Classifying symmetry sets
Margaret M. Fleck · 1990
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. One method of representing region shapes is to extract symmetry sets, 1 i.e. sets of edge points tangent to a common circle (the symmetry circle), and then group these sets into extended regions (Figure 1). These local symmetry relationships form a intermediate representation between raw edge points and descriptions of whole regions. Thus, a wider variety of regions can be identified than with whole region models as in [1].