Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Weakly differentiable functions
Weakly differentiable functions
Variational methods in image segmentation
Variational methods in image segmentation
A variational level set approach to multiphase motion
Journal of Computational Physics
Primal-dual interior-point methods
Primal-dual interior-point methods
On the Topological Derivative in Shape Optimization
SIAM Journal on Control and Optimization
A PDE-based fast local level set method
Journal of Computational Physics
Shapes and geometries: analysis, differential calculus, and optimization
Shapes and geometries: analysis, differential calculus, and optimization
Clustering Algorithms
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)
Solving the Chan-Vese model by a multiphase level set algorithm based on the topological derivative
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
A new method for inverse electromagnetic casting problems based on the topological derivative
Journal of Computational Physics
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Topological sensitivity analysis is performed for the piecewise constant Mumford-Shah functional. Topological and shape derivatives are combined in order to derive an algorithm for image segmentation with fully automatized initialization. Segmentation of 2D and 3D data is presented. Further, a generalized Mumford-Shah functional is proposed and numerically investigated for the segmentation of images modulated due to, e.g., coil sensitivities.