Bilinear factorization via augmented lagrange multipliers

Authors:
Alessio Del Bue;João Xavier;Lourdes Agapito;Marco Paladini
Affiliations:
Istituto Italiano di Tecnologia, Genova, Italy;ISR - Istituto Superior Técnico, Lisbon, Portugal;Queen Mary University of London, London, UK;Queen Mary University of London, London, UK
Venue:
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part IV
Year:
2010

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Abstract

This paper presents a unified approach to solve different bilinear factorization problems in Computer Vision in the presence of missing data in the measurements. The problem is formulated as a constrained optimization problem where one of the factors is constrained to lie on a specific manifold. To achieve this, we introduce an equivalent reformulation of the bilinear factorization problem. This reformulation decouples the core bilinear aspect from the manifold specificity. We then tackle the resulting constrained optimization problem with Bilinear factorization via Augmented Lagrange Multipliers (BALM). The mechanics of our algorithm are such that only a projector onto the manifold constraint is needed. That is the strength and the novelty of our approach: it can handle seamlessly different Computer Vision problems. We present experiments and results for two popular factorization problems: Non-rigid Structure from Motion and Photometric Stereo.