Approximations of the Mumford-Shah and Mumford-Shah-Euler Functionals for Unit Vector Fields

The Mumford-Shah and Mumford-Shah-Euler functionals were introduced in the seventies for grayscale image segmentation and inpainting, respectively. A sphere constraint is added to the minimisation and gradient flow problems of these functionals in order to apply them to colour image segmentation and inpainting in the Chromaticity & Brightness colour model. Approximations exactly observing the sphere constraint are compared to penalising ones