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Shape-Tree Semilattice

  • Renato KeshetEmail author
Article

Abstract

A new, self-dual approach for morphological image processing, based on a semilattice framework, is introduced. The related morphological erosion, in particular, shrinks all ’objects‘ in an image, regardless to whether they are bright or dark.

The theory is first developed for the binary case, where it is closely related to the adjacency tree. Under certain constraints, it is shown to yield a lattice structure, which is complete for discrete images. It is then generalized to grayscale functions thanks to the tree of shapes, a recently introduced generalization of adjacency trees.

Keywords

mathematical morphology complete inf-semilattices self-dual tree of shapes separated sets disconnected sets 

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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.HP Labs—IsraelTechnion CityIsrael

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