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Improved Sub-pixel Stereo Correspondences



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Improved Sub pixel Stereo Correspondences through Symmetric Refinement Diego Nehab1 Szymon Rusinkiewicz1 James Davis2 1 2 Princeton University University of California at Santa Cruz Abstract Most dense stereo correspondence algorithms start by establishing discrete pixel matches and later refine these matches to sub pixel precision Traditional sub pixel refinement methods attempt to determine the precise location of points in the secondary image that correspond to discrete positions in the reference image We show that this strategy can lead to a systematic bias associated with the violation of the general symmetry of matching cost functions This bias produces random or coherent noise in the final reconstruction but can be avoided by refining both image coordinates simultaneously in a symmetric way We demonstrate that the symmetric sub pixel refinement strategy results in more accurate correspondences by avoiding bias while preserving detail a b c d Figure 1 Examples of matching cost functions a Sum of squared differences b Normalized cross correlation c Birchfield and Tomasi 1 d Sum of absolute differences Note the matching ridge and how the functions are symmetric with regard to it be experienced as random or coherent noise as the texture embossing addressed by Curless and Levoy 4 or as the striping effect addressed by Zhang et al 16 To avoid bias our symmetric sub pixel refinement strategy refines both the reference and the matching image coordinates simultaneously in a symmetric way by looking for the minimum of the matching cost function along a direction that is insensitive to its confidence variations section 3 We present results on both synthetic data and real scans obtained using active stereo section 4 which show that this new method significantly reduces bias in highvariance situations Additionally we demonstrate that one of its variants avoids the pixel locking effect addressed by Shimizu and Okutomi 12 1 Introduction The computation of precise sub pixel



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