Bilinear Factorization via Augmented Lagrange Multipliers
| Autor: | Marco Paladini, Joao Xavier, Lourdes Agapito, Alessio Del Bue |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2010 |
| Předmět: |
Mathematical optimization
021103 operations research ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION 0211 other engineering and technologies Bilinear interpolation 02 engineering and technology Manifold Algebra Constraint algorithm symbols.namesake Photometric stereo Factorization Lagrange multiplier 0202 electrical engineering electronic engineering information engineering symbols Structure from motion 020201 artificial intelligence & image processing System of bilinear equations Mathematics |
| Zdroj: | Lecture Notes in Computer Science Computer Vision – ECCV 2010 ISBN: 9783642155604 ECCV (4) |
| ISSN: | 0302-9743 |
| DOI: | 10.1007/978-3-642-15561-1_21 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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