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.