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Computing rigorous bounds to the accuracy of calibrated stereo reconstruction

Fusiello, A. and Farenzena, A. and Busti, A. and Benedetti, A. (2005) Computing rigorous bounds to the accuracy of calibrated stereo reconstruction. IEE Proccedings Vision, Image and Signal Processing, 152 (6). pp. 695-701. ISSN 1350-245X . http://resolver.caltech.edu/CaltechAUTHORS:20110817-085833696

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Abstract

The authors deal with the problem of computing rigorous bounds on the position of 3D points obtained by stereo triangulation when both the camera matrix and the coordinates of image points are affected by measurement errors. By 'rigorous bounds' it is meant that the true unknown 3D points are guaranteed to lie within the intervals computed by the method, with mathematical certainty. To this end, the calibration process is first modelled by assuming a bounded error in the localisation of the reference points in the image, then narrow intervals are computed for the entries of the camera matrix using numerical methods based on interval analysis. Finally, triangulation is applied to obtain cuboids that bound point coordinates. Two state-of-the-art methods were employed for the solution of linear systems of interval equations, namely Rump's and Shary's methods. It is concluded that a careful selection of numerical techniques allows the use of interval analysis as a tool for obtaining realistic bounds on the output error, even in the presence of significant errors in the input data.


Item Type:Article
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http://dx.doi.org/10.1049/ip-vis:20041054 DOIUNSPECIFIED
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1520853PublisherUNSPECIFIED
Additional Information:© 2005 IEE. Paper first received 8th September 2003 and in revised form 30th July 2004. Date of Current Version: 24 October 2005. IEE Proceedings online no. 20041054. The authors are grateful to S.P. Shary for providing the implementation of his linear systems solver. The use of the INTLAB toolbox for MATLAB by S.M. Rump is here acknowledged.
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INSPEC Accession Number8625628
Record Number:CaltechAUTHORS:20110817-085833696
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20110817-085833696
Official Citation:Computing rigorous bounds to the accuracy of calibrated stereo reconstruction [computer vision applications] Fusiello, A. Farenzena, M. Busti, A. Benedetti, A. Page(s): 695 - 701 Digital Object Identifier : 10.1049/ip-vis:20041054
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:24903
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:17 Aug 2011 16:20
Last Modified:17 Aug 2011 16:20

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