider the first hyperbolic term at zero ie hyp 0 MDL_AFF_HYP2_NULL 2D affine motion model with 5 parameters c1 c2 41 42 44 with gt u pi C1 a1 a2 Ti If we express the parameter vector A in another basis of elementary mo tion sub fields c1 c2 div rot hypi hyp2 with div a1 a4 rot a3 a2 hypl 5 a1 a4 and hyp2 5 a2 as this motion model has the particularity to consider the second hyperbolic term at zero ie hypa 0 MDL_AFF_TR_ROT_DIV 2D affine motion model with 4 parameters c1 c2 41 42 able to consider motion like 2D translation with 2D rotation and diver gence gt u pi C1 a a2 Ti w Ei alpi v pi C2 42 a4 Yi If we express the parameter vector A in another basis of elementary mo tion sub fields 6 c1 c2 div rot hyp1 hyp2 with div 5 a1 04 rot a3 a2 hypl 5 a1 a4 and hyp2 5 a2 as this motion model has the particularity to consider the hyperbolic terms at zero ie hyp hyp2 0 MDL_AFF_COMPLET 2D affine motion model with 6 parameters c1 C2 a1 42 taking into account constant and affine parameters le 10 CHAPTER 1 ABOUT MOTION2D This m
4. FF_ROT_NULL same as ARN same as ARD same as ARR same as AXN same as AYN MDL_AFF_HYP1_NULL MDL_AFF_HYP2_NULL MDL_AFF_TR_ROT_DIV MDL_AFF_COMPLET MDL_QUA_PAN_DIV MDL_QUA_PAN_TILT MDL_QUA_PAN_TILT_DIV MDL_QUA_2D MDL_QUA_COMPLET same as AH N same as AH2N same as ARRD same as AC same as QPD same as QPT same as QPTD same as Q2D same as QC Specify that the global illumination parameter will be estimated 16 CHAPTER 2 USAGE Uses the previous estimation to initialize the motion model to estimate x model_col_orig f Sets the origin column coordinate of the motion model By default this parameter is initialized to the mid image column number y model_row_orig f Sets the origin row coordinate of the motion model By default this parameter is initialized to the mid image line number Computes the covariance matrix of the motion model parameters 2 1 5 Estimation support options input a fs support image or video path Motion2D makes it possible to estimate motion either on all the image by defect or on a part of the image In this case it is necessary to indicate to the software the position of the area on which the motion estimation must be done This is carried out while associating each image of the video sequence a file called estimation support corres ponding to an image with same size numbering and extension as the images to be treat
5. Motion2D User Manual Release 1 3 11 Fabien Spindler Irisa Inria Campus universiatire de Beaulieu 35042 Rennes Cedex France e mail Fabien spindlerQirisa fr January 2005 Contents 1 About Motion2D 1 1 Introduction 132 7 MDESCTIPUONT rn zu Se Soc AR ON es 1 3 Supported 2D polynomial motion models 1 4 Contact information 2 Usage 2 1 Motion2D options 2 2 Example of 2D parametric motion models estimation CONTENTS Chapter 1 About Motion2D 1 1 Introduction The Motion2D software estimates 2D parametric motion models between two successive images It can handle several types of motion models respectively constant model translation affine and quadratic models Moreover it inte grates the possibility of taking into account the global variation of illumination Motivations for the use of such models are on one hand their efficiency which has been demonstrated in numerous contexts such as estimation segmentation tracking and interpretation of motion and on the other hand their low com putational cost compared to optical flow estimation Moreover to have the best accuracy for the estimated parameters and to take into account the problem of multiple motion Motion2D exploit a robust multiresolution and incremen tal estimation method exploiting only the spatio temporal derivatives of the intensity function Motion2D was developped at I
6. ated parameters and to take into account the problem of multiple motion Motion2D exploit a robust multireso lution and incremental estimation method exploiting only the spatio temporal derivatives of the intensity function 2 1 3 Input video sequence options p fs image or video path Dealing with an image sequence 13 back warped image row origin u back warped image col origin 14 CHAPTER 2 USAGE By image sequence we mean one file per image Specify the path and the generic name of the files containing the images to process The following image file formats PNG PNM PGM P5 PPM P6 and RAW RAW8 RAW16 are supported The format is selected by analysing the filename extension Example p rond point 04d png Dealing with a video By video we mean one file for all images of the video Specify the video file Only Mpeg2 file are supported Warning in a Mpeg2 video stream the first frame has the number zero Example p video mpg f 0 R d Number of rows in RAW image Specify the number of rows for RAW sequences C d Number of columns in RAW image Specify the number of columns for RAW sequences f fs first frame 1 Specify the number of the first frame in the video sequence If the image sequence numbering uses a fixed number of digits complete whith O before the image number Warning the first frame of a Mpeg2 video stream has the number zero s hd step 1 Specify the step between two f
7. ed Thus this option specify the path and the generic name of the files containing the images corresponding to the estimation support The images format depends on the filename extension We support only Mpeg2 PNG PNM PGM P5 PPM P6 and RAW RAW8 RAW16 image file formats Be aware images to proceed those specified by option p and option a must have the same size For example to estimate the motion between images rond point0001 png and rond point0002 png the support file name must be support0001 png c 4d support label This option is associated to the previous one It fixes the value of the estimation support label where the estimation will be achieved 2 1 6 Multi resolution framework options input q d nbsubsample Number of subsampling to apply to the images before 2 1 MOTION2D OPTIONS 17 starting the motion estimation process If this parameter is equal to zero images are not subsampled If this parameter is greater than zero images are resized at a lower resolution where the number of lines and columns is divided by 2 nbsubsample Be aware the estimated parametric motion model is returned at the highest resolution n ul number of pyramid levels Specify the number of levels in the Gaussian image pyramids and image gradients pyramids used in the multi resolution framework In general when the size of the images to be treated is close to CIF format 352 X 288 it is advised to fix this parame
8. med leading to the expression rao pi linear with respect to AQ rae Pi Vies pit O gt Pi Ba a pi AG LH pit WF pi pi Cr where Vie pi denotes the spatial gradient of the intensity function at location p and at time t 1 Then we substitute for the minimization of E O the minimization of the expression given by E A x Y plrac ps C pick which is equivalent to minimizing 5 wi rAo Pi 3 pi ER with wi p rao pi 4 rae Pi where w is the derivative of the p function The error function E AO is minimized using an Iterative Reweighted Least Squares procedure with 0 as an initial value for AO For more details about the method and its performances see the Motion 2D related references 1 2 1 Motion2D supported platforms The Motion2D software runs on Unix Linux SunOS Solaris and Irix and Windows 95 98 ME Windows NT 4 Windows 2000 Windows XP operating systems 1 3 SUPPORTED 2D POLYNOMIAL MOTION MODELS 7 Operating system Linux EA C Sw Oo gt Motion2D does not require any special libraries 1 3 Supported 2D polynomial motion models Using matrix notation supported 2D polynomial motion models can always be stated in the general way by Wa pi a B p A which is linear with respect to the n motion parameters A c1 C2 G1 44 q1 96 and where p x yi denotes the spatial position of a point in C
9. motion model between each couple of images of the round about sequence in PNG format and put the results in the tmp result txt file try Motion2D m AC p test sequence png rond point 04d png f 1 i 33 r tmp result txt v To estimate the dominant motion using a quadratic motion model between each couple of images of the round about sequence in PPM P6 format and generate a back warped sequence in PNG format try Motion2D m QPTD p test sequence ppm rond point 04d ppm f 1 i 33 b tmp bwarp 04d png j 264 k 450 t 30 u 20 v To estimate the motion of the mobile vehicle in the round about sequence in PNG format using a quadratic motion model and an input estimation support sequence in PNG format too try 20 CHAPTER 2 USAGE Motion2D m QC p test sequence png rond point 04d png f 1 i 33 a test sequence png support 04d png c 255 v
10. odel is a good tradeoff between complexity and representativeness It can take into account many kind of motion translation rotation scal ing deformation and even if a rigid 3D motion gives rise to a quadratic model in the image plane the affine flow recovers the essential part 1 3 3 Quadratic motion models MDL_QUA_PAN_DIV 2D quadratic motion model with 4 parameters c a1 91 92 taking into account the translation along the x axis some affine and quadratic parameters E Yi MDL_QUA_PAN_TILT 2D quadratic motion model with 4 parameters c1 C2 q1 92 taking into account the 2D translation and some quadratic parameters u pi y hi 0 al 4 e h 1 1 2 As Walpi v p T C2 0 q e ee MDL_QUA_PAN_TILT_DIV Quadratic 2D motion model with 5 parame ters c1 C2 41 91 G2 taking into account the 2D translation some affine and quadratic parameters sate 0 a 2 NE MDL_QUA_2D 2D quadratic motion model with 8 parameters c1 C2 1 4 91 q2 taking into account the constants the linear and some quadratic param eters MDL_QUA_COMPLET 2D quadratic motion model with 12 parameters C1 C2 1 44 1 46 taking into account the constants the linear and all the quadratic parameters 2 Ti ss u pi C1 ay ag Ti q q2 93 ziyi v pi C2 d3 a4 Yi da 95 06 j a 1 4 CONTACT INFORMATION 11 1 4 Contact information For general information on the Vista team please visit the Vi
11. rames in the video sequence If step gt 0 images are processed forward If step lt 0 images are processed backward This parameter allow the video temporal subsampling i lu iterations 33 Specify the number of motion estimation iterations to process The number of the last image computed is given by first_frame iterations step 2 1 4 Motion model options input m model_id s AC Specify the parametric motion model id to estimate The table below gives the list of possible model_id strings 2 1 MOTION2D OPTIONS TX constant 1 c1 TY constant 1 c2 TR constant 2 c1 c2 steps o a o e AXD affine 2 c1 al ARD affine 3 c1 c2 a1 ARR affine 3 c1 c2 a1 AXN affine 5 c2 ai a4 AYN affine 5 ci ai a4 ADN affine 5 ci c2 ai a2 a3 ARN affine 5 c1 c2 al a2 a4 AHIN affine 5 c1 c2 a1 a2 a3 AH2N affine 5 c1 c2 al a2 a4 ARRD affine 4 c1 c2 a1 a2 AC affine 6 c1 c2 a1 a4 A en ae Pen ren QPD quadratic 4 c1 al q1 q2 QPT quadratic 4 c1 c2 q1 q2 QPTD quadratic 5 ct c2 a1 q1 q2 Q2D quadratic 8 c1 c2 a1 a4 q1 q2 Qc quadratic 12 c1 c2 a1 a4 q1 q6 MDL_TX same as TX MDL_TY same as TX MDL_TR same as TR MDL_AFF_TX_DIV MDL_AFF_TR_DIV MDL_AFF_TR_ROT MDL_AFF_TX_NULL MDL_AFF_TY_NULL MDL_AFF_DIV_NULL same as ADN l l same as AXD MDL_A
12. risa INRIA Rennes http www irisa fr by the Vista team http www irisa fr vista 1 2 Description The CMotion2D software implements a robust multiresolution estimation of parametric motion models We consider the displaced frame difference corresponding to the motion mod el DF Do pi Le41 pi Wa pi lpi E where I and I are two successive images Ot At the motion model to estimate including a global intensity shift to account for global illumination change and gt u pi A pi v p pi denotes the flow vector modeled at the image point p 5 6 CHAPTER 1 ABOUT MOTION2D To ensure the goal of robustness we introduce a M estimation criterion with a hard redescending robust estimator Thus the motion model is given by 8 argmin 2 p DFDa p C 1 where p x is the Tukey Talwar Cauchy or Welsh biweight function which is bounded for high values of x and C a scale parameter to be set The estimation support R usually consists of the whole image If required it can also be restricted to a specific area of the image The minimization is embedded in a multiresolution and incremental scheme based on the Gauss Newton method At each incremental step k at a given resolution level or from a resolution level to a finer one we have A AA G AC 6 A0 with where O is the current estimate of the parameter vector O A linearization of DFDe p around is perfor
13. scaled in 0 255 This map can be used to see if a pixel participate to the robust motion estimation pixel in white or is more considered as an outlier pixel in black We support only PNG PNM PGM P5 PPM P6 and RAW RAW8 RAW16 image file formats The format is selected by analysing the filename extension Example w tmp W 04 png F s field vector image path Specify the path and the generic name of the files contain ing the displacement vectors in fieldshow format Example w tmp F 04 field 2 2 EXAMPLE OF 2D PARAMETRIC MOTION MODELS ESTIMATION 19 2 1 8 Other options v Activate the verbose mode h Print the help Print the help 2 2 Example of 2D parametric motion models estimation Here are given some examples of Motion2D usage to estimate 2D parametric motion models between two successive images of a video sequence It can han dle several types of motion models respectively constant model translation affine and quadratic models Moreover it integrates the possibility of taking into account the global variation of illumination To get help or to see the available options try Motion2D To estimate the dominant 2D affine motion model between each couple of images of the round about sequence in Mpeg2 format and put the results in the tmp result txt file try Motion2D m AC p test sequence mpeg2 rond point mpg f 0 i 31 r tmp result txt v To estimate the dominant 2D affine
14. sta website http www irisa fr vista For technical information on Motion2D contact Motion2D irisa fr 12 CHAPTER 1 ABOUT MOTION2D Chapter 2 Usage 2 1 Motion2D options 2 1 1 Synopsis Motion2D p image or video path R rows number for RAW images C columns number for RAW images f first frame s step i iterations m model id g x model col orig y model row orig a support image or video path z c support label q nbsubsample n number of pyramid levels l pyramid stop level r dominant motion filename r multiplier factor b back warped image path j back warped image nrows k back warped image ncols t W mmm UE seag BE aor TM NM DA D weights image path F optic flow field I v h 2 1 2 Description The Motion2D software provides a method to estimate 2D parametric motion models between two successive images It can handle several types of motion models respectively constant model translation affine and quadratic models Moreover it integrates the possibility of taking into account the global variation of illumination Motivations for the use of such models are on one hand their efficiency which has been demonstrated in numerous contexts such as estima tion segmentation tracking and interpretation of motion and on the other hand their low conputational cost compared to optical flow estimation More over to have the best accuracy for the estim
15. ter at 4 When the images are with QCIF format 176 X 144 this parameter can be fixed at 3 This parameter implicitly fix the index of the initial level in the pyramids where the robust estimate begins This initial level is than equal to the number of levels in the pyramids minus one The selected level is then that of lower resolution 1 fu pyramid stop level Specify the level of the image pyramids where the estimation process will be stopped This parameter in general fixed at zero corresponds then to the level of higher resolution can vary in the range 0 number_of_pyramid_levels 1 The coarsest level is given by number_of_pyramid_levels 1 The finest level is 0 2 1 7 Result options output r s dominant motion filename Specify the name of the file which will contain the estimated parametric dominant motion model results This result file contains the values of the estimated 2D parametric motion model given at the highest image resolution The parameters of the estimated motion model are very small especially affine and quadratic terms To increase these parameters resolution a multiplier factor can be applied to all the parameters see option e e 1 multiplier factor for the motion parameter 1 This option is associated with the r option It defines a multiplier factor applied to all the motion model parameter c1 c2 a1 a4 q1 q6 when those are saved in a result filename specified with option r
16. ull ie cy 0 MDL_AFF_TY_NULL 2D affine motion model with 5 parameters c1 a1 42 43 4 with eae El a 4 If we express the parameter vector A in another basis of elementary mo tion sub fields dt c ca div rot hyp1 hyp2 with div ai a4 rot a3 a2 hypl 5 a1 a4 and hyp2 4 az as this motion model has the particularity to consider the translation along the y axis as null ie co 0 MDL_AFF_DIV_NULL 2D affine motion model with 5 parameters c1 C2 41 42 43 with a a a If we express the parameter vector A in another basis of elementary mo tion sub fields dt c1 ca div rot hyp1 hyp2 with div 5 a1 04 rot a3 a2 hypl 5 a1 a4 and hyp2 5 a2 as this motion model has the particularity to consider the divergence term at zero ie div 0 1 3 SUPPORTED 2D POLYNOMIAL MOTION MODELS 9 MDL_AFF_ROT_NULL 2D affine motion model with 5 parameters c1 C2 41 42 a4 with m u pi C1 a1 a2 Ti a Ca a a If we express the parameter vector A in another basis of elementary mo tion sub fields 8 c1 c2 div rot hypi hyp2 with div a1 as rot 3 a3 a2 hypl tla a4 and hyp2 az a3 this motion model has the particularity to consider the curl term at zero ie rot 0 MDL_AFFHYP1 NULL 2D affine motion model with 5 parameters c1 c2 41 42 43 with u pi C1 a a2 Ti alp P ee E a e If we express
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