REPRESENTING PLANAR CURVES BY USING A SCALE VECTOR

This paper introduces a new approach to solving the problem of representing planar curves. We describe the 2-D curve C not at all different scales sigma, but each curve part C(i) of C, isolating a different structure at its single scale sigma(i). Therefore, we represent the planar curve at a scale vector (sigma(1) ..., sigma(L)) supposing that the curve is partitioned in L parts C1, ..., C(L). We propose an automatic method to divide the contour into the number of nonoverlapping parts C1, ..., C(L), each of them showing a different underlying structure. This process requires neither the number of parts in the curve nor the minimum level of homogeneity for the entities within a particular part. The partition is based on three elements: a vector phi of statistical measures calculated to each class, a distance function d(phi(i), phi(j)) between vectors corresponding to two different classes, and a halt criterion based on a measure of the improvement in the disimilarity between the elements of the partition.