The Curvature Primal Sketch

TLDR

The paper introduces the Curvature Primal Sketch, a novel representation of significant curvature changes along planar shape contours. The authors define primitive curvature discontinuities, derive their Gaussian convolution expressions, and implement an algorithm that matches multiscale convolutions to compute the sketch. The algorithm is demonstrated on tool shapes, and the representation’s potential applications are outlined.

Abstract

In this paper we introduce a novel representation of the significant changes in curvature along the bounding contour of planar shape. We call the representation the Curvature Primal Sketch because of the close analogy to the primal sketch representation advocated by Marr for describing significant intensity changes. We define a set of primitive parameterized curvature discontinuities, and derive expressions for their convolutions with the first and second derivatives of a Gaussian. We describe an implemented algorithm that computes the Curvature Primal Sketch by matching the multiscale convolutions of a shape, and illustrate its performance on a set of tool shapes. Several applications of the representation are sketched.