Resumen de The M-components of level sets of continuous functions in WBV

Coloma Ballester Nicolau , Vicent Caselles Costa

• We prove that the topographic map structure of upper semicontinuous functions, defined in terms of classical connected components of its level sets, and of functions of bounded variation (or a generalization, the WBV functions), defined in terms of M-connected components of its level sets, coincides when the function is a continuous function in WBV. Both function spaces are frequently used as models for images. Thus, if the domain O' of the image is Jordan domain, a rectangle, for instance, and the image u Î C(O') n WBV(O) (being constant near ?O), we prove that for almost all levels ? of u, the classical connected components of positive measure of [u = ?] coincide with the M-components of[ u = ?]. Thus the notion of M-component can be seen as a relaxation ofthe classical notion of connected component when going from C(O') to WBV(O).