A Theory of Multiscale, Torsion-Based Shape Representation for Space Curves

Abstract

It is argued that space curves are useful for representing 3-D surfaces and objects. This paper introduces a multiscale shape representation, referred to as the torsion scale space image(or TSS), for space curves. Experiments show that the representation is robust and suitable for recognition of noisy curves at any scale or orientation. The method rests on the concept of describing curves at varying levels of detail using invariant geometric features. Three different ways of computing the representation, each with different properties, are described here. A two-phase matching algorithm consisting of TSS matching followed by transformation parameter optimization demonstrates the usefulness of the representations in recognition tasks. The process of describing curves at increasing levels of abstraction is referred to as the evolutionof those curves. Several evolution properties of space curves are described in this paper. Together, these results provide a sound theoretical foundation for the representation methods introduced here.