Numerical approximations of the Mumford-Shah functional for unit vector fields. (English) Zbl 1238.49061
Summary: Two numerical approximation schemes for minimising the Mumford-Shah functional for unit vector fields are proposed, analyzed, and compared. The first uses a projection strategy, the second a penalization strategy to enforce the sphere constraint. Both schemes are then applied to the segmentation of colour images using the Chromaticity and Brightness colour model.
MSC:
49Q20 | Variational problems in a geometric measure-theoretic setting |
49M25 | Discrete approximations in optimal control |
49M30 | Other numerical methods in calculus of variations (MSC2010) |
94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |