1988 Reports

On the Recovery of Superellipsoids

Boult, Terrance E.; Gross, Ari D.

Superellipsoids are parameterized solids which can appear like cubes or spheres or octahedrons or 8-pointed stars or anything in between. They can also be stretched bent tapered and combined with boolean to model a wide range of objects. Columbia's vision group is interested in using superquadrics as model primitives for computer vision applications because they are flexible enough to allow modeling of many objects, yet they can be described by a few (5-14) numbers. This paper discusses research into the recovery of superellipsoids from 3-D information, in particular range data. This research can be divided into two parts, a study of potential error-of-fit measures for recovering superquadrics, and implementation and experimentation with a system which attempts to recover superellipsoids by minimizing an error-of-fit measure. This paper presents an overview of work in both areas. Included are data from an initial comparison of 4 error-of-fit measures in terms of the inter-relationship between each measure and the parameters defining the superellipsoid. Also discussed is an experimental system which employs a nonlinear least square minimization technique to recover the parameters. This paper discusses both the advantages of this technique, and some of its major drawbacks. Examples are presented, using both synthetic and range-data, where the system successfully recovers superlliposids. Including "negative" volumes as would occur if superellipsoids were used in a constructive solid modeling system.