NDLI: General and nested Wiberg minimization

Content Provider	IEEE Xplore Digital Library
Author	Strelow, D.
Copyright Year	2012
Description	Author affiliation: Google, Mountain View, CA (Strelow, D.)
Abstract	Wiberg matrix factorization breaks a matrix Y into low-rank factors U and V by solving for V in closed form given U, linearizing V (U) about U, and iteratively minimizing ‖Y-UV (U)‖2 with respect to U only. This approach factors the matrix while effectively removing V from the minimization. Recently Eriksson and van den Hengel extended this approach to L1, minimizing ‖Y-UV (U)‖1. We generalize their approach beyond factorization to minimize an arbitrary function that is nonlinear in each of two sets of variables. We demonstrate the idea with a practical Wiberg algorithm for L1 bundle adjustment. We also show that one Wiberg minimization can be nested inside another, effectively removing two of three sets of variables from a minimization. We demonstrate this idea with a nested Wiberg algorithm for L1 projective bundle adjustment, solving for camera matrices, points, and projective depths. We also revisit L1 factorization, giving a greatly simplified presentation of Wiberg L1 factorization, and presenting a successive linear programming factorization algorithm. Successive linear programming outperforms L1 Wiberg for most large inputs, establishing a new state-of-the-art for for those cases.
Starting Page	1584
Ending Page	1591
File Size	412964
Page Count	8
File Format	PDF
ISBN	9781467312264
ISSN	10636919
e-ISBN	9781467312288
e-ISBN	9781467312271
DOI	10.1109/CVPR.2012.6247850
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-06-16
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Minimization Linear programming Convergence Cameras Algorithm design and analysis Maximum likelihood estimation Programming
Content Type	Text
Resource Type	Article
Subject	Computer Vision and Pattern Recognition Software

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