Visual reconstruction
Variational methods in image segmentation
Variational methods in image segmentation
SIAM Journal on Applied Mathematics
Minimal Surfaces Based Object Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Global Minimum for Active Contour Models: A Minimal Path Approach
International Journal of Computer Vision
The fast construction of extension velocities in level set methods
Journal of Computational Physics
SIAM Review
Shapes and geometries: analysis, differential calculus, and optimization
Shapes and geometries: analysis, differential calculus, and optimization
Fast computation of weighted distance functions and geodesics on implicit hyper-surfaces: 730
Journal of Computational Physics
Rapid and accurate computation of the distance function using grids
Journal of Computational Physics
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
Topology Design of Structures, Materials and Mechanisms - Status and Perspectives
Proceedings of the 19th IFIP TC7 Conference on System Modelling and Optimization: Methods, Theory and Applications
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Incorporating topological derivatives into level set methods
Journal of Computational Physics
Signal segmentation and denoising algorithm based on energy optimisation
Signal Processing
A Mumford-Shah level-set approach for the inversion and segmentation of X-ray tomography data
Journal of Computational Physics
A nonlinear variational method for signal segmentation and reconstruction using level set algorithm
Signal Processing - Special section: Distributed source coding
International Journal of Computer Vision
Algorithmic Differentiation: Application to Variational Problems in Computer Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
An Active Contour Approach for a Mumford-Shah Model in X-Ray Tomography
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part II
The piecewise smooth Mumford-Shah functional on an arbitrary graph
IEEE Transactions on Image Processing
A Mumford-Shah-Like Method for Limited Data Tomography with an Application to Electron Tomography
SIAM Journal on Imaging Sciences
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The problem of segmentation of a given gray scale image by minimization of the Mumford-Shah functional is considered. The minimization problem is formulated as a shape optimization problem where the contour which separates homogeneous regions is the (geometric) optimization variable. Expressions for first and second order shape sensitivities are derived using the speed method from classical shape sensitivity calculus. Second order information (the shape Hessian of the cost functional) is used to set up a Newton-type algorithm, where a preconditioning operator is applied to the gradient direction to obtain a better descent direction. The issue of positive definiteness of the shape Hessian is addressed in a heuristic way. It is suggested to use a positive definite approximation of the shape Hessian as a preconditioner for the gradient direction. The descent vector field is used as speed vector field in the level set formulation for the propagating contour. The implementation of the algorithm is discussed in some detail. Numerical experiments comparing gradient and Newton-type flows for different images are presented.