Incorporating constraints and prior knowledge into factorization algorithms - An application to 3D recovery

Amit Gruber*, Yair Weiss

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

Matrix factorization is a fundamental building block in many computer vision and machine learning algorithms. In this work we focus on the problem of "structure from motion" in which one wishes to recover the camera motion and the 3D coordinates of certain points given their 2D locations. This problem may be reduced to a low rank factorization problem. When all the 2D locations are known, singular value decomposition yields a least squares factorization of the measurements matrix. In realistic scenarios this assumption does not hold: some of the data is missing, the measurements have correlated noise, and the scene may contain multiple objects. Under these conditions, most existing factorization algorithms fail while human perception is relatively unchanged. In this work we present an EM algorithm for matrix factorization that takes advantage of prior information and imposes strict constraints on the resulting matrix factors. We present results on challenging sequences.

Original languageEnglish
Title of host publicationSubspace, Latent Structure and Feature Selection - Statistical and Optimization Perspectives Workshop, SLSFS 2005, Revised Selected Papers
Pages151-162
Number of pages12
DOIs
StatePublished - 2006
EventSubspace, Latent Structure and Feature Selection - Statistical and Optimization Perspectives Workshop, SLSFS 2005 - Bohinj, Slovenia
Duration: 23 Feb 200525 Feb 2005

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3940 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceSubspace, Latent Structure and Feature Selection - Statistical and Optimization Perspectives Workshop, SLSFS 2005
Country/TerritorySlovenia
CityBohinj
Period23/02/0525/02/05

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