This article explores the sub-pixel 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 shows first 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 sub-pixel 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 RMSE in stereo pairs with good SNR 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.
Sabater et al. REF considered theoretical limits of the disparity accuracy in the presence of pixel noise.
How Accurate Can Block Matches Be in Stereo Vision?
SIAM Journal on Imaging Sciences
SIAM Journal on Imaging Sciences
Mathematics Computer Science