Partitioning sparse matrices with eigenvectors of graphs
SIAM Journal on Matrix Analysis and Applications
Deflation Techniques for an Implicitly Restarted Arnoldi Iteration
SIAM Journal on Matrix Analysis and Applications
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
Contour and Texture Analysis for Image Segmentation
International Journal of Computer Vision
Segmentation Using Eigenvectors: A Unifying View
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Mean Shift Based Clustering in High Dimensions: A Texture Classification Example
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Segmentation Given Partial Grouping Constraints
IEEE Transactions on Pattern Analysis and Machine Intelligence
ACM SIGGRAPH 2004 Papers
"GrabCut": interactive foreground extraction using iterated graph cuts
ACM SIGGRAPH 2004 Papers
Spectral Segmentation with Multiscale Graph Decomposition
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Handbook of Mathematical Models in Computer Vision
Handbook of Mathematical Models in Computer Vision
Graph Cuts and Efficient N-D Image Segmentation
International Journal of Computer Vision
Graph transduction as a noncooperative game
Neural Computation
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In this paper, we propose a novel framework, called Dinkelbach NCUT (DNCUT), which efficiently solves the normalized graph cut (NCUT) problem under general, convex constraints, as well as, under given priors on the nodes of the graph. Current NCUT methods use generalized eigen-decomposition, which poses computational issues especially for large graphs, and can only handle linear equality constraints. By using an augmented graph and the iterative Dinkelbach method for fractional programming (FP), we formulate the DNCUT framework to efficiently solve the NCUT problem under general convex constraints and given data priors. In this framework, the initial problem is converted into a sequence of simpler sub-problems (i.e. convex, quadratic programs (QP's) subject to convex constraints). The complexity of finding a global solution for each sub-problem depends on the complexity of the constraints, the convexity of the cost function, and the chosen initialization. However, we derive an initialization, which guarantees that each sub-problem is a convex QP that can be solved by available convex programming techniques. We apply this framework to the special case of linear constraints, where the solution is obtained by solving a sequence of sparse linear systems using the conjugate gradient method. We validate DNCUT by performing binary segmentation on real images both with and without linear/nonlinear constraints, as well as, multi-class segmentation. When possible, we compare DNCUT to other NCUT methods, in terms of segmentation performance and computational efficiency. Even though the new formulation is applied to the problem of spectral graph-based, low-level image segmentation, it can be directly applied to other applications (e.g. clustering).