Curve Segmentation by Relaxation Labeling

This correspondence discusses parallel iterative methods of segmenting the border of a shape into "angles" and "sides." Initially, smoothed "slope" and "curvature" values of the border are measured at every point, and the curvature value determines the point's initial probabilities of being an angle or a side. The values are then iteratively adjusted, and the probabilities are reinforced or weakened, in a manner dependent on the values and probabilities at neighboring points. For example, a point p's probability of being on a side is reinforced if p and its neighbors have similar slopes, and our estimate of p's slope can be improved by (say) averaging with these slopes. Similarly, p's probability of being an angle is reinforced if appropriate slope or curvature differences exist between p and its neighbors, and our estimate of p's curvature can be improved by taking the neighbors' slopes into account. A set of such reinforcement and adjustment rules is formulated, and examples are given of their effects on various types of shapes.