How Accurate Can Block Matches Be in Stereo Vision?

Sabater, Neus; Morel, J.-M.; Almansa, Andrés

doi:10.1137/100797849

by Neus Sabater, J.-M. Morel, Andrés Almansa

Abstract:

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 ma jority of pixels (but only for those pixels with meaningful matches) with a 1/20 pixel precision.

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Reference:

How Accurate Can Block Matches Be in Stereo Vision? (Neus Sabater, J.-M. Morel, Andrés Almansa), In SIAM Journal on Imaging Sciences, volume 4, 2011.

Bibtex Entry:

@article{Sabater2011,
	Abstract = {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 ma jority of pixels (but only for those pixels with meaningful matches) with a 1/20 pixel precision.},
	Annote = {Code by Monasse {\&} Sabater available here
https://www.ipol.im/pub/art/2011/m{\_}qer/MissStereo.tar.gz},
	Author = {Sabater, Neus and Morel, J.-M. and Almansa, Andr{\'{e}}s},
	Doi = {10.1137/100797849},
	Issn = {1936-4954},
	Journal = {SIAM Journal on Imaging Sciences},
	Keywords = {block matching,noise error estimate,subpixel accuracy},
	Month = {jan},
	Number = {1},
	Pages = {472--500},
	Title = {{How Accurate Can Block Matches Be in Stereo Vision?}},
	Url = {http://hal-institut-telecom.archives-ouvertes.fr/hal-00671759},
	Volume = {4},
	Year = {2011},
	Bdsk-Url-1 = {http://hal-institut-telecom.archives-ouvertes.fr/hal-00671759},
	Bdsk-Url-2 = {https://doi.org/10.1137/100797849}}