Visual reconstruction
Markov random field modeling in image analysis
Markov random field modeling in image analysis
Fast Approximate Energy Minimization via Graph Cuts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Pairwise Data Clustering by Deterministic Annealing
IEEE Transactions on Pattern Analysis and Machine Intelligence
Semidefinite programming for discrete optimization and matrix completion problems
Discrete Applied Mathematics
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
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
A Graph Cut Algorithm for Generalized Image Deconvolution
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Semidefinite Programming Heuristics for Surface Reconstruction Ambiguities
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part I
A structured learning approach to attributed graph embedding
SSPR&SPR'10 Proceedings of the 2010 joint IAPR international conference on Structural, syntactic, and statistical pattern recognition
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We propose a semidefinite relaxation technique for multiclass image labeling problems. In this context, we consider labeling as a special case of supervised classification with a predefined number of classes and known but arbitrary dissimilarities between each image element and each class. Using Markov random fields to model pairwise relationships, this leads to a global energy minimization problem. In order to handle its combinatorial complexity, we apply Lagrangian relaxation to derive a semidefinite program, which has several advantageous properties over alternative methods like graph cuts. In particular, there are no restrictions concerning the form of the pairwise interactions, which e.g. allows us to incorporate a basic shape concept into the energy function. Based on the solution matrix of our convex relaxation, a suboptimal solution of the original labeling problem can be easily computed. Statistical ground-truth experiments and several examples of multiclass image labeling and restoration problems show that high quality solutions are obtained with this technique.