Towards effective planar shape representation with multiscale digital curvature analysis based on signal processing techniques

Abstract This paper presents and discusses a new approach to multiscale curvature analysis of digital contours that is based on digital signal processing techniques. The shape contour is expressed in terms of two one-dimensional signals (linearized x - and y -coordinates) and the derivative theorem is applied as a means of obtaining an interesting expression relating contour curvature and the spectra of its parametrized x - and y -signals. Multiscale curvature analysis is achieved through Gaussian lowpass filtering and the “shrinkage” of the original signals implied by such a process is effectively circumvented by an energy-based compensation scheme, which has allowed accurate quantitative identification of the curvature value. The concept of curvegram is introduced and exemplified and the overall performance of the proposed technique for curvature estimation is formally assessed with respect to a contour defined in terms of B-splines. Application examples to synthetic and real images have been included.