Numerical approximations of the Mumford-Shah functional for unit vector fields

Abstract

Two numerical approximation schemes for minimising the Mumford-Shah functional for unit vector fields are proposed, analysed, and compared. The first uses a projection strategy, the second a penalisation strategy to enforce the sphere constraint. Both schemes are then applied to the segmentation of colour images using the Chromaticity and Brightness colour model. © European Mathematical Society 2011.