Marching Chains algorithm for Alexandroff-Khalimsky spaces

Xavier Daragon; Michel Couprie; Gilles Bertrand

doi:10.1117/12.453595

24 November 2002 Marching Chains algorithm for Alexandroff-Khalimsky spaces

Xavier Daragon, Michel Couprie, Gilles Bertrand

Proceedings Volume 4794, Vision Geometry XI; (2002) https://doi.org/10.1117/12.453595
Event: International Symposium on Optical Science and Technology, 2002, Seattle, WA, United States

Abstract

The Marching Cubes algorithm is a popular method which allows the rendering of 3D binary images, or more generally of iso-surfaces in 3D digital gray-scale images. Yet the original version does not give satisfactory results from a topological point of view, more precisely the extracted mesh is not a coherent surface. This problem has been solved in the framework of digital topology, through the use of different connectivities for the object and the background, and the definition of ad-hoc templates. Another framework for discrete topology is based on an heterogeneous grid (introduced by E.D. Khalimsky) which is an order, or a discrete topological space in the sense of P.S. Alexandroff. These spaces possess nice topological properties, in particular, the notion of surface has a natural definition. This article introduces a Marching Chains algorithm for the 3D Khalimsky grid H³. Given an object X which is a subset of H³, we define, in a natural way, the frontier of X which is also an order. We prove that this frontier order is always a union of surfaces. Then we show how to use frontier order to design a Marching Cubes-like algorithm. We discuss the implementation of such an algorithm and show the results obtained on both artificial and real objects.

Citation Download Citation

Xavier Daragon, Michel Couprie, and Gilles Bertrand "Marching Chains algorithm for Alexandroff-Khalimsky spaces", Proc. SPIE 4794, Vision Geometry XI, (24 November 2002); https://doi.org/10.1117/12.453595

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