A variational shape optimization approach for image segmentation with the Mumford-Shah functional

G. DOGAN; PEDRO MORIN; R.H. NOCHETTO

SIAM JOURNAL ON SCIENTIFIC COMPUTING

Society for Industrial and Applied Mathematics

Año: 2008 vol. 30 p. 3028 - 3049

1064-8275

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 non-linear 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-to-fine 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