Topological Operators on the Topological Graph of Frontiers
The Topological Graph of Frontiers is in our opinion a good graph structure representing the topology of segmented images. In this paper we deal with topological operators which achieve directly on the graph current operations performed on segmented images.
Well known graph structures such as the Region Adjacency Graph [Pav77] [Ros74] do not (and cannot) keep track of the topology and so cannot maintain it. We claim that the structures and operators described here, on the contrary, allow and do this maintenance. One of the most important informations in such images is the inclusion of nested regions and one of the most important operators is the union of regions. We deal essentially with these in this paper. They are described in detail herein and we show how the topological coherence is maintained. This is why we entitle them topological operators. Other operators that we have already developed are briefly described.
Keywordstopological operator enclosed region topological graph of frontiers topological representation segmented image manipulation
- AAF95.E. Ahronovitz, J.-P. Aubert, and C. Fiorio. The star-topology: a topology for image analysis. In 5 th Discrete Geometry for Computer Imagery, Proceedings, pages 107–116. Groupe GDR PRC/AMI du CNRS, september 1995.Google Scholar
- Edm60.J. Edmonds. A combinatorial representation for polyhedral surfaces. Notices of the American Mathematical Society, 7, 1960.Google Scholar
- Fio95.C. Fiorio. Approche interpixel en analyse d’images: une topologie et des algorithmes de segmentation. Thése de doctorat, Université Montpellier II, 24 novembre 1995.Google Scholar
- Fio96.C. Fiorio. A topologically consistent representation for image analysis: the frontiers topological graph. In S. Ubeda S. Miguet, A. Montanvert, editor, 6th International Workshop, DGCI’96, number 1176 in Lecture Notes in Computer Sciences, pages 151–162, Lyon, France, November 1996.Google Scholar
- Gla98.S. Glaize. Manipulations topologiques et opérations sur les graphes topologiques des frontières. Technical Report 98122, Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier, 161, rue Ada-F-34392 Montpellier Cedex 5, november 1998.Google Scholar
- KM95.W. Kropatsch and H. Macho. Finding the structure of connected components using dual irregular pyramids. In 5 th Discrete Geometry for Computer Imagery, Proceedings, pages 147–158. Groupe GDR PRC/AMI du CNRS, september 1995.Google Scholar
- Kov89.V.A. Kovalevsky. Finite topology as applied to image analysis. 46:141–161, 1989.Google Scholar
- Lie89.P. Lienhardt. Subdivision of n-dimensional spaces and n-dimensional generalized maps. In 5 th Annual ACM Symposium on Computational Geometry, pages 228–236, Saarbrücken, Germany, 1989.Google Scholar