A Topological Method of Surface Representation
A new method of representing a surface in the 3D space as a single digitally continuous sequence of faces is described. The method is based on topological properties of quasi-manifolds. It is realized as tracing the boundary of a growing set of labeled faces. As the result the surface is encoded as a single sequence of mutually adjacent faces. Each face is encoded by one byte. The code of the surface of a three-dimensional object takes much less memory space then the raster representation of the object. The object may be exactly reconstructed from the code. Surfaces of a genus greater that zero (e.g. that of a torus) may also be encoded by a single continuous sequence. The traversal algorithm recognizes the genus of the surface.
KeywordsAdjacent Pixel Euler Number Surface Representation Boundary Pixel Boundary Crack
- [GorUd89]Gordon, D., Udupa, J.K., Fast Surface Tracking in Three-Dimensional Binary Images, CVGIP, v. 45, pp. 196–214, 1989.Google Scholar
- [Kong92]T. Young Kong, „On Boundaries and Boundary Crack-Codes of Multidimensional Digital Images“, in „Shape in Picture“, Ying-Lie O et. all (Eds.), Springer-Verlag, 1992.Google Scholar
- [Kov92]Kovalevsky, V.A., “Finite Topology and Image Analysis”, In “Image Mathematics and Image Processing”, P. Hawkes(Ed.), „Advances in Electronics and Electron Physics“, v. 84, pp. 197–259, Academic Press 1992.Google Scholar
- [Kov93]Kovalevsky, V.A., “Digital Geometry Based on the Topology of Abstract Cell Complexes”, Proceedings of the Third International Colloquium “Discrete Geometry for Computer Imagery”, pp. 259–284, University of Strasbourg 1993.Google Scholar
- [Kov97]Kovalevsky, V.A., „Applications of Digital Straight Segments to Economical Image Encoding“, In: Ahronovitz, E. and Fiorio, C: (eds.), “Discrete Geometry for Computer Imagery”, Proceedings of the 7th International Workshop, DGCI’97, pp. 51–62, Springer 1997.Google Scholar