<title>Digital snakes</title>

Abstract

We derive a digital version of snakes for the extraction of the boundary of discrete images as a variational problem in the digital space. The method of the snakes extracts the boundary of a region deforming the boundary curves and surfaces dynamically. In this paper, we propose a digital version of this variational problem for boundary detection. Since we deal with the optimization for a functional for curvatures of points on the boundary, we first define the curvature indices of verteces for discrete objects. Second using these indices, we define the principal normal vectors of discrete curves and surfaces. These definitions permit us to derive a discrete snakes, since the minimization criterion of the snakes is defined using the curvatures of points on the boundary. Furthermore, we prove the digital boundary detected by mathematical morphology is derived as the solution of this digital variational problem.