1. Stereo Matching Vision for Graphics CSE 590SS, Winter 2001 Richard Szeliski

2. 1/31/2001Vision for Graphics2 Stereo Matching Given two or more images of the same scene or object, compute a representation of its shape What are some possible applications?

3. 1/31/2001Vision for Graphics3 Face modeling From one stereo pair to a 3D head model [Frederic Deverney, INRIA]Frederic Deverney

4. 1/31/2001Vision for Graphics4 Z-keying: mix live and synthetic Takeo Kanade, CMU (Stereo Machine)Stereo Machine

5. 1/31/2001Vision for Graphics5 Virtualized Reality TM Takeo Kanade, CMU collect video from 50+ stream reconstruct 3D model sequences http://www.cs.cmu.edu/afs/cs/project/VirtualizedR/www/VirtualizedR.html http://www.cs.cmu.edu/afs/cs/project/VirtualizedR/www/VirtualizedR.html

6. 1/31/2001Vision for Graphics6 Virtualized Reality TM Takeo Kanade, CMU generate new video steerable version used for SuperBowl XXV “eye vision” system

7. 1/31/2001Vision for Graphics7 View Interpolation Given two images with correspondences, morph (warp and cross-dissolve) between them [Chen & Williams, SIGGRAPH’93] input depth image novel view [Matthies,Szeliski,Kanade’88]

8. 1/31/2001Vision for Graphics8 More view interpolation Spline-based depth map inputdepth imagenovel view [Szeliski & Kang ‘95]

9. 1/31/2001Vision for Graphics9 View Morphing Morph between pair of images using epipolar geometry [Seitz & Dyer, SIGGRAPH’96]

10. 1/31/2001Vision for Graphics10 Additional applications Real-time people tracking (systems from Pt. Gray Research and SRI) “Gaze” correction for video conferencing [Ott,Lewis,Cox InterChi’93] Other ideas?

11. 1/31/2001Vision for Graphics11 Stereo Matching Given two or more images of the same scene or object, compute a representation of its shape What are some possible representations? depth maps volumetric models 3D surface models planar (or offset) layers

12. 1/31/2001Vision for Graphics12 Stereo Matching What are some possible algorithms? match “features” and interpolate match edges and interpolate match all pixels with windows (coarse-fine) use optimization: –iterative updating –dynamic programming –energy minimization (regularization, stochastic) –graph algorithms

13. 1/31/2001Vision for Graphics13 Outline (remainder of talk) Image rectification Matching criteria Local algorithms (aggregation) iterative updating Optimization algorithms: energy (cost) formulation Markov Random Fields mean-field, stochastic, and graph algorithms

14. 1/31/2001Vision for Graphics14 Stereo: epipolar geometry Match features along epipolar lines viewing ray epipolar plane epipolar line

15. 1/31/2001Vision for Graphics15 Stereo: epipolar geometry for two images (or images with collinear camera centers), can find epipolar lines epipolar lines are the projection of the pencil of planes passing through the centers Rectification: warping the input images (perspective transformation) so that epipolar lines are horizontal

16. 1/31/2001Vision for Graphics16 Rectification Project each image onto same plane, which is parallel to the epipole Resample lines (and shear/stretch) to place lines in correspondence, and minimize distortion [Zhang and Loop, MSR-TR-99-21]MSR-TR-99-21

17. 1/31/2001Vision for Graphics17 Rectification

18. 1/31/2001Vision for Graphics18 Rectification

19. 1/31/2001Vision for Graphics19 Matching criteria Raw pixel values (correlation) Band-pass filtered images [Jones & Malik 92] “Corner” like features [Zhang, …] Edges [many people…] Gradients [Seitz 89; Scharstein 94] Rank statistics [Zabih & Woodfill 94]

20. 1/31/2001Vision for Graphics20 Finding correspondences apply feature matching criterion (e.g., correlation or Lucas-Kanade) at all pixels simultaneously search only over epipolar lines (many fewer candidate positions)

21. 1/31/2001Vision for Graphics21 Image registration (revisited) How do we determine correspondences? block matching or SSD (sum squared differences) d is the disparity (horizontal motion) How big should the neighborhood be?

22. 1/31/2001Vision for Graphics22 Neighborhood size Smaller neighborhood: more details Larger neighborhood: fewer isolated mistakes w = 3w = 20

23. 1/31/2001Vision for Graphics23 Stereo: certainty modeling Compute certainty map from correlations input depth map certainty map

24. 1/31/2001Vision for Graphics24 Plane Sweep Stereo Sweep family of planes through volume each plane defines an image  composite homography virtual camera composite input image projective re-sampling of (X,Y,Z)  projective re-sampling of (X,Y,Z)

25. 1/31/2001Vision for Graphics25 Plane Sweep Stereo For each depth plane compute composite (mosaic) image — mean compute error image — variance convert to confidence and aggregate spatially Select winning depth at each pixel

26. 1/31/2001Vision for Graphics26 Plane sweep stereo Re-order (pixel / disparity) evaluation loops for every pixel,for every disparity for every disparity for every pixel compute cost compute cost

27. 1/31/2001Vision for Graphics27 Stereo matching framework 1.For every disparity, compute raw matching costs Why use a robust function? occlusions, other outliers Can also use alternative match criteria

28. 1/31/2001Vision for Graphics28 Stereo matching framework 2.Aggregate costs spatially Here, we are using a box filter (efficient moving average implementation) Can also use weighted average, [non-linear] diffusion…

29. 1/31/2001Vision for Graphics29 Stereo matching framework 3.Choose winning disparity at each pixel Can interpolate to sub-pixel accuracy

30. 1/31/2001Vision for Graphics30 Traditional Stereo Matching Advantages: gives detailed surface estimates fast algorithms based on moving averages sub-pixel disparity estimates and confidence Limitations: narrow baseline  noisy estimates fails in textureless areas gets confused near occlusion boundaries

31. 1/31/2001Vision for Graphics31 Stereo with Non-Linear Diffusion Problem with traditional approach: gets confused near discontinuities New approach: use iterative (non-linear) aggregation to obtain better estimate provably equivalent to mean-field estimate of Markov Random Field

32. 1/31/2001Vision for Graphics32 Linear diffusion Average energy with neighbors windowdiffusion

33. 1/31/2001Vision for Graphics33 Linear diffusion Average energy with neighbors + starting value windowdiffusion

34. 1/31/2001Vision for Graphics34 Non-linear diffusion Stopping criterion: only update (x,y) column is entropy goes down (distribution is more peaked)

35. 1/31/2001Vision for Graphics35 Summary Applications Image rectification Matching criteria Local algorithms (aggregation) area-based; iterative updating Optimization algorithms: energy (cost) formulation Markov Random Fields mean-field; dynamic programming; stochastic; graph algorithms

36. 1/31/2001Vision for Graphics36 More stereo…(next 2 lectures) Multi-image stereo Volumetric techniques Graph cuts Transparency Surfaces and level sets

37. 1/31/2001Vision for Graphics37 Bibliography See the references in the readings… D. Scharstein and R. Szeliski. Stereo matching with nonlinear diffusion. International Journal of Computer Vision, 28(2):155-174, July 1998 R. Szeliski. Stereo algorithms and representations for image-based rendering. In British Machine Vision Conference (BMVC'99), volume 2, pages 314-328, Nottingham, England, September 1999. R. Szeliski and R. Zabih. An experimental comparison of stereo algorithms. In International Workshop on Vision Algorithms, pages 1- 19, Kerkyra, Greece, September 1999.