Singular sets of minimizers for the Mumford-Shah functional

by Guy David

"This book studies regularity properties of Mumford-Shah minimizers. The Mumford-Shah functional was introduced in the 1980s as a tool for automatic image segmentation, but its study gave rise to many questions of analysis and geometric measure theory. The main object under scrutiny is a free boundary K where the minimizer may have jumps. The book presents an extensive description of the known regularity properties of the singular sets K, and the techniques to get them." "The book is largely self-contained and should be accessible to graduate students in analysis. The core of the book is composed of regularity results that were proven in the last ten years and which are presented in a more detailed and unified way."--Jacket.