Simplification of implicit skeletal models

Abstract

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).