Displaying similar documents to “On the equivalence of certain coincidence theorems and fixed point theorems”

The tree of shapes of an image

Coloma Ballester, Vicent Caselles, P. Monasse (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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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...

The tree of shapes of an image

Coloma Ballester, Vicent Caselles, P. Monasse (2003)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

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...