Trace Inference, Curvature Consistency, and Curve Detection

We describe a novel approach to curve inference based on curvature information. The inference procedure is divided into two stages: a trace inference stage, to which this paper is devoted, and a curve synthesis stage, which will be treated in a separate paper. It is shown that recovery of the trace of a curve requires estimating local models for the curve at the same time, and that tangent and curvature information are sufficient. These make it possible to specify powerful constraints between estimated tangents to a curve, in terms of a neighborhood relationship called cocircularity and between curvature estimates, in terms of a curvature consistency relation. Because all curve information is quantized, special care must be taken to obtain accurate estimates of trace points, tangents and curvatures. This issue is addressed specifically by the introduction of a smoothness constraint and a maximum curvature constraint. The procedure is applied to two types of images, artificial images designed to evaluate curvature and noise sensitivity, and natural images. Zndex Terms-Consistency relationship, curve detection, trace inference.