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Bilinear Factorization via Augmented Lagrange Multipliers

  • Alessio Del Bue
  • João Xavier
  • Lourdes Agapito
  • Marco Paladini
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6314)

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.

Keywords

Constrain Optimization Problem Structure From Motion Photometric Stereo Augmented Lagrange Multiplier Manifold Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Supplementary material

978-3-642-15561-1_21_MOESM1_ESM.wmv (11.7 mb)
Electronic Supplementary Material (11,991 KB)

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Alessio Del Bue
    • 1
  • João Xavier
    • 2
  • Lourdes Agapito
    • 3
  • Marco Paladini
    • 3
  1. 1.Istituto Italiano di TecnologiaGenovaItaly
  2. 2.ISR - Istituto Superior TécnicoLisbonPortugal
  3. 3.Queen Mary University of LondonLondonUK

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