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Class Note for COSC 6373 with Professor Shah at UH


Class Note for COSC 6373 with Professor Shah at UH

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This 24 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 21 views.

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Date Created: 02/06/15
6056 6373 Computer Vision Motion Estimation Acknowledgement Notes by Profs R Szeliski S Seitz L Shapiro and S Shah Why estimate motion IWe live in a 4D world IWide applications I Object Tracking Camera Stabilization Image Mosaics 3D Shape Reconstruction SFM I I I I Special Effects Match Move Frame frqm an ARDA Sam le Vid 0 Change detection for surveillance Vioeo frames F2 F3 Objects appear move disappear 0 Background pixels remain the same simple case How do you detect the moving objects 0 Simple answer pixelwise subtraction Example Person detected entering room Pixel changes detected as difference components 0 Regions are 1 person 2 opened door and 3 computer monitor 0 System can know about the door and monitor Only the person region is unexpected Change Detection via Image Subtactio for each pixel mi 7 if lll rc 12rc gt threshold then Ioutrc 1 else Ioutrc 0 Perform connected components on Iout Remove small regions Perform a closing with a small disk for merging close neighbors Compute and return the bounding boxes B of each remaining region What assumption does this make about the changes Known regions are ignored and system attends to the unexpected region of change Region has bounding box similar to that of a person System might then zoom in on head area and attempt face recognition Optical flow W 7 Problem definition optical quot22 f H I 39 Hazy 3379 I How to estimate pixel motion from image H to image I Solve pixel correspondence problem given a pixel in H look for nearbv pixels of the same colol in l Key assumptions color constancy a point in H looks the same in l For grayscale images this is brightness constancy small motion points do not move very far This is called the optical flow problem Optical flow constraints gr scale Images I iv 9 displacement uv ltx39uyv H 8 y 1513 y I Let s look at these constraints more closely brightness constancy Q what s the equation HX y IXu yv small motion u and v are less than 1 pixel suppose we take the Taylor series expansion of l Iauy u I Ey I I 35 I higher order terms Ixyug v Optical flow e f I Combining these two equations 0muyv Hxy shorthand 362 Icy Ix va HQ Thexcomporientof the gradient vector 3 101379 H7y Izculyv e1t1xu1yv mItVI u 1 What is It The time derivative of the image at Xy How do we calculate it Optica39 flow 9 ua onA o 2 5 VI u v f I Q how many unknowns and equations per pixel 1 equation but 2 unknowns u and V Intuitively what does this constraint mean The component of the flow in the gradient direction is determined The component of the flow parallel to an edge is unknown Aperture robem Aperture problem V Solving the aperture problem I Basic idea assume motion field is smooth I Lukas amp Kanade assume locally constant motion I pretend the pixel s neighbors have the same uv I If we use a 5X5 window that gives us 25 equations per pixel O ItPi VIpi u v I Many other methods exist Here s an overview I Barron JL Fleet DJ and Beauchemin S Performance of optical flow techniques International Journal of Computer Vision 1214377 1994 Lusde o I How to get more equations for a pixel I Basic idea impose additional constraints most common is to assume that the flow field is smooth locally I one method pretend the pixel s neighbors have the same uv o If we use a 5x5 window that gives us 25 equations per pixel O ItPi Wm u 12 IaP1 IyP1 ItP1 LIX132 IyP2 U Iti gt2 ImI25 1140325 141325 RG ysln I How to get more equations for a pixel I Basic idea impose additional constraints most common is to assume that the flow field is smooth locally I one method pretend the pixel s neighbors have the same uv o If we use a 5x5 window that gives us 253 equations per pixel O ItPiOa 1 2 Vlpi0 1 2 u v IaP10 IyP10 ItP10 IxP11 IyP11 ItP11 ImPi2 IyP12 u ItPt2 Ixltp 5gtioi Iyp2395gtioi Itltp2395ioi IxP251 IyP251 ItP251 IxP252 IyP252 ItP252 Conditions forsolvability I Optimal u v satisfies LucasKanade zlxrx39jrxry u 21x1 1ny 1ny v 21917 When is This Solvable ATA should be invertible ATA should not be too small due to noise eigenvalues l1 and I2 of ATA should not be too small ATA should be wellconditioned I1 2 should not be too large I1 larger eigenvalue Edges cause rpblems No NwhmmJmm Z VIVIT large gradients all the same largel1 small I2 gradients have small magnitude smalll1 small I2 ionwork best High textured re Z WINDT 6 gradients are different large magnitudes 12 o 2 largel1 large I2 Errors in LukasKanade I What are the potential causes of errors in this procedure I Suppose ATA is easily invertible I Suppose there is not much noise in the image When our assumptions are violated Brightness constancy is not satisfied The motion is not small A point does not move like its neighbors window size is too large what is the ideal window size Revisiting the small motion aquot 7 ii I 0 quotl v I Is this motion small enough I Probably not it s much larger than one pixel 2nd order terms dominate I How might we solve this problem Iterative Refinement M I Estimate velocity at each pixel using one iteration of Lucas and Kanade estimation I Warp one image toward the other using the estimated flow field easier said than done I Refine estimate by repeating the process


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