Curvature consistency and curve detection

Abstract

Curvature is an integral part of every curve, yet it is an astonishing fact of computational vision that virtually no algorithms for detection of curves have fully utilized it. We propose two levels of constraints over neighborhoods of tangents to curves to supplement the rather weak constraint of good continuation used in traditional approaches to curve finding. These are curvature, a relation of consistency between neighboring tangents, and curvature consistency, a relation between neighboring estimates of curvature. The effect of introducing curvature constraints is to enhance both the power of a detection algorithm and its robustness in the presence of noise. The foundation for the approach is differential geometry, and our contribution is to discretize essential notions such as curvature and osculating circles. This brought us to consider a relation between neighboring tangents to curves which we call cocircularity. The cocircularity coefficients derived from position and orientation of unit tangents to a curve in a neighborhood form the basis of a network of compatibilities in a relaxation labeling procedure. Curvature consistency then integrates contextual information into the curve detection process more effectively than previously proposed constraints.