Shape Interpolations with Unions of Spheres

Shape interpolation is the process of transforming continuously one object into another. This is useful in applications such as object recognition, object registration and computer animation. Unfortunately, "good" shape interpolation is as ill-defined as "shape" itself. To be able to control the process in a useful way, we need a representation for the objects using primitives which capture at least some aspects of their shape, with methods to convert other representations to this one. We present here a method to interpolate between two objects represented as a union of spheres. We briefly describe the representation and its properties, and show how to use it to interpolate. Once a distance metric between the spheres is defined (we show different metric producing controlled effects), the algorithm optimally matches the spheres in the two models using a bipartite graph. The transformation then consists in interpolating between the matched spheres. If the union of spheres has been simplified, the other spheres are matched as a function of their positions within their representative cluster. Examples are shown and discussed with two- and three-dimensional objects. The results show that the union of spheres helps capture some notion of shape, and helps to automatically match and interpolate shapes.