1. Fast Cost-volume Filtering For Visual Correspondence and Beyond Asmaa Hosni, Member, IEEE, Christoph Rhemann, Michael Bleyer, Member, IEEE, Carsten Rother, Member, IEEE, and Margrit Gelautz,Senior Member, IEEE IEEE Transactions on Pattern Analysis and Machine Intelligence,2013 1

2. Outline Introduction Related Work Stereo Matching Optical Flow Interactive Image Segmentation Method ： Cost-Volume Filtering Applications Experimental Results Conclusion 2

3. Introduction 3

4. Many computer vision tasks can be formulated as labeling problems. Solution : a spatially smooth labeling where label transitions are aligned with color edges. => very fast edge preserving filter A generic and simple framework (i) constructing a cost volume (ii) fast cost volume filtering (iii) winner-take-all label selection 4

5. Related Work 5

6. Related Work--Stereo Matching Global method Energy minimization process (GC,BP,DP,Cooperative) Per-processing (mean-sift) Accurate but slow Local method A local support region with winner take all Fast but inaccurate. 6

7. Related Work--Optical Flow Optical flow ： the pattern of apparent motion caused by the relative motion between an observer and the scene. A vector field subject to Image Brightness Constancy Equation (IBCE) Application ： motion detection, object segmentation, motion compensated encoding, and stereo disparity measurement...... 7

8. Related Work--Optical Flow Each flow vector is a label and subpixel accuracy further increases the label space Method ： continuous optimization strategies (coarse-to-fine) SSD Local convolution with oriented Gaussians[13] Local convolution with bilateral filter[14] Adaptive support weights[15,16] Trade off search space (quality) against speed. 8 [13] D. Tschumperle` and R. Deriche, “Vector-Valued Image Regularization with PDE’s: A Common Framework for Different Applications,” CVPR, 2003. [14] J. Xiao, H. Cheng, H. Sawhney, C. Rao, and M. Isnardi, “Bilateral Filtering-Based Optical Flow Estimation with Occlusion Detection,” ECCV, 2006. [15] M. Werlberger, T. Pock, and H. Bischof, “Motion Estimation with Non-Local Total Variation Regularization,” CVPR, 2010. [16] D. Sun, S. Roth, and M. Black, “Secrets of Optical Flow Estimation and Their Principles,” CVPR, 2010.

9. Related Work--Interactive Image Segmentation Interactive Image Segmentation is a binary labeling problem. Goal ： Separate the image into foreground and background regions given some hints by the user. Method ： SNAKE Geodesic morphological operator [8,21] Alpha matte [5,22] 9 [5] K. He, J. Sun, and X. Tang, “Guided Image Filtering,” ECCV, 2010. [8] A. Criminisi, T. Sharp, and C. Rother, “Geodesic Image and Video Editing,” ACM Graphics, 2010. [21] A. Criminisi, T. Sharp, and A. Blake, “GeoS: Geodesic Image Segmentation,”ECCV, 2008. [22] C. Rhemann, C. Rother, J. Wang, M. Gelautz, P. Kohli, and P. Rott, “A Perceptually Motivated Online Benchmark for Image Matting,” CVPR, 2009.

10. Cost-volume Filtering 10

11. Edge-preserving filtering Edge-preserving filtering methods Weighted Least Square [Lagendijk et al. 1988] Anisotropic diffusion [Perona and Malik 1990] Bilateral filter [Aurich and Weule 95], [Tomasi and Manduchi 98] Digital TV (Total Variation) filter [Chan et al. 2001] 11

12. Bilateral filter [6] 12 [6] K. Yoon and S. Kweon, “Adaptive Support-Weight Approach for Correspondence Search,” IEEE Trans. Pattern Analysis and Machine Intelligence, Apr. 2006.

13. Bilateral filter Advantages Preserve edges in the smoothing process Simple and intuitive Non-iterative Disadvantages Complexity O(Nr 2 ) Gradient distortion Preserves edges,but not gradients 13

14. Guided filter [5] 14 [5] K. He, J. Sun, and X. Tang, “Guided Image Filtering,” Proc. European Conf. Computer Vision, 2010.

15. Guided filter 15 Bilateral filter does not have this linear model

16. Guided filter 16

17. Bilateral filter V.S. Guided filter 17

18. Guided filter Edge-preserving filtering Non-iterative O(1) time, fast and non-approximate No gradient distortion 18 Advantages of bilateral filter Disadvantages of bilateral filter

19. Cost-volume Filtering Label l from C’ : the filtered cost volume i and j : pixel indices. W i,j : The filter weights depend on the guidance image I ： the mean vector and covariance of I : a smoothness parameter U : Identity matrix Winner take all ： 19 k r r w=(2r+1)^2

20. Cost-volume Filtering 20

21. [5] K. He, J. Sun, and X. Tang, “Guided Image Filtering,” Proc. European Conf. Computer Vision, 2010. [6] K. Yoon and S. Kweon, “Adaptive Support-Weight Approach for Correspondence Search,” IEEE Trans. Pattern Analysis and Machine Intelligence, Apr. 2006. [9] F. Crow. Summed-area tables for texture mapping. SIGGRAPH, 1984. Cost-volume Filtering 21 (a)Zoom of the green line in the input image. (b)Slice of the cost volume for the line(white/black/red: high/low/lowest costs) (c)The box filter [9] (d)The joint bilateral filter [6] (e)The guided filter [5] (f)Ground-truth labeling

22. Application 22

23. Stereo Matching 23

24. Stereo Matching Cost computation : grayscale gradients in x direction : balances the color and gradient terms : truncation values 24

25. Stereo Matching Cost computation : grayscale gradients in x and y direction : balances the color and gradient terms : truncation values Occlusion detection : 25

26. Stereo Matching Cost computation : grayscale gradients in x and y direction : balances the color and gradient terms : truncation values Occlusion detection : Postprocessing 1.Scanline filling : the lowest disparity of the spatially closest nonoccluded pixel 2.Median filter : : adjust the spatial and color similarity : normalization factor 26

27. Stereo Matching Alternative—symmetric cost aggregation The cost aggregation can be formulated symmetrically for both input images. Replace the 3*1 vector I i in (3) with a 6*1 vector whose entries are given by the RGB color channels of both I i and I’ i-l. 27

28. Stereo Matching 28 Effect of postprocessing Disparity map with invalidated pixels in red After scanline-based fillingAfter median filtering

29. Optical flow Cost computation : grayscale gradients in x and y direction : balances the color and gradient terms : truncation values Postprocessing ： Median filter and iteration 29

30. Optical flow Upscale : To find subpixel accurate flow vectors. Color of subpixel filled with bicubic interpolation. 30

31. Interactive Image Segmentation ： foreground F or background B ： background color histograms [25] b(i) ： the bin of pixel i Cost computation : (binary labeling) => Five iterations [26] 31 [25] S. Vicente, V. Kolmogorov, and C. Rother, “Joint Optimization of Segmentation and Appearance Models,” Proc. IEEE Int’l Conf. Computer Vision, 2009. [26] C. Rother, V. Kolmogorov, and A. Blake, “Grabcut-Interactive Foreground Extraction Using Iterated Graph Cuts,” Proc. ACM Siggraph, 2004.

32. Experimental Results 32

33. Experimental Results Device ： an Intel Core 2 Quad, 2.4 GHZ PC with GeForce GTX480 graphics card with 1.5GB of memory from NVIDIA. Settings parameters:  : depends on the signal-to-noise ratio of an image 0.008 for stereo 0.016 for optical flow  Source : Middlebury http://vision.middlebury.edu/stereo/http://vision.middlebury.edu/stereo/ 33

34. Stereo Matching 34

35. Stereo Matching 35

36. Stereo Matching 36 disparity maps without occlusion filling and postprocessing (invalidated pixels are black)

37. Stereo Matching 37 [27] A. Hosni, M. Bleyer, M. Gelautz, and C. Rhemann, “Local Stereo Matching Using Geodesic Support Weights,” Int’l Conf. Image Processing, 2009. [6] K. Yoon and S. Kweon, “Adaptive Support-Weight Approach for Correspondence Search,” PAMI, 2006. [7] C. Richardt, D. Orr, I. Davies, A. Criminisi, and N. Dodgson, “Real-Time Spatiotemporal Stereo Matching Using the Dual-Cross-Bilateral Grid,”ECCV,2010.

38. Stereo Matching Million Disparity Estimations per second (MDE/s) W : width H : height D : disparity levels FPS : number of frames per second A larger MDE number means a better performing system. 38

39. Stereo Matching 39

40. Stereo Matching 40

41. Stereo Matching 41 Table 2. Rankings and run times for selected local stereo methods. Run times in the table are averaged over the four Middlebury test images. *The run time in [15] was reported before left-right consistency check in the corresponding paper. Hence, for fairness, we have multiplied the reported time by a factor of 2.

42. Stereo Matching 42

43. Optical flow 43

44. Optical flow 44 The respective AEE and AAE are given in parentheses (AEE/AAE).

45. Optical flow 45 Large displacement flow (b)-(e) and (l)-(o) Motion magnitude for different methods. (f), (p) Our flow vectors with the color coding as in middleburry. (h)-(k) Backward warping results using flow of different methods—the tip of the foot is correctly recovered by our method. Occluded regions cannot be handled by any method.

46. Interactive Image Segmentation 46

47. Interactive Image Segmentation 47

48. Interactive Image Segmentation Our methodGrabCut [26] Time2.85 ms300 ms error5.3%6.2% 48 [26] C. Rother, V. Kolmogorov, and A. Blake, “Grabcut-Interactive Foreground Extraction Using Iterated Graph Cuts,” Proc. ACM Siggraph, 2004.

49. Conclusion 49

50. Conclusion Contribution Propose a edge-preserving property Runtime independent of the filter size Achieved both accuracy and efficiency Future Work Leverage this framework to other application areas Process slanted surfaces [32] 50 [32] M. Bleyer, C. Rhemann, and C. Rother, “Patchmatch Stereo—Stereo Matching with Slanted Support Windows,” Proc. British Machine Vision Conf., 2011.