A Shape Representation with Elastic Quadratic Polynomials—Preservation of High Curvature Points under Noisy Conditions

Abstract

We present a new shape representation technique for a planar shape using overlapping quadratic splines. The technique refines the shape by iteratively updating each spline to reduce the cost associated with C 1 discontinuity. It consists of a series of affine commutative linear operators, producing a smooth bandpass frequency response. The primary purpose of the technique is to remove minute high-curvature points while preserving salient ones. We compare the performance of the technique against those that are based on either linear splines, cubic splines, or wavelets. We consider three criteria: sensitivity of detecting salient high-curvature points, Hausdorff distance between the representation and the original shape, and computation time. The results show that the proposed technique is highly effective in preserving salient high curvature points with a relatively small Hausdorff distance and a computational cost.