Hypergraph model of digital topology for grey level images
This paper gives a hypergraph based theoretical approach of digital topology. The study of digital topology is in connection with most image processing research. An application of hypergraph based digital topology to grey level images segmentation is presented.
The originality of this work comes from the introduction of a new topology concept based on hypergraphs but above all from the possibility to modelize grey level images as well as colored images.
The model is based on the fundamental Helly property of Hypergraphs. This paper introduces the Helly filter which gives to the neighborhood hypergraph associated with an image, the Helly property. As an application example, the model is successfully used to build a segmentation process.
KeywordsGrey Level Gravity Center Neighborhood Relation Grey Level Image Image Segmentation Technique
- Berge. Hypergraphes. Authier-Villard.Google Scholar
- P. Bertolino. Contribution des pyramides irrégulières en segmentation d'images. PhD thesis, INPG, 1995.Google Scholar
- A. Bretto and B. Laget. Neighborhood hypergraph and image analysis. In Signal processing II (Fontainebleau, France), pages 62–69, 1994.Google Scholar
- U. Eckhardt and L. Latecki. Digital topology. Research report, Univ. Hambourg, Dept. of Applied Math., 1989.Google Scholar
- Gondran and Minoux. Graphs and algorithms. Wiley — Introduction Series in Discrete Math. and Optimization.Google Scholar
- R.M. Haralick and L.G. Shapiro. Survey: Image segmentation technique. Computer Vision and Image Processing, (29):100–132, 1985.Google Scholar
- A. Montanvert, P. Meer, and P. Bertolino. Hierarchical shape analysis in grey level images. In NATO Advance Research Workshop Shape in Picture (The Netherlands), 1992.Google Scholar
- N.R. Pal and S.K. Pal. A review on image segmentation techniques. Pattern Recognition, 26(9):1277–1294, 1993.Google Scholar
- A. Rosenfeld and A. C. Kak. Digital Picture Processing. Academic Press, New-York, 1989.Google Scholar
- J. Serra. Image Analysis and Mathematical Morphology. Academy Press, 1982.Google Scholar
- J. Serra and L. Vincent. An overview of morphological filtering. circuits systems signal process, 11(1), 1992.Google Scholar
- S.W. Zucker. Survey region growing: Childhood and adolescence. Computer Vision, Graphics and Image Processing, (5):382–399, 1976.Google Scholar