This chapter presents an overview of the Mumford and Shah model for image segmentation. It discusses its various formulations, some of its properties, the mathematical framework, and several approximations. It also presents numerical algorithms and segmentation results using the Ambrosio-Tortorelli phase-field approximations on one hand and level set formulations on the other hand. Several applications of the Mumford-Shah problem to image restoration are also presented.
|Title of host publication||Handbook of Mathematical Methods in Imaging|
|Subtitle of host publication||Volume 1, Second Edition|
|Publisher||Springer New York|
|Number of pages||59|
|State||Published - 1 Jan 2015|