4 frameatt Imaging Department Siemens Corporate Research, Inc Princeton, N J 08540 W e studied a Markov random field ( M R F ) formubat i o n f o r the problem of optical flow computation. W e first consider a n adaptive window matching scheme t o obtain a good measure of the correlation between the t w o images. W e also considered a confidence measure f o r each match. Thus, the input t o our system is a n adaptive correlation and the corresponding confidence. W e t h e n use the M R F model t o estimate the velocity field and the velocity discontinuities. Finally, w e address the problem of occlusions and establish a relation between occlusions and m o t i o n discontinuities.
Image PreprocessingBefore computing velocities for every pixel, we need to obtain an estimate for the correspondence between points in two successive frames at times tl and t z . Let Px,y a pixel at location (z,y) at frame tl. At time t z it will have moved by (v,, vy). , To reduce the effects of noise and illumination, instead of directly comparing intensities, one performs correlations with windows centered at the pixel currently examined. Since large window correlations average out noise better and small windows give better localization, it is advantageous to adaptively select the window size based on the local contrast in the image f5].We define a searching window S of size s x s withwhere v , , , is the maximum possible velocity. We also define a matching window'M of size m x m which is used to find matches within the searching window (Figure 1). The matching criterion used is the standard deviation of intensities within the matching window. More precisely, a window in frame tl located at (c, y) when matched with frame t 2 at location (k, I ) gives the standard deviation D. Geiger frame at t+l . X Figure 1: Searching and Matching windows where A . l~~~~, '~\ is the intensity difference between pixels (z + a, y + b) in tl and (k + a, 2 + b) in t z with (a, b) in M and ar is the average intensity difference of M accounting for illumination changes. The smaller cm is, the better the match between windows.Looking at the distribution of Q , over the searching window S we observe that in uniform regions, Q , will be low everywhere while in regions with .high contrast (i.e. containing edges), am will vary greatly. Based on these observations we can use the variance of a , over S to locally determine the size of M. More precisely, We define\ i ; k , l € S the variance of um over the searching window S centered at pixel Px,y. Low Q, denotes a low contrast (uniform) region while high Q, denotes high contrast therefore a region that contains strong features (i.e. edges, texture). The range of U, is divided into four intervals and for high Q, we use a 3 x 3 window and 853 0-8186-2855-3/92 $3.00 (81992 IEEE
