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. Academie 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.

[1]  Alexandre Lenoir,et al.  Des outils pour les surfaces discretes, estimation d'invariants geometriques, preservation de la topologie, trace de geodesiques, visualisation , 1999 .

[2]  Rémy Malgouyres,et al.  Intersection number and topology preservation within digital surfaces , 2002, Theor. Comput. Sci..

[3]  Gilles Bertrand,et al.  On P-simple points , 1995 .

[4]  Alexandre Lenoir,et al.  Fast Estimation of Mean Curvature on the Surface of a 3D Discrete Object , 1997, DGCI.

[5]  Gabor T. Herman,et al.  Discrete multidimensional Jordan surfaces , 1992, CVGIP Graph. Model. Image Process..

[6]  Jean Françon,et al.  Polyhedrization of the Boundary of a Voxel Object , 1999, DGCI.

[7]  Rémy Malgouyres,et al.  Intersection Number of Paths Lying on a Digital Surface and a New Jordan Theorem , 1999, DGCI.

[8]  Azriel Rosenfeld,et al.  A Characterization of Parallel Thinning Algorithms , 1975, Inf. Control..

[9]  R. Nagel,et al.  3-D Visual simulation , 1971 .

[10]  Jayaram K. Udupa,et al.  Boundary and object labelling in three-dimensional images , 1990, Comput. Vis. Graph. Image Process..

[11]  Azriel Rosenfeld,et al.  A Note on Thinning , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[12]  Rolf Klein,et al.  Concrete and Abstract Voronoi Diagrams , 1990, Lecture Notes in Computer Science.

[13]  Alexandre Lenoir,et al.  Topology Preservation Within Digital Surfaces , 2000, Graph. Model..

[14]  Thomas C. Henderson,et al.  CAGD-Based Computer Vision , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  Rémy Malgouyres.  Presentation of the Fundamental Group in Digital Surfaces , 1999, DGCI.

[16]  Gerald Farin,et al.  Curves and surfaces for computer aided geometric design , 1990 .

[17]  Azriel Rosenfeld,et al.  Digital topology: Introduction and survey , 1989, Comput. Vis. Graph. Image Process..

[18]  Rémy Malgouyres.  Homotopy in Two-Dimensional Digital Images , 2000, Theor. Comput. Sci..

[19]  Ramakant Nevatia,et al.  Recognizing 3-D Objects Using Surface Descriptions , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[20]  Dominique Attali.  R-regular Shape Reconstruction from Unorganized Points , 1998, Comput. Geom..

[21]  J FlynnPatrick,et al.  CAD-Based Computer Vision , 1991 .

[22]  Gilles Bertrand,et al.  Simple points, topological numbers and geodesic neighborhoods in cubic grids , 1994, Pattern Recognit. Lett..

[23]  Ari Rappoport,et al.  Interactive Boolean operations for conceptual design of 3-D solids , 1997, SIGGRAPH.