Representing planar curves by using a scale vector

Abstract 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 σ, but each curve part C i of C , isolating a different structure at its single scale σ i . Therefore, we represent the planar curve at a scale vector ( σ 1 , …, σ L supposing that the curve is partitioned in L parts C 1 , …, C L ). We propose an automatic method to divide the contour into the number of nonoverlapping parts C 1 , …, 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 φ of statistical measures calculated to each class, a distance function d ( φ i , φ 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.