Recovery Of Superquadrics From 3-D Information
Terrance E. Boult, Ari Gross · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1988
Super-quadrics are a volumetric primitive which can model many objects ranging from cubes to spheres to octahedrons to 8-pointed stars and anything in between. They also can be stretched, bent, tapered and combined with boolean to model a wide range of objects. A restricted class of these have been used as the basic primitives of a volumetric modeling system developed ar SRI. At Columbia, we are 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 small (5-14) number of parameters. In this paper, we discuss our research into the recovery of superellipsoids (a restricted class of superquadrics) from 3-D information, in particular range data. We recall the formulation of superellipsoids in terms of their inside-out function, which divides 3 space into regions inside the volume, on the boundary, and outside the volume. Using this function, we employ a nonlinear least square minimization technique to recover the parameters. We discuss both the advantages of this technique, and some of its major drawbacks. Examples are presented, using both synthetic and actual range-data, where the system successfully recovers negative superquadrics, and superquadrics from sparse data including synthetically generated sparse data from multiple viewpoints. While the system was successful in recovering the examples presented, there are some obvious problems. One of these is the relationship between the inside-out function, and the true least-squared distance of the data from recovered model. We discuss this relationship for three different functions based on the inside-out function.