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.
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.},
Author = {Sabater, Neus and Morel, J.-M. and Almansa, Andr\'{e}s},
Date-Added = {2015-02-18 16:55:16 +0000},
Date-Modified = {2015-02-18 16:55:16 +0000},
Doi = {10.1137/100797849},
File = {:Users/almansa/Documents/Mendeley Desktop/PDFs/Sabater, Morel, Almansa - 2011 - How Accurate Can Block Matches Be in Stereo Vision.pdf:pdf},
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 = {http://dx.doi.org/10.1137/100797849}}