Simplification of implicit skeletal models

In this paper, we describe a hierarchical representation of unions of balls (UoB) applied to volume graphics. We present an algorithm that generates stable implicit volumes at different levels of resolution in the form of primitives of overlapping spheres from various data sources such as volumetric datasets and other existing models. This is achieved as follows. First, an unstructured set of valued points called "UoB skeleton" is extracted from an exact Euclidean Distance Transform (implicits are centered at the skeletal voxels). Next, the skeletal points are connected and arranged in a "structural graph" called spanning graph, which can be used to obtain simplified multi-scale models. This simplification process consists in gradually removing nodes in this graph while respecting topological and geometrical constraints. The goal is to build an interactive system of visualization for the analysis of volumetric data. The speed of treatment associated with a good visualization should enable to achieve a 3D survey of a natural object in an interactive manner. The method has been successfully applied to both synthetic and real data (medical imaging).

[1]  Grégoire Malandain,et al.  Squelettes euclidiens d'objets discrets n-dimensionnels , 1996 .

[2]  Shigeru Muraki,et al.  Volumetric shape description of range data using “Blobby Model” , 1991, SIGGRAPH.

[3]  Paolo Cignoni,et al.  Multiresolution modeling and visualization of volume data , 1997 .

[4]  Laurent Lucas,et al.  An efficient voxel‐based visualization system from an implicit skeletal surface characterization , 2000 .

[5]  Christophe Lohou,et al.  Poset approach to 3D parallel thinning , 1999, Optics & Photonics.

[6]  Peter Meer,et al.  Stochastic image pyramids , 1989, Comput. Vis. Graph. Image Process..

[7]  Jun-ichiro Toriwaki,et al.  Reverse Distance Transformation and Skeletons Based upon the Euclidean Metric for n -Dimensional Digital Binary Pictures , 1994 .

[8]  Arie E. Kaufman,et al.  Voxel based object simplification , 1995, Proceedings Visualization '95.

[9]  Jean-Michel Jolion,et al.  The adaptive pyramid: A framework for 2D image analysis , 1991, CVGIP Image Underst..

[10]  Gilles Bertrand,et al.  A three-dimensional holes closing algorithm , 1996, Pattern Recognit. Lett..

[11]  Ingela Nyström,et al.  Efficient shape representation by minimizing the set of centres of maximal discs/spheres , 1997, Pattern Recognit. Lett..

[12]  Gilles Bertrand,et al.  New Notions for Discrete Topology , 1999, DGCI.

[13]  Melvin E. D. Jacobson,et al.  Skeleton Graph Generation for Feature Shape Description , 2000 .

[14]  Laurent Lucas,et al.  Multiresolution and Shape Optimization of Implicit Skeletal Model , 2001, WSCG.

[15]  Jun-ichiro Toriwaki,et al.  New algorithms for euclidean distance transformation of an n-dimensional digitized picture with applications , 1994, Pattern Recognit..

[16]  Mathieu Desbrun,et al.  Animation of Deformable Models Using Implicit Surfaces , 1997, IEEE Trans. Vis. Comput. Graph..

[17]  Marie-Paule Cani,et al.  Skeletal Reconstruction of Branching Shapes , 1996, Comput. Graph. Forum.

[18]  Marie-Paule Cani,et al.  Automatic Reconstruction of Unstructured 3D Data: Combining a Medial Axis and Implicit Surfaces , 1995, Comput. Graph. Forum.