Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
An Eigendecomposition Approach to Weighted Graph Matching Problems
IEEE Transactions on Pattern Analysis and Machine Intelligence
A semidefinite framework for trust region subproblems with applications to large scale minimization
Mathematical Programming: Series A and B
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast Approximate Energy Minimization via Graph Cuts
IEEE Transactions on Pattern Analysis and Machine Intelligence
A New Matrix-Free Algorithm for the Large-Scale Trust-Region Subproblem
SIAM Journal on Optimization
Minimization of a Large-Scale Quadratic Function Subject to a Spherical Constraint
SIAM Journal on Optimization
A Spectral Bundle Method for Semidefinite Programming
SIAM Journal on Optimization
Segmentation Using Eigenvectors: A Unifying View
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Binary Partitioning, Perceptual Grouping, and Restoration with Semidefinite Programming
IEEE Transactions on Pattern Analysis and Machine Intelligence
What Energy Functions Can Be Minimizedvia Graph Cuts?
IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficient Graph-Based Image Segmentation
International Journal of Computer Vision
Convex Optimization
Shape Matching and Object Recognition Using Low Distortion Correspondences
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Graph Partitioning by Spectral Rounding: Applications in Image Segmentation and Clustering
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Image segmentation with context
SCIA'07 Proceedings of the 15th Scandinavian conference on Image analysis
Probabilistic subgraph matching based on convex relaxation
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
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In this paper, we introduce two new methods for solving binary quadratic problems. While spectral relaxation methods have been the workhorse subroutine for a wide variety of computer vision problems-segmentation, clustering, subgraph matching to name a few-it has recently been challenged by semidefinite programming (SDP) relaxations. In fact, it can be shown that SDP relaxations produce better lower bounds than spectral relaxations on binary problems with a quadratic objective function. On the other hand, the computational complexity for SDP increases rapidly as the number of decision variables grows making them inapplicable to large scale problems. Our methods combine the merits of both spectral and SDP relaxations-better (lower) bounds than traditional spectral methods and considerably faster execution times than SDP. The first method is based on spectral subgradients and can be applied to large scale SDPs with binary decision variables and the second one is based on the trust region problem. Both algorithms have been applied to several large scale vision problems with good performance.