Union of Spheres (UoS) Model for Volumetric Data

A stable representation of an object means that the representation is unique, is independent of the sampling geometry, resolution, noise, and other small distortions in the data, and is instead linked to the shape of the object. Stable representations help characterize shapes for comparison or recognition; skeletal (or medial axis) and volumetric primitive models have been popular in vision for the same reason. Piecewise polyhedral representations, e.g., tetrahedra, and voxel representations, e.g., octrees, generally tend to be unstable. We propose a representation for 3D objects based on the set union of overlapping sphere primitives. This union of spheres (UoS) model has some attractive properties for computer graphics, computational vision, and scientific visualization.