Contains and inside relationships within combinatorial pyramids

Hierarchical Watersheds Within the Combinatorial Pyramid Framework

Watershed is one of the most popular tool defined by mathematical morphology. The algorithms which implement the watershed transform generally produce an over segmentation which includes the right image’s boundaries. Based on this last assumption, the segmentation problem turns out to be equivalent to a proper valuation of the saliency of each contour. Using such a measure, hierarchical watersh...

Inside and Outside Within Combinatorial Pyramids

Construction of Combinatorial Pyramids

Irregular pyramids are made of a stack of successively reduced graphs embedded in the plane. Each vertex of a reduced graph corresponds to a connected set of vertices in the level below. One connected set of vertices reduced into a single vertex at the above level is called the reduction window of this vertex. In the same way, a connected set of vertices in the base level graph reduced to a sin...

A First Step toward Combinatorial Pyramids in n-D Spaces

Combinatorial maps define a general framework which allows to encode any subdivision of an nD orientable quasi-manifold with or without boundaries. Combinatorial pyramids are defined as stacks of successively reduced combinatorial maps. Such pyramids provide a rich framework which allows to encode fine properties of the objects (either shapes or partitions). Combinatorial pyramids have first be...

Connecing Walks and Connecting Dart Sequences for N-d Combinatorial Pyramids Connecting Walks and Connecting Dart Sequences for N-d Combinatorial Pyramids

Combinatorial maps define a general framework which allows to encode any subdivision of an n-D orientable quasi-manifold with or without boundaries. Combinatorial pyramids are defined as stacks of successively reduced combinatorial maps. Such pyramids provide a rich framework which allows to encode fine properties of objects (either shapes or partitions). Combinatorial pyramids have first been ...