Classifying symmetry sets

This paper presents a fast algorithm for computing local symmetry descriptions of region shape. Like previous algorithms, it extracts groups of edge points tangent to a common circle. However, by examining the number of distinct points of tangency, the new algorithm separates groups belonging to round regions from those belonging to elongated regions. Thus, when these relations are connected to form extended regions, round and elongated regions can be processed differently. The new implementation uses an edge-tracking algorithm to build extended regions. This handles the effects of limited precision and shape irregularities better than axistracking methods. In particular, Blum's idea of locating SAT branch points can be converted into a practical method of detecting locations at which three or more regions join. By combining a new density constraint with constraints used previously, the output and much of the processing is made linear in the image area.