Paper Info
Title
GPCA with denoising: A moments-based convex approach
Abstract
This paper addresses the problem of segmenting a combination of linear subspaces and quadratic surfaces from sample data points corrupted by (not necessarily small) noise. Our main result shows that this problem can be reduced to minimizing the rank of a matrix whose entries are affine in the optimization variables, subject to a convex constraint imposing that these variables are the moments of an (unknown) probability distribution function with finite support. Exploiting the linear matrix inequality based characterization of the moments problem and appealing to well known convex relaxations of rank leads to an overall semi-definite optimization problem. We apply our method to problems such as simultaneous 2D motion segmentation and motion segmentation from two perspective views and illustrate that our formulation substantially reduces the noise sensitivity of existing approaches.
Year
DOI
Venue
2010
10.1109/CVPR.2010.5540075
Computer Vision and Pattern Recognition
Keywords
Field
DocType
convex programming,image denoising,image motion analysis,image segmentation,linear matrix inequalities,principal component analysis,2D motion segmentation,GPCA,convex constraint,generalized principal component analysis,linear matrix inequality,linear subspaces,moments problem,probability distribution function,quadratic surfaces,semidefinite optimization problem
Affine transformation,Rank (linear algebra),Computer science,Convex combination,Artificial intelligence,Optimization problem,Linear matrix inequality,Kernel (linear algebra),Mathematical optimization,Pattern recognition,Algorithm,Convex optimization,Constrained optimization
Conference
Volume
Issue
ISSN
2010
1
1063-6919
ISBN
Citations 
PageRank 
978-1-4244-6984-0
7
0.68
References 
Authors
14
4
Name
Order
Citations
PageRank
Necmiye Ozay139041.51
Mario Sznaier265656.66
Constantino M. Lagoa316425.38
Octavia I. Camps463143.56