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.