Morphological algorithms based on Voronoi and Delaunay graphs: microscopic and medical applications

Etienne Bertin; Raphael Marcelpoil; Jean-Marc Chassery

doi:10.1117/12.60655

1 June 1992 Morphological algorithms based on Voronoi and Delaunay graphs: microscopic and medical applications

Etienne Bertin, Raphael Marcelpoil, Jean-Marc Chassery

Proceedings Volume 1769, Image Algebra and Morphological Image Processing III; (1992) https://doi.org/10.1117/12.60655
Event: San Diego '92, 1992, San Diego, CA, United States

Abstract

We illustrate a cooperation between Voronoi diagram and Mathematical Morphology in 2-D and 3-D. Domains of application are multiple: 2-D image segmentation, and 3-D image representation, cellular sociology in 2-D and 3-D. The principal tool that we use is the algorithm of research of connected components in a graph abiding by constraints. The originality takes place in the choice of the constraint parameters. Other tools are used: binary dilation, labeling, and influence zone on graphs. The graph support of our work is the Voronoi diagram, well known for its power of modelling for natural reality. The dual graph of this space partition is the Delaunay graph containing all the neighboring information. The first developed application concerns a method for 2-D and 3-D images segmentation. We have elaborated tools to measure intra-graph structures distance, search of connected component under constraints to extract a 3-d object included in a volume data. The second application we developed concerns the theory of cellular sociology where the set of points identified the location of cells. Our method makes it possible to determine for a given set of cells, a model including its nearest homogeneous set, and the intrinsic disorder to which it refers. In this paper, our methods will be discussed and illustrated in the biological domain.

Citation Download Citation

Etienne Bertin, Raphael Marcelpoil, and Jean-Marc Chassery "Morphological algorithms based on Voronoi and Delaunay graphs: microscopic and medical applications", Proc. SPIE 1769, Image Algebra and Morphological Image Processing III, (1 June 1992); https://doi.org/10.1117/12.60655

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