A new approach to the maximum flow problem
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Fast Approximate Energy Minimization via Graph Cuts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Convex Optimization
"GrabCut": interactive foreground extraction using iterated graph cuts
ACM SIGGRAPH 2004 Papers
Efficient Minimization Methods of Mixed l2-l1 and l1-l1 Norms for Image Restoration
SIAM Journal on Scientific Computing
Random Walks for Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Closed-Form Solution to Natural Image Matting
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image and video matting: a survey
Foundations and Trends® in Computer Graphics and Vision
Graph Cuts via $\ell_1$ Norm Minimization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Concurrent number cruncher: an efficient sparse linear solver on the GPU
HPCC'07 Proceedings of the Third international conference on High Performance Computing and Communications
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Image matting and segmentation are two closely related topics that concern extracting the foreground and background of an image. While the methods based on global optimization are popular in both fields, the cost functions and the optimization methods have been developed independently due to the different interests of the fields: graph cuts optimize combinatorial functions yielding hard segments, and closedform matting minimizes quadratic functions yielding soft matte. In this paper, we note that these seemingly different costs can be represented in very similar convex forms, and suggest a generalized framework based on convex optimization, which reveals a new insight. For the optimization, a primal-dual interior point method is adopted. Under the new perspective, two novel formulations are presented showing how we can improve the state-of-the-art segmentation and matting methods. We believe that this will pave the way for more sophisticated formulations in the future.