Characterizing the shape of anatomical structures with poisson's equation

Abstract

This paper presents a novel approach to analyze the shape of anatomical structures. Our methodology is rooted in classical physics and in particular Poisson's equation, a fundamental partial differential equation [1]. The solution to this equation and more specifically its equipotential surfaces display properties that are useful for shape analysis. We demonstrate the solution of this equation on synthetic and medical images. We present a numerical algorithm to calculate the length of streamlines formed by the gradient field of the solution to this equation for 3D objects. We used the length of streamlines of equipotential surfaces to introduce a new function to characterize the shape of objects. A preliminary study on the shape of the caudate nucleus in Schizotypal Personality Disorder (SPD) illustrates the power of our method. © Springer-Verlag Berlin Heidelberg 2004.