# How Accurate Can Block Matches Be in Stereo Vision?

Abstract : This article explores the subpixel accuracy attainable for the disparity computed from a rectified stereo pair of images with small baseline. In this framework we consider translations as the local deformation model between patches in the images. A mathematical study first shows how discrete block-matching can be performed with arbitrary precision under ShannonWhittaker conditions. This study leads to the specification of a block-matching algorithm which is able to refine disparities with subpixel accuracy. Moreover, a formula for the variance of the disparity error caused by the noise is introduced and proved. Several simulated and real experiments show a decent agreement between this theoretical error variance and the observed root mean squared error in stereo pairs with good signal-to-noise ratio and low baseline. A practical consequence is that under realistic sampling and noise conditions in optical imaging, the disparity map in stereo-rectified images can be computed for the majority of pixels (but only for those pixels with meaningful matches) with a $1/20$ pixel precision.
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N. Sabater, J.-M. Morel, A. Almansa. How Accurate Can Block Matches Be in Stereo Vision?. SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2011, 4 (1), pp.472-500. ⟨10.1137/100797849⟩. ⟨hal-00671759⟩

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