*Title*: **Selection of the regularization parameter in the Ambrosio-Tortorelli approximation of the
Mumford-Shah functional for image segmentation**

*Abstract*: Image segmentation is a process to find the boundary sets of a given image.
In 1989, Mumford and Shah propose a functional whose minimization leads to optimal segmentation.
However, the Mumford-Shah functional is inconvenient to carry out in practical computation due to its lack in regularity.
Ambrosio and Tortorelli (1992) propose a phase-field regularization of the functional and show that it gamma-converges
to the original functional as the regularization parameter goes to zero. On the other hand, in actual computation,
people find that the regularization parameter has physical dimension and its choice can result in very different results.
Even worse, the functional is found not to gamma-converge to the Mumford-Shah functional in some cases.
In this talk we will present some theoretical explanations for this behavior.
Moreover, we will present a strategy for choosing the regularization parameter for better segmentation effects.
Numerical examples will be presented.

CAM Seminar Fall 2017 - Spring 2018