Threshold dynamics for the piecewise constant Mumford-Shah functional

Authors:
Selim Esedoglu;Yen-Hsi Richard Tsai
Affiliations:
Mathematics Department, University of California, Los Angeles, CA 90095-1555, United States;Mathematics Department, University of Texas, Austin, TX 78712, United States
Venue:
Journal of Computational Physics
Year:
2006

Citing 15
Cited 13

Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations

Journal of Computational Physics
Fast reaction, slow diffusion, and curve shortening

SIAM Journal on Applied Mathematics
Scale-Space and Edge Detection Using Anisotropic Diffusion

IEEE Transactions on Pattern Analysis and Machine Intelligence
Visual reconstruction with discontinuities using variational methods

Image and Vision Computing
Motion of multiple junctions: a level set approach

Journal of Computational Physics
Variational methods in image segmentation

Variational methods in image segmentation
A simple proof of convergence for an approximation scheme for computing motions by mean curvature

SIAM Journal on Numerical Analysis
A variational level set approach to multiphase motion

Journal of Computational Physics
Efficient algorithms for diffusion-generated motion by mean curvature

Journal of Computational Physics
A diffusion-generated approach to multiphase motion

Journal of Computational Physics
Convolution-generated motion and generalized Huygens' principles for interface motion

SIAM Journal on Applied Mathematics
Convolution—thresholding methods for interface motion

Journal of Computational Physics
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model

International Journal of Computer Vision
Discretization of Dirac delta functions in level set methods

Journal of Computational Physics
Active contours without edges

IEEE Transactions on Image Processing

Diffusion generated motion of curves on surfaces

Journal of Computational Physics
An Unconstrained Multiphase Thresholding Approach for Image Segmentation

SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Color image segmentation by the vector-valued Allen-Cahn phase-field model: a multigrid solution

IEEE Transactions on Image Processing
Piecewise constant level set method for 3D image segmentation

SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
A soft multiphase segmentation model via Gaussian mixture

ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
A boundary piecewise constant level set method for boundary control of eigenvalue optimization problems

Journal of Computational Physics
Environmentally robust motion detection for video surveillance

IEEE Transactions on Image Processing
A fast level set-like algorithm for region-based active contours

ISVC'10 Proceedings of the 6th international conference on Advances in visual computing - Volume Part III
A new framework of multiphase segmentation and its application to partial volume segmentation

Applied Computational Intelligence and Soft Computing
Unsupervised texture segmentation with nonparametric neighborhood statistics

ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
Statistical Density Estimation Using Threshold Dynamics for Geometric Motion

Journal of Scientific Computing
A new level set method for inhomogeneous image segmentation

Image and Vision Computing
Special Section on CAD/Graphics 2013: Multi-branched cerebrovascular segmentation based on phase-field and likelihood model

Computers and Graphics

Quantified Score

Hi-index	31.46

Visualization

Abstract

We propose an efficient algorithm for minimizing the piecewise constant Mumford-Shah functional of image segmentation. It is based on the threshold dynamics of Merriman, Bence, and Osher for evolving an interface by its mean curvature. We show that a very fast minimization can be achieved by alternating the solution of a linear parabolic partial differential equation and simple thresholding.