A Variational Shape Optimization Approach for Image Segmentation with a Mumford--Shah Functional

We introduce a novel computational method for a Mumford-Shah functional, which decomposes a given image into smooth regions separated by closed curves. Casting this as a shape optimization problem, we develop a gradient descent approach at the continuous level that yields nonlinear PDE flows. We propose time discretizations that linearize the problem, and space discretization by continuous piecewise linear finite elements. The method incorporates topological changes, such as splitting and merging for detection of multiple objects, space-time adaptivity and a coarse-tofine approach to process large images efficiently. We present several simulations that illustrate the performance of the method, and investigate the model sensitivity to various parameters. Key words. image segmentation, Mumford-Shah, shape optimization, finite element method AMS subject classifications. 49M15,49M25,65D15,65K10,68T45,90C99

• Type: Journal
• Year: 2008
• Where: SIAMSC
• Authors: Günay Dogan, Pedro Morin, Ricardo H. Nochetto
• Keywords: Shape Optimization, Shape Optimization Problem, SIAMSC 2008, Yields Nonlinear Pde