Darboux frames, snakes, and super-quadrics: geometry from the bottom-up

Abstract

A representation and a computational model for deriving three-dimensional articulated volumetric descriptions of objects from laser range-finder data are described. What differentiates this work from other approaches is that it is purely bottom up, relying on general assumptions cast in terms of differential geometry. Darboux frames, snakes, and superquadrics form the basis of this representation, and curvature consistency provides the computational framework. The organization is hierarchical. Darboux frames are used to describe the local surface, while snakes are used to interpolate between features, particularly those that serve to partition a surface into its constituent parts. Superquadrics are subsequently used to characterize the 3-D shape of each surface partition. The result is a set of connected volumetric primitives which serve to describe the overall shape of an object. A set of examples showing how the approach performs on data acquired with a laser range finder is included.