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...
In [30], Kronrod proves that the connected components of isolevel sets of a continuous function can be endowed with a tree structure. Obviously, the connected components of upper level sets are an inclusion tree, and the same is true for connected components of lower level sets. We prove that in the case of semicontinuous functions, those trees can be merged into a single one, which, following its use in image processing, we call “tree of shapes”. This permits us to solve a classical representation...
In [CITE], Kronrod proves that the connected components of isolevel
sets of a continuous function can be endowed with a tree
structure. Obviously, the connected components of upper level sets are an
inclusion tree, and the same is true for connected components of lower level
sets. We prove that in the case of semicontinuous functions, those trees can
be merged into a single one, which, following its use in image processing, we
call “tree of shapes”. This permits us to solve a classical representation
problem...
Download Results (CSV)