Topologically Defined Iso-surfaces

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.

Proc. 6th Discrete Geometry for Computer Imagery (DGCI'96), Lyon, France, volume 1176 of Lecture Notes in Computer Science, pp 245-256, 1996. Springer