Congruence Conditions for Nonplanar Developable Surfaces and Their Application to Surface Recognition

This paper presents a new methodology of representing and matching nonplanar developable surfaces (NPDS) for the purpose of three-dimensional objects recognition. The constant-ratio property, a special property of an NPDS, is presented. Using this property, congruence conditions for two NPDS segments are derived that depend only on geometric and numerically computable properties of a surface. Based on these theoretical results, a developable surface description is presented and an algorithm is developed that matches an unknown NPDS with surface models to identify the unknown surface. The practical feasibility of this methodology is studied and is illustrated by various concrete examples using range images. The numerical computation involved in and the noise sensitivity of the approach are also addressed.