Geometric properties computation for discrete curves based on discrete derivatives

Abstract

Many applications rely on the geometric properties of discrete curves. In this paper, a novel method is proposed for computing the geometric properties of discrete curves. Geometric properties are dependent on derivatives. In order to obtain the reliable derivatives of discrete curves, the derivative of a discrete function at a point, also called the discrete derivative, is defined. By using discrete derivatives, classical differential geometry is discretized and the geometric properties of discrete curves are computed from differential geometry theory. The experimental results demonstrate that the proposed method is accurate, robust to noise, and suitable for different geometric shapes of discrete curves.