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Mechanical Engineering Commons

Open Access. Powered by Scholars. Published by Universities.®

2008

University of Pennsylvania

Mumford-Shah

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Full-Text Articles in Mechanical Engineering

A Variational Shape Optimization Approach For Image Segmentation With A Mumford-Shah Functional, Günay Doğam, Pedro Morin, Ricardo H. Nochetto Oct 2008

A Variational Shape Optimization Approach For Image Segmentation With A Mumford-Shah Functional, Günay Doğam, Pedro Morin, Ricardo H. Nochetto

Departmental Papers (MEAM)

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-to-fine approach to process large images efficiently. We present several simulations that illustrate the performance of the method ...