Shape analysis of left ventricle using spherical harmonics functions

This paper presents an approach for the parameterization of 3D triangular mesh surfaces of spherical topology objects. Our approach is decomposed in two steps. The first step consists in parameterizing the surface by defining a continuous one-to-one mapping from the surface of the object to the surface of a unit sphere [10]. The optimization of initial parameterization is formulated as a constrained optimization problem. The second step consists in expanding the surface into a series of spherical harmonic functions. The new approach is illustrated with modelling the left ventricle at stress and at rest using the sphercical harmonics model and myocardial scintigraphic data. Since we are interested in measuring and analysing left ventricle model deformation between stress and rest, normalization of the spherical harmonics descriptors set is accomplished to eliminate differences due to rotation, translation and magnification. Key-Words spherical harmonics model, 3D reconstruction, 3D shape descriptors, surface parameterization, left ventricle, myocardial scintigraphy.