Perturbation Estimation of the Subspaces for Structure from Motion with Noisy and Missing Data

Jia, Hongjun; Fortuna, J.; Martı́nez, Aleix M.

doi:10.1109/3dpvt.2006.106

Cited by 5 publications

(3 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is an extension of our preliminary work presented in [17]. In Section IV, we show how the derived algorithm can be efficiently used to resolve the problems of noise and missing data in affine and projective SFM.…”

mentioning

confidence: 75%

Low-Rank Matrix Fitting Based on Subspace Perturbation Analysis with Applications to Structure from Motion

Jia

Martı́nez

2009

IEEE Trans. Pattern Anal. Mach. Intell.

View full text Add to dashboard Cite

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 which 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 which 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 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.

show abstract

mentioning

confidence: 75%

Low-Rank Matrix Fitting Based on Subspace Perturbation Analysis with Applications to Structure from Motion

Jia

Martı́nez

2009

IEEE Trans. Pattern Anal. Mach. Intell.

View full text Add to dashboard Cite

show abstract

“…In Ref. [13], Jia et al present an algorithm that aims the SFM recovery with noisy and missing data. It is similar to the aforementioned one [12], but instead of selecting several r-tuple of columns, it uses the most reliable sub-matrix to recover the 3D structure.…”

Section: Related Workmentioning

confidence: 99%

An iterative multiresolution scheme for SFM with missing data: Single and multiple object scenes

Julií¹,

Sappa

Lumbreras

et al. 2010

Image and Vision Computing

View full text Add to dashboard Cite

“…Then, other columns and rows are projected on it using an imputation method. In [16], Jia et al present an algorithm that aims the SFM recovery with noisy and missing data. It is similar to the aforementioned one [15], but instead of selecting several r-tuple of columns, it uses the most reliable sub-matrix to recover the 3D structure.…”

Section: Related Workmentioning

confidence: 99%

An Iterative Multiresolution Scheme for SFM with Missing Data

Julià¹,

Sappa²,

Lumbreras³

et al. 2009

J Math Imaging Vis

View full text Add to dashboard Cite

Several techniques have been proposed for tackling the Structure from Motion problem through factorization in the case of missing data. However, when the percentage of unknown data is high, most of them may not perform as well as expected. Focussing on this problem, an iterative multiresolution scheme, which aims at recovering missing entries in the originally given input matrix, is proposed. Information recovered following a coarse-to-fine strategy is used for filling in the missing entries. The objective is to recover, as much as possible, missing data in the given matrix. Thus, when a factorization technique is applied to the partially or totally filled in matrix, instead of to the originally given input one, better results will be obtained. An evaluation study about the robustness to missing and noisy data is reported. Experimental results obtained with synthetic and

show abstract

Perturbation Estimation of the Subspaces for Structure from Motion with Noisy and Missing Data

Abstract: It is common when analyzing experimental data to encounter

Cited by 5 publications

References 10 publications

Low-Rank Matrix Fitting Based on Subspace Perturbation Analysis with Applications to Structure from Motion

Low-Rank Matrix Fitting Based on Subspace Perturbation Analysis with Applications to Structure from Motion

An iterative multiresolution scheme for SFM with missing data: Single and multiple object scenes

An Iterative Multiresolution Scheme for SFM with Missing Data

Contact Info

Product

Resources

About