28 apr 2016 -- 15:00
sala riunioni, dipartimento di matematica di Pisa
The Mumford-Shah functional is one of the most studied variational approach to image processing and edge detection, proposed by Mumford and Shah in the late 80's. In the first part of the talk we present it, giving basic properties, known results and conjectures about that. Then, we focus on a suitable calibration technique for this functional, introduced by Alberti, Bouchitté and Dal Maso in 1999 and we show how it can be used to prove that some candidate functions are minimizers. Lastly we will deal with the opposite question: we ask if, given a minimizer, there always exists a calibration for it. We will state some partial results in this direction and some open problems.