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UBC CS TR-90-01 Summary

A Theory of Multi-Scale, Curvature- and Torsion-Based Shape Representation for Space Curve, January 1990 Farzin Mokhtarian

This paper introduces a novel and new multi-scale shape representation technique for space curves which satisfies several criteria considered necessary for any shape representation method. This property makes the representation suitable for tasks which call for recognition of a noisy curve at any scale or orientation. \n The method rests on the concept of describing a curve at varying levels of detail using features that are invariant with respect to transformations which do not change the shape of the curve. Three different ways of computing the representation are described in this paper. These three methods result in the following representations: the curvature and torsion scale space images, the renormalized curvature and torsion scale space images, and the resampled curvature and torsion scale space images. \n The process of describing a curve at increasing levels of abstraction is referred to as the evolution of that curve. Several evolution properties of space curves are described in this paper. Some of these properties show that evolution is a physically plausible operation and characterize possible behaviours of space curves during evolution. Some show that the representations proposed in this paper in fact satisfy the required criteria. Others impose constraints on the location of a space curve as it evolves. Together, these evolution properties provide a theoretical foundation for the representation methods introduced in this paper.

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