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| Research article summary (published 29 Apr 2009): |
Low-rank matrix fitting based on subspace perturbation analysis with applications to structure from motion.
Full Abstract
The task of finding a low-rank (r) matrix that best fits an original data matrix of higher rank is a recurring problem in science and engineering. The problem becomes especially difficult when the original data matrix has some missing entries and contains an unknown additive noise term in the remaining elements. The former problem can be solved by concatenating a set of r-column matrices that share a common single r-dimensional solution space. Unfortunately, the number of possible submatrices is generally very large and, hence, the results obtained with one set of r-column matrices will generally be different from that captured by a different set. Ideally, we would like to find that solution that is least affected by noise. This requires that we determine which of the r-column matrices (i.e., which of the original feature points) are less influenced by the unknown noise term. This paper presents a criterion to successfully carry out such a selection. Our key result is to formally prove that the more distinct the r vectors of the r-column matrices are, the less they are swayed by noise. This key result is then combined with the use of a noise model to derive an upper bound for the effect that noise and occlusions have on each of the r-column matrices. It is shown how this criterion can be effectively used to recover the noise-free matrix of rank r. Finally, we derive the affine and projective structure-from-motion (SFM) algorithms using the proposed criterion. Extensive validation on synthetic and real data sets shows the superiority of the proposed approach over the state of the art.
Author information
Author/s: Jia, Hongjun (H); Martinez, Aleix M (AM);
Affiliation: Department of Electrical and Computer Engineering, The Ohio State University, 205 Dreese Lab, 2015 Neil Ave.,Columbus, OH 43210, USA. jia.22(-atsign-)osu.edu
Grants: DC 005241 (Agency:NIDCD NIH HHS)
Journal and publication information
Publication Type: Journal Article; Research Support, N.I.H., Extramural; Research Support, U.S. Gov't, Non-P.H.S.
Journal: IEEE transactions on pattern analysis and machine intelligence (IEEE Trans Pattern Anal Mach Intell), published in United States. (Language: eng)
Reference: 2009-May; vol 31 (issue 5) : pp 841-54
Dates: Created 2009/03/20; Completed 2009/06/10;
PMID: 19299859, status: MEDLINE (last retrieval date: 6/10/2009, IMS Date: 10 Jun 2009 00:00:00)
Sourced from the National Library of Medicine. Abstract text and other information may be subject to copyright.
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