Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Using Dynamic Programming for Solving Variational Problems in Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
The robust estimation of multiple motions: parametric and piecewise-smooth flow fields
Computer Vision and Image Understanding
Image Sequence Analysis via Partial Differential Equations
Journal of Mathematical Imaging and Vision
A Theoretical Framework for Convex Regularizers in PDE-Based Computation of Image Motion
International Journal of Computer Vision
Diffusion Snakes: Introducing Statistical Shape Knowledge into the Mumford-Shah Functional
International Journal of Computer Vision
Computing Geodesics and Minimal Surfaces via Graph Cuts
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics
Foundations of Computational Mathematics
What Metrics Can Be Approximated by Geo-Cuts, Or Global Optimization of Length/Area and Flux
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Conformal Metrics and True "Gradient Flows" for Curves
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Globally Minimal Surfaces by Continuous Maximal Flows
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Image Processing
Graph Cuts and Efficient N-D Image Segmentation
International Journal of Computer Vision
ACM SIGGRAPH 2007 papers
Topology cuts: A novel min-cut/max-flow algorithm for topology preserving segmentation in N-D images
Computer Vision and Image Understanding
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part I
On Total Variation Minimization and Surface Evolution Using Parametric Maximum Flows
International Journal of Computer Vision
Efficient Global Minimization for the Multiphase Chan-Vese Model of Image Segmentation
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Graph cut optimization for the Mumford-Shah model
VIIP '07 The Seventh IASTED International Conference on Visualization, Imaging and Image Processing
The piecewise smooth Mumford-Shah functional on an arbitrary graph
IEEE Transactions on Image Processing
Finsler tractography for white matter connectivity analysis of the cingulum bundle
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention - Volume Part I
Global Minimization for Continuous Multiphase Partitioning Problems Using a Dual Approach
International Journal of Computer Vision
A survey of graph theoretical approaches to image segmentation
Pattern Recognition
Segmentation with non-linear regional constraints via line-search cuts
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part I
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We introduce a new approach to modelling gradient flows of contours and surfaces. While standard variational methods (e.g. level sets) compute local interface motion in a differential fashion by estimating local contour velocity via energy derivatives, we propose to solve surface evolution PDEs by explicitly estimating integral motion of the whole surface. We formulate an optimization problem directly based on an integral characterization of gradient flow as an infinitesimal move of the (whole) surface giving the largest energy decrease among all moves of equal size. We show that this problem can be efficiently solved using recent advances in algorithms for global hypersurface optimization [4,2,11]. In particular, we employ the geo-cuts method [4] that uses ideas from integral geometry to represent continuous surfaces as cuts on discrete graphs. The resulting interface evolution algorithm is validated on some 2D and 3D examples similar to typical demonstrations of level-set methods. Our method can compute gradient flows of hypersurfaces with respect to a fairly general class of continuous functionals and it is flexible with respect to distance metrics on the space of contours/surfaces. Preliminary tests for standard L2 distance metric demonstrate numerical stability, topological changes and an absence of any oscillatory motion.