Título inglés |
The M-components of level sets of continuous functions in WBV. |
Título español |
Los M-componentes de conjuntos de nivel de funciones continuas en WBV. |
Autor/es |
Ballester, Coloma ; Caselles, Vicent |
Organización |
Dep. Tecnol. Univ. Pompeu-Fabra, Barcelona, España |
Revista |
0214-1493 |
Publicación |
2001, 45 (2): 477-527, 48 Ref. |
Tipo de documento |
articulo |
Idioma |
Inglés |
Resumen inglés |
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 Ω' of the image is Jordan domain, a rectangle, for instance, and the image u Î C(Ω') ∩ WBV(Ω) (being constant near ∂Ω), we prove that for almost all levels λ of u, the classical connected components of positive measure of [u ≥ λ] coincide with the M-components
of[ u ≥ λ]. Thus the notion of M-component can be seen as a relaxation ofthe classical notion of connected component when going from C(Ω') to WBV(Ω). |
Clasificación UNESCO |
120210 ; 121005 |
Palabras clave español |
Teoría de la medida ; Funciones de variación acotada ; Funciones de variable real ; Funciones continuas ; Mapa topográfico ; Teoría de Morse |
Código MathReviews |
MR1876918 |
Acceso al artículo completo |