Joint Histogram Based Cost Aggregation For Stereo Matching Dongbo Min, Member, IEEE, Jiangbo Lu, Member, IEEE, Minh N. Do, Senior Member, IEEE IEEE TRANSACTION ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 2013

Outline Introduction Related Works Proposed Method : Improve Cost Aggregation Experimental Results Conclusion

Introduction

Goal ： Perform efficient cost aggregation. Solution : Joint histogram + reduce redundancy Advantage : Low complexity but keep high-quality.

Related Works

Complexity of aggregation ： O(NBL) Reduce complexity approach Scale image [8] Bilateral filter [9,10] Geodesic diffusion [11] Guided filter [12] =>O(NL) N : all pixels (W*H) B : window size L : disparity level

Reference Paper [8] D. Min and K. Sohn, “Cost aggregation and occlusion handling with WLS in stereo matching,” IEEE Trans. on Image Processing, [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, [11] L. De-Maeztu, A. Villanueva, and R. Cabeza, “Near real-time stereo matching using geodesic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell., [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

Proposed Method

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, [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.

Improve Cost Aggregation 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

New formulation for aggregation Remove normalization => Joint histogram representaion

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 select D c (<<D) with descending order to be disparity candidates.

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

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

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 ●●● ●●●●● ● ●●● ●●●●● ● ●●● ●●●●● ● ●●● ●●●

Spatial Sampling of Matching Window Cost aggregation => S : sampling ratio O( NBD c ) O( NBD c / S 2 )

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

Experimental Results

Pre-processing 5*5 Box filter Post-processing Cross-checking technique Weighted median filter (WMF) Device ： Intel Xeon 2.8-GHz CPU (using a single core only) and a 6-GB RAM Parameter setting ( ) = (1.5, 1.7, 31*31, 0.11, 13.5, 2.0)

Experimental Results (a)(b) (c)(d)

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

Experimental Results 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 The smaller S, the better

Experimental Results The smaller S, the longer The bigger Dc, the longer

Experimental Results APBP : Average Percentage of Bad Pixels

Ground truth Error maps ResultsOriginal images

Experimental Results

Conclusion

Contribution Re-formulate the problem with the relaxed joint histogram. Reduce the complexity of the joint histogram-based aggregation. Achieved both accuracy and efficiency. Future work More elaborate algorithms for selecting the subset of label hypotheses. Estimate the optimal number Dc adaptively. Extend the method to an optical flow estimation.