Visual reconstruction
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Fast Approximate Energy Minimization via Graph Cuts
IEEE Transactions on Pattern Analysis and Machine Intelligence
A level set algorithm for minimizing the Mumford-Shah functional in image processing
VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)
Computing Geodesics and Minimal Surfaces via Graph Cuts
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
What Energy Functions Can Be Minimizedvia Graph Cuts?
IEEE Transactions on Pattern Analysis and Machine Intelligence
"GrabCut": interactive foreground extraction using iterated graph cuts
ACM SIGGRAPH 2004 Papers
An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast Global Minimization of the Active Contour/Snake Model
Journal of Mathematical Imaging and Vision
Graph cut optimization for the Mumford-Shah model
VIIP '07 The Seventh IASTED International Conference on Visualization, Imaging and Image Processing
Discrete regularization on weighted graphs for image and mesh filtering
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
An integral solution to surface evolution PDEs via geo-cuts
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part III
Efficient and reliable schemes for nonlinear diffusion filtering
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
A Fast Anisotropic Mumford-Shah Functional Based Segmentation
IbPRIA '09 Proceedings of the 4th Iberian Conference on Pattern Recognition and Image Analysis
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
Computer Vision and Image Understanding
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Active contour formulations predominate current minimization of the Mumford-Shah functional (MSF) for image segmentation and filtering. Unfortunately, these formulations necessitate optimization of the contour by evolving via gradient descent, which is known for its sensitivity to initialization and the tendency to produce undesirable local minima. In order to reduce these problems, we reformulate the corresponding MSF on an arbitrary graph and apply combinatorial optimization to produce a fast, low-energy solution. The solution provided by this graph formulation is compared with the solution computed via traditional narrow-band level set methods. This comparison demonstrates that our graph formulation and optimization produces lower energy solutions than gradient descent based contour evolution methods in significantly less time. Finally, by avoiding evolution of the contour via gradient descent, we demonstrate that our optimization of the MSF is capable of evolving the contour with non-local movement.