1. © 2004 by Davi GeigerComputer Vision April 2004 L1.1 Binocular Stereo Left Image Right Image

2. © 2004 by Davi GeigerComputer Vision April 2004 L1.2 Each potential match is represented by a square. The black ones represent the most likely scene to “explain” the image, but other combinations could have given rise to the same image (e.g., red) Stereo Correspondence: Ambiguities What makes the set of black squares preferred/unique is that they have similar disparity values, the ordering constraint is satisfied and there is a unique match for each point. Any other set that could have given rise to the two images would have disparity values varying more, and either the ordering constraint violated or the uniqueness violated. The disparity values are inversely proportional to the depth values

3. © 2004 by Davi GeigerComputer Vision April 2004 L1.3 Right boundary no match Boundary no match Left depth discontinuity Surface orientation discontinuity AB C D E F A B A C D D C F F E Stereo Correspondence: Matching Space F D C B A AC DEFAC DEF

4. © 2004 by Davi GeigerComputer Vision April 2004 L1.4 Stereo Correspondence: Constraints Left Epipolar Line ooooooo ooooooo ooooooo ooooooo ooooooo ooooooo ooooooo j-1 j=3 j+1 t+1 t=5 t-1 w w=2 Right Epipolar Line Smoothness (+Ordering) Smoothness : In nature most surfaces are smooth in depth compared to their distance to the observer, but depth discontinuities also occur. Usually implies an ordering constraint, where points to the right of match point to the right of. Uniqueness: There should be only one disparity value associated to each point.

5. © 2004 by Davi GeigerComputer Vision April 2004 L1.5 Stereo Algorithm: Data C 0 (e,x,w) Є [0,1] representing how good is a match between a point (e,j) in the left image and a point (e,t) in the right image (x=t+j, w=t-j is the disparity.) The epipolar lines are indexed by e. We use a correlation technique that computes the “angle” between two vectors representing the window values of the intensity. 

6. © 2004 by Davi GeigerComputer Vision April 2004 L1.6 We also consider the matching of intensity edges, where x+w is odd, and so we enhance C 0 (e,x,w) Є [0,1] Stereo Algorithm: Data (cont.) We would like to distinguish the “common” cases (i) where low intensity edges match well low intensity edges from the ”rare” cases (ii) where high intensity edges match high intensity edges So this formula must be modified….

7. © 2004 by Davi GeigerComputer Vision April 2004 L1.7 The stereovision algorithm produces a series of matrices C n, which converges to a good solution for many cases, with 0 <  The positive feedback is given by the two neighbors of node (e,j,t) (or (e,x,w)) with matches at the same disparity w=t-j. Stereo: Smoothing and Limit Disparity The matrix is updated only within a range of disparity : 2D+1, i.e., The rational is: (i)Less computations (ii)Larger disparity matches imply larger errors in 3D estimation.

8. © 2004 by Davi GeigerComputer Vision April 2004 L1.8 Result

9. © 2004 by Davi GeigerComputer Vision April 2004 L1.9 Regi on A Regi on B Region A Left Region A Right Region B Left Region B Right Junctions and its properties (false matches that reveal information from vertical disparities (see Malik 94, ECCV) Some Issues in Stereo: