Strong thinning and polyhedric approximation of the surface of a voxel object

We first propose for digital surfaces an analog to the notion of strong homotopy existing in 3D (On P-Simple points, no. 321, C.R. Academic des Sciences, 1995, p. 1077). We present the associated parallel thinning algorithm. The surface of an object composed of voxels is a set of surfels (faces of voxels). This discrete representation is not the classical one to visualize and to work on 3D objects. Then, we propose a method for passing efficiently from the discrete representation to the continuous one, using the presented thinning algorithm. This way is more efficient than the existing methods (Proceedings of DGC'99, Lecture Notes in Computer Science, Vol. 1562, Springer, Berlin, 1999, p. 425). Some examples and a method to make the reverse operation (discretization) are presented. (C) 2002 Elsevier Science B.V. All rights reserved.