Abstract
In this article, we present a new process for defining and building the set of configurations of Marching-Cubes algorithms. Our aim is to extract a topologically correct isosurface from a volumetric image. Our approach exploits the underlying discrete topology of voxels. Our main contribution is to provide a formal proof of the validity of the generated isosurface. The generated isosurface is a closed, oriented surface without singularity with no self-intersection. Furthermore, we demonstrate that it separates the foreground from the background. Finally we show that the graph defining the isosurface is closely linked to the surfel-adjacency graph of the digital surface of the same image.
Jacques-Olivier Lachaud
Professor of Computer Science
My research interests include digital geometry, geometry processing, image analysis, variational models and discrete calculus.