Approximate Labeling via the Primal-Dual Schema

A linear programming based framework is presented which is capable of providing combinatorial-based approximation algorithms to a certain class of NP-complete classification problems. The resulting algorithms utilize tools from the duality theory of linear programming and have guaranteed optimality properties. Finally, it is shown that state-of-the-art classification techniques can be derived merely as a special case of the considered framework.

[1]  Frank Harary,et al.  Graph Theory , 2016 .

[2]  James A. McHugh,et al.  Algorithmic Graph Theory , 1986 .

[3]  Ingemar J. Cox,et al.  A maximum-flow formulation of the N-camera stereo correspondence problem , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[4]  Davi Geiger,et al.  Segmentation by grouping junctions , 1998, Proceedings. 1998 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No.98CB36231).

[5]  Olga Veksler,et al.  Markov random fields with efficient approximations , 1998, Proceedings. 1998 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No.98CB36231).

[6]  Olga Veksler,et al.  Fast approximate energy minimization via graph cuts , 2001, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[7]  R. Zabih,et al.  Efficient Graph-Based Energy Minimization Methods in Computer Vision , 1999 .

[8]  Éva Tardos,et al.  A constant factor approximation algorithm for a class of classification problems , 2000, STOC '00.

[9]  Marie-Pierre Jolly,et al.  Interactive graph cuts for optimal boundary & region segmentation of objects in N-D images , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[10]  Marie-Pierre Jolly,et al.  Interactive Graph Cuts for Optimal Boundary and Region Segmentation of Objects in N-D Images , 2001, ICCV.

[11]  Joseph Naor,et al.  Approximation algorithms for the metric labeling problem via a new linear programming formulation , 2001, SODA '01.

[12]  D. Scharstein,et al.  A Taxonomy and Evaluation of Dense Two-Frame Stereo Correspondence Algorithms , 2001, Proceedings IEEE Workshop on Stereo and Multi-Baseline Vision (SMBV 2001).

[13]  Vladimir Kolmogorov,et al.  Multi-camera Scene Reconstruction via Graph Cuts , 2002, ECCV.

[14]  Éva Tardos,et al.  Approximation algorithms for classification problems with pairwise relationships: metric labeling and Markov random fields , 2002, JACM.

[15]  Vijay V. Vazirani,et al.  Approximation Algorithms , 2001, Springer Berlin Heidelberg.

[16]  Vladimir Kolmogorov,et al.  Computing geodesics and minimal surfaces via graph cuts , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[17]  Vladimir Kolmogorov,et al.  Spatially coherent clustering using graph cuts , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

[18]  Vladimir Kolmogorov,et al.  What energy functions can be minimized via graph cuts? , 2002, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[19]  Robert Krauthgamer,et al.  Approximate classification via earthmover metrics , 2004, SODA '04.