The study of segmentation problems, i.e., variational problems where the unknown is a piecewise-constant function, allows the introduction of a new type of weak convergence, related to the weak* convergence of measures, and the corresponding variational concepts. In particular, lower semicontinuity of segmentation functionals is proved to be equivalent to sub-additivity of integrands. Correspondingly, the notions of relaxation and Gamma-convergence can be expressed through suitable sub-additive envelopes. The theory of Caccioppoli partitions in higher dimension is outlined.
Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.
If you think you should have access to this title, please contact your librarian.