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
"GrabCut": interactive foreground extraction using iterated graph cuts
ACM SIGGRAPH 2004 Papers
Image segmentation with context
SCIA'07 Proceedings of the 15th Scandinavian conference on Image analysis
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Normalized Cuts has successfully been applied to a wide range of tasks in computer vision, it is indisputably one of the most popular segmentation algorithms in use today. A number of extensions to this approach have also been proposed, ones that can deal with multiple classes or that can incorporate a priori information in the form of grouping constraints. It was recently shown how a general linearly constrained Normalized Cut problem can be solved. This was done by proving that strong duality holds for the Lagrangian relaxation of such problems. This provides a principled way to perform multi-class partitioning while enforcing any linear constraints exactly. The Lagrangian relaxation requires the maximization of the algebraically smallest eigenvalue over a one-dimensional matrix sub-space. This is an unconstrained, piece-wise differentiable and concave problem. In this paper we show how to solve this optimization efficiently even for very large-scale problems. The method has been tested on real data with convincing results.