Trace inference, curvature consistency, and curve detection

Abstract

An approach is described for curve inference that is based on curvature information. The inference procedure is divided into two stages: a trace inference stage, which is the subject of the present work, and a curve synthesis stage. 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 to 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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>