Volume models for volumetric data

Abstract

Given a set of points on the boundary of an object derived from volumetric data, how can one represent the object and, in particular visualize it from these points? This problem is addressed by our research on the representation of points at the boundary of an object as a union of simple boundary primitives. We use volumetric data in the customary sense, but an additional feature for our purpose is the availability of an inside-outside test for any point within the volume. Our problem is, therefore, a restricted form of the general problem of visualizing an arbitrary cloud of points. Representing and visualizing can be vague concepts. As an intuitive example of the kind of representation we are looking for, assume we have data somehow representing a human head. In the first approximation, the head can be represented by a sphere. The surface area and the volume of the sphere give us rough, but useful, estimates of the corresponding properties for the head. At the same time, the position and radius of the sphere give us an idea of the translation and scaling to apply to get the head in some canonical position. If, instead, we fit an ellipsoid, the additional degrees of freedom might let us obtain the parameters of the rotations to apply. Of course, we cannot independently obtain estimates for the scaling, volume, or area. The obtainable estimates depend on the context. Whereas human perception deals very well with these ambiguities, computer visualization tends to fall short. The new representation of volumetric data based on union of spheres shows promise in achieving stability.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>