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.>

Relaxation labeling uses contextual information for finding consistent labelings of graphs. Although relaxation labeling is parallel and iterative, the complexity of updating with standard rules is too costly for practical implementation. A description is given of a computationally more efficient updating rule that utilizes radial projection instead of normal projection to avoid the complexities incurred by previous update rules when boundaries to the labeling space are encountered. This reduction in complexity is achieved by first restricting support vectors to the positive quadrant, and then using radial projection onto the constraint instead of normal projection. Crucial order information is conserved through smooth convergence towards the optimum and a rate of convergence proportional to the magnitudes of the support functions.>