Visual reconstruction
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Motion of multiple junctions: a level set approach
Journal of Computational Physics
SIAM Journal on Applied Mathematics
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
A variational level set approach to multiphase motion
Journal of Computational Physics
Matrix computations (3rd ed.)
Fast Approximate Energy Minimization via Graph Cuts
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
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
Journal of Mathematical Imaging and Vision
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Space-variant computer vision: a graph-theoretic approach
Space-variant computer vision: a graph-theoretic approach
"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
Optimal Surface Segmentation in Volumetric Images-A Graph-Theoretic Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Mumford-Shah level-set approach for the inversion and segmentation of X-ray tomography data
Journal of Computational Physics
International Journal of Computer Vision
Fast Global Minimization of the Active Contour/Snake Model
Journal of Mathematical Imaging and Vision
Mumford–Shah based registration: a comparison of a level set and a phase field approach
Computing and Visualization in Science
International Journal of Computer Vision
Graph cut optimization for the Mumford-Shah model
VIIP '07 The Seventh IASTED International Conference on Visualization, Imaging and Image Processing
A note on the discrete binary Mumford-Shah model
MIRAGE'07 Proceedings of the 3rd international conference on Computer vision/computer graphics collaboration techniques
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
On the statistical interpretation of the piecewise smooth Mumford-Shah functional
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Efficient segmentation of piecewise smooth images
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Γ-convergence approximation to piecewise smooth medical image segmentation
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention
Faster graph-theoretic image processing via small-world and quadtree topologies
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
An integral solution to surface evolution PDEs via geo-cuts
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part III
A comparative study of energy minimization methods for markov random fields
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
Efficient and reliable schemes for nonlinear diffusion filtering
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Mumford–Shah Model for One-to-One Edge Matching
IEEE Transactions on Image Processing
Nonlocal Discrete Regularization on Weighted Graphs: A Framework for Image and Manifold Processing
IEEE Transactions on Image Processing
Integrating local distribution information with level set for boundary extraction
Journal of Visual Communication and Image Representation
A graph-based framework for sub-pixel image segmentation
Theoretical Computer Science
Discrete optimization of the multiphase piecewise constant mumford-shah functional
EMMCVPR'11 Proceedings of the 8th international conference on Energy minimization methods in computer vision and pattern recognition
A framework for intrinsic image processing on surfaces
Computer Vision and Image Understanding
Combinatorial Continuous Maximum Flow
SIAM Journal on Imaging Sciences
Automatic segmentation of unknown objects, with application to baggage security
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part II
Luggage visualization and virtual unpacking
Proceedings of the Workshop at SIGGRAPH Asia
Detecting, segmenting and tracking unknown objects using multi-label MRF inference
Computer Vision and Image Understanding
Iterative Graph Cuts for Image Segmentation with a Nonlinear Statistical Shape Prior
Journal of Mathematical Imaging and Vision
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The Mumford-Shah functional has had a major impact on a variety of image analysis problems, including image segmentation and filtering, and, despite being introduced over two decades ago, it is still in widespread use. Present day optimization of the Mumford-Shah functional is predominated by active contour methods. Until recently, these formulations necessitated optimization of the contour by evolving via gradient descent, which is known for its overdependence on initialization and the tendency to produce undesirable local minima. In order to reduce these problems, we reformulate the corresponding Mumford-Shah functional on an arbitrary graph and apply the techniques of combinatorial optimization to produce a fast, low-energy solution. In contrast to traditional optimization methods, use of these combinatorial techniques necessitates consideration of the reconstructed image outside of its usual boundary, requiring additionally the inclusion of regularization for generating these values. The energy of the solution provided by this graph formulation is compared with the energy of the solution computed via traditional gradient descent-based narrow-band level set methods. This comparison demonstrates that our graph formulation and optimization produces lower energy solutions than the traditional gradient descent based contour evolution methods in significantly less time. Finally, we demonstrate the usefulness of the graph formulation to apply the Mumford-Shah functional to new applications such as point clustering and filtering of nonuniformly sampled images.