Joint Histogram Based Cost Aggregation For Stereo Matching

1. Joint Histogram Based Cost Aggregation For Stereo Matching DongboMin, Member, IEEE, JiangboLu, Member, IEEE, Minh N. Do, Senior Member, IEEE IEEE TRANSACTION ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE,2013

2. Outline • Introduction • RelatedWorks • Proposed Method:ImproveCostAggregation • ExperimentalResults • Conclusion

3. Introduction

4. Introduction • Goal：Perform efficient cost aggregation. • Solution : Jointhistogram+reduceredundancy • Advantage : Low complexitybutkeephigh-quality.

5. RelatedWorks

6. RelatedWorks N : all pixels (W*H) B : window size L : disparity level • Complexityofaggregation：O(NBL) • Reducecomplexityapproach • Scaleimage[8] • Bilateralfilter[9,10] • Geodesic diffusion[11] • Guidedfilter[12]=>O(NL)

7. ReferencePaper • [8] D. Min and K. Sohn, “Cost aggregation and occlusion handling with WLS in stereo matching,” IEEE Trans. on Image Processing, 2008. • [9] C. Richardt, D. Orr, I. P. Davies, A. Criminisi, and N. A. Dodgson, “Real-time spatiotemporal stereo matching using the dual-cross- bilateral grid,” in European Conf. on Computer Vision, 2010 • [10] S. Paris and F. Durand, “A fast approximation of the bilateral filter using a signal processing approach,” International Journal of Computer Vision, 2009. • [11] L. De-Maeztu, A. Villanueva, and R. Cabeza, “Near real-time stereo matching using geodesic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell., 2012. • [12] C.Rhemann,A.Hosni,M.Bleyer,C.Rother,andM.Gelautz,“Fast cost-volume filtering for visual correspondence and beyond,” in IEEE Conf. on Computer Vision and Pattern Recognition, 2011

8. Proposed Method

9. Local Method Algorithm • Cost initialization=>Truncated Absolute Difference => • Cost aggregation=>Weighted filter • Disparity computation=>Winner take all [4,8] [4] K.-J. Yoon and I.-S. Kweon, “Adaptive support-weight approach for correspondence search,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 28, no. 4, pp. 650–656, 2006. [8] D. Min and K. Sohn, “Cost aggregation and occlusion handling with WLS in stereo matching,” IEEE Trans. on Image Processing, vol. 17, no. 8, pp. 1431–1442, 2008.

10. Improve CostAggregation • New formulation for aggregation • Remove normalization • Joint histogram representaion • Compact representation for search range • Reduce disparity levels • Spatial sampling of matching window • Regularly sampled neighboring pixels • Pixel-independent sampling

11. New formulation for aggregation • Remove normalization => • Joint histogram representaion

12. Compact Search Range • Reason • The complexity of non-linear filtering is very high. • Lower cost values do NOT provide really influence. • Solution • Choose the local maximum points. • Only selectDc(<<D) with descending order to be disparity candidates.

13. Compact Search Range • Cost aggregation => • MC(q)：a subset of disparity levels whose size is Dc. N : all pixels (W*H) B : window size D : disparity level O( NBD ) O( NBDc )

14. Compact Search Range Dc= 5 (Best) Final acc. = 94.2% Dc= 60 Final acc. = 93.7% Dc= 6 Include GT = 91.8% Final acc. = 94.1% • Non-occluded region of ‘Teddy’ image

15. Spatial Sampling of Matching Window • Reason • A large matching window and a well-defined weighting function leads to high complexity. • Pixels should aggregate in the same object, NOT in the window. • Solution • Color segmentation => time comsuming • Spatial sampling => easy but powerful ● ● ● ● ● ● ●●●●●● ●●● ●●●●●● ●●● ●●●●●● ●●●

16. Spatial Sampling of Matching Window • Cost aggregation => • S : sampling ratio O( NBDc ) O( NBDc / S2)

17. Parameter definition N : size of image B : size of matching window N(p)=W×W MD : disparity levels size=D MC : The subset of disparity size=DC<<D S : Sampling ratio Pre-procseeing

18. ExperimentalResults

19. ExperimentalResults • Pre-processing • 5*5 Box filter • Post-processing • Cross-checking technique • Weightedmedian filter (WMF) • Device：Intel Xeon 2.8-GHz CPU (using a single core only) and a 6-GB RAM • Parametersetting ( ) = (1.5, 1.7, 31*31, 0.11, 13.5, 2.0)

20. ExperimentalResults (a) (b) (c) (d)

21. ExperimentalResults • Using too large box windows (7×7, 9×9) deteriorates the quality, and incurs more computational overhead. • Pre-filteringcan be seen as the first cost aggregation step and serves the removal of noise.

22. ExperimentalResults The smaller S, the better Fig. 5. Performance evaluation: average percent (%) of bad matching pixels for ‘nonocc’, ‘all’ and ‘disc’ regions according to Dc and S. 2 better than 1

23. ExperimentalResults The smaller S, the longer The bigger Dc, the longer

24. ExperimentalResults • APBP : Average Percentage of Bad Pixels

25. Original images Results Error maps Ground truth

26. ExperimentalResults

27. Conclusion

28. Conclusion • Contribution • Re-formulate the problem withthe relaxed joint histogram. • Reduce the complexity of the joint histogram-based aggregation. • Achieved both accuracy and efficiency. • Futurework • Moreelaborate algorithms for selecting the subset of labelhypotheses. • Estimate the optimal number Dcadaptively. • Extendthemethodtoanopticalflowestimation.