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

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

Introduction 3

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

Related Work 5

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

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

Related Work--Optical Flow Temporal Persistence 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. 9 [13] D. Tschumperle` and R. Deriche, “Vector-Valued Image Regularization with PDE’s: A Common Framework for Different Applications,” CVPR, [14] J. Xiao, H. Cheng, H. Sawhney, C. Rao, and M. Isnardi, “Bilateral Filtering-Based Optical Flow Estimation with Occlusion Detection,” ECCV, [15] M. Werlberger, T. Pock, and H. Bischof, “Motion Estimation with Non-Local Total Variation Regularization,” CVPR, [16] D. Sun, S. Roth, and M. Black, “Secrets of Optical Flow Estimation and Their Principles,” CVPR, 2010.

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] 10 [5] K. He, J. Sun, and X. Tang, “Guided Image Filtering,” ECCV, [8] A. Criminisi, T. Sharp, and C. Rother, “Geodesic Image and Video Editing,” ACM Graphics, [21] A. Criminisi, T. Sharp, and A. Blake, “GeoS: Geodesic Image Segmentation,”ECCV, [22] C. Rhemann, C. Rother, J. Wang, M. Gelautz, P. Kohli, and P. Rott, “A Perceptually Motivated Online Benchmark for Image Matting,” CVPR, 2009.

Cost-volume Filtering 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] 12

Bilateral filter [6] 13 [6] K. Yoon and S. Kweon, “Adaptive Support-Weight Approach for Correspondence Search,” IEEE Trans. Pattern Analysis and Machine Intelligence, Apr

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 14

Guided filter [5] 15 [5] K. He, J. Sun, and X. Tang, “Guided Image Filtering,” Proc. European Conf. Computer Vision, 2010.

Guided filter 16 Bilateral filter does not have this linear model

Guided filter 17

Bilateral filter V.S. Guided filter 18

Guided filter Edge-preserving filtering Non-iterative O(1) time, fast and non-approximate No gradient distortion 19 Advantages of bilateral filter Disadvantages of bilateral filter

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 ： 20 k r r w=(2r+1)^2

Cost-volume Filtering 21

[5] K. He, J. Sun, and X. Tang, “Guided Image Filtering,” Proc. European Conf. Computer Vision, [6] K. Yoon and S. Kweon, “Adaptive Support-Weight Approach for Correspondence Search,” IEEE Trans. Pattern Analysis and Machine Intelligence, Apr [9] F. Crow. Summed-area tables for texture mapping. SIGGRAPH, Cost-volume Filtering 22 (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

Application 23

Stereo Matching 24

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

Stereo Matching Cost computation : grayscale gradients in x and y direction : balances the color and gradient terms : truncation values Occlusion detection : 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 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. 28

Stereo Matching 29 Effect of postprocessing Disparity map with invalidated pixels in red After scanline-based fillingAfter median filtering

Optical flow Cost computation : grayscale gradients in x and y direction : balances the color and gradient terms : truncation values Postprocessing ： Median filter and iteration 30

Optical flow Upscale : To find subpixel accurate flow vectors. Color of subpixel filled with bicubic interpolation. 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] 32 [25] S. Vicente, V. Kolmogorov, and C. Rother, “Joint Optimization of Segmentation and Appearance Models,” Proc. IEEE Int’l Conf. Computer Vision, [26] C. Rother, V. Kolmogorov, and A. Blake, “Grabcut-Interactive Foreground Extraction Using Iterated Graph Cuts,” Proc. ACM Siggraph, 2004.

Experimental Results 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 for stereo for optical flow  Source : Middlebury 34

Stereo Matching 35

Stereo Matching 36

Stereo Matching 37

Stereo Matching 38 disparity maps without occlusion filling and postprocessing (invalidated pixels are black)

Stereo Matching 39 [27] A. Hosni, M. Bleyer, M. Gelautz, and C. Rhemann, “Local Stereo Matching Using Geodesic Support Weights,” Int’l Conf. Image Processing, [6] K. Yoon and S. Kweon, “Adaptive Support-Weight Approach for Correspondence Search,” PAMI, [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.

Stereo Matching 40

Stereo Matching 41

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. 42

Stereo Matching 43

Stereo Matching 44

Stereo Matching 45 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.

Stereo Matching 46

Optical flow 47

Optical flow 48 The respective AEE and AAE are given in parentheses (AEE/AAE).

Optical flow 49 Comparison of two sequences with thin structure, where many competitors fail to preserve flow discontinuities. (We boosted the colors in the second row from the top for better visualization.)

Optical flow 50 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.

Interactive Image Segmentation 51

Interactive Image Segmentation 52

Interactive Image Segmentation Our methodGrabCut [26] Time2.85 ms300 ms error5.3%6.2% 53 [26] C. Rother, V. Kolmogorov, and A. Blake, “Grabcut-Interactive Foreground Extraction Using Iterated Graph Cuts,” Proc. ACM Siggraph, 2004.

Experimental Results 54 Video

Conclusion 55

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] 56 [32] M. Bleyer, C. Rhemann, and C. Rother, “Patchmatch Stereo—Stereo Matching with Slanted Support Windows,” Proc. British Machine Vision Conf., 2011.