NDLI: The generalized trace-norm and its application to structure-from-motion problems

Content Provider	IEEE Xplore Digital Library
Author	Angst, R. Zach, C. Pollefeys, M.
Copyright Year	2011
Description	Author affiliation: Computer Vision and Geometry Group, Eidgenössische Technische Hochschule Zürich, Switzerland (Angst, R.; Zach, C.; Pollefeys, M.)
Abstract	In geometric computer vision, the structure from motion (SfM) problem can be formulated as a optimization problem with a rank constraint. It is well known that the trace norm of a matrix can act as a convex proxy for a low rank constraint. Hence, in recent work [7], the trace-norm relaxation has been applied to the SfM problem. However, SfM problems often exhibit a certain structure, for example a smooth camera path. Unfortunately, the trace norm relaxation can not make use of this additional structure. This observation motivates the main contribution of this paper. We present the so-called generalized trace norm which allows to encode prior knowledge about a specific problem into a convex regularization term which enforces a low rank solution while at the same time taking the problem structure into account. While deriving the generalized trace norm and stating its different formulations, we draw interesting connections to other fields, most importantly to the field of compressive sensing. Even though the generalized trace norm is a very general concept with a wide area of potential applications we are ultimately interested in applying it to SfM problems. Therefore, we also present an efficient algorithm to optimize the resulting generalized trace norm regularized optimization problems. Results show that the generalized trace norm indeed achieves its goals in providing a problem-dependent regularization.
Starting Page	2502
Ending Page	2509
File Size	644846
Page Count	8
File Format	PDF
ISBN	9781457711015
ISSN	15505499
e-ISBN	9781457711022
DOI	10.1109/ICCV.2011.6126536
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-11-06
Publisher Place	Spain
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Transportation Vectors Computer vision Cost function Bayesian methods Covariance matrix
Content Type	Text
Resource Type	Article
Subject	Computer Vision and Pattern Recognition Software

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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