Hemispherical Harmonic Surface Description and Applications to Medical Image Analysis

The use of surface harmonics for rigid and nonrigid shape description is well known. In this paper we define a set of complete hemispherical harmonic basis functions on a hemisphere domain and propose a novel parametric shape description method to efficiently and flexibly represent the surfaces of anatomical structures in medical images. As the first application of hemispherical harmonic theory in shape description, our technique differs from the previous surface harmonics shape descriptors, all of which don´t work efficiently on the hemisphere-like objects that often exist in medical anatomical structures (e.g., ventricles, atriums, etc.). We demonstrate the effectiveness of our approach through theoretic and experimental exploration of a set of medical image applications. Furthermore, an evaluation criterion for surface modeling efficiency is described and the comparison results demonstrated that our method outperformed the previous approaches using spherical harmonic models.