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This paper defines the basis of a new hierarchical framework for segmentationalgorithms based on energy minimization schemes. This new framework is based ontwo formal tools. First, a combinatorial pyramid encode efficiently a hierarchyof partitions. Secondly, discrete geometric estimators measure precisely someimportant geometric parameters of the regions. These measures combined withphotometrical and topological features of the partition allows to design energyterms based on discrete measures. Our segmentation framework exploits theseenergies to build a pyramid of image partitions with a minimization scheme.Some experiments illustrating our framework are shown and discussed.

Combinatorial pyramids and discrete geometry for energy-minimizing segmentation