# A Topological Method of Surface Representation

Conference paper

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## Abstract

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.

## Keywords

Adjacent Pixel Euler Number Surface Representation Boundary Pixel Boundary Crack
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## References

- [GorUd89]Gordon, D., Udupa, J.K.,
*Fast Surface Tracking in Three-Dimensional Binary Images*, CVGIP, v.**45**, pp. 196–214, 1989.Google Scholar - [KhalKM90]Khalimsky, E., Kopperman, R. and Meyer, P.R.,
*Computer Graphics and Connected Topologies on Finite Ordered Sets*, Topology and Applications, v.**36**, pp. 1–17, 1990.MATHCrossRefMathSciNetGoogle 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 - [Kov89]Kovalevsky, V.A., “
*Finite Topology as Applied to Image Analysis*”, Computer Vision, Graphics and Image Processing, v.**46**, pp. 141–161, 1989.CrossRefGoogle 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 7^{th}International Workshop, DGCI’97, pp. 51–62, Springer 1997.Google Scholar - [RosKW91]A. Rosenfeld, T. Young Kong and A.Y. Wu, „
*Digital Surfaces*“, CVGIP GMIP, v.**53**, pp. 305–312, 1991.MATHCrossRefGoogle Scholar

## Copyright information

© Springer-Verlag Berlin Heidelberg 1999