Abstract
Usual approaches for constructing topological maps on discrete structures are based on cellular complexes topology. This paper aims to construct a coherent topological map defined on a square grid from a watershed transformation. We propose a definition of well-composed grayscale images based on the well-composed set theory and the cross-section topology. Properties of two different thinning algorithms are studied within this scope, and we show how to obtain a thin crest network. We derive an efficient algorithm that permits the construction of a meaningful topological map. Finally, we demonstrate the usefulness of this algorithm for multilevel image segmentation.
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