A vectorial rotation-invariant 3-D shape descriptor

Shape remains a major descriptive and discriminant feature of objects, especially in clinical settings where it forms an integral part (for example) of radiological morphometry as well as anthropometry and biometrics. Most successful descriptions of shape are functional rather than descriptive, and it is often the goal that any such functional description of shape be unique (but generalizable, see below) as well as invariant under some (or all) rigid motions of the base object. When these goals are combined with a desire to keep the descriptor reasonably computationally efficient then often a compromise had to be made in which one or other of the goals is relaxed. In this paper we describe a vectorial formulation of an invariant shape descriptor which is reasonably computationally efficient but for which we cannot guarantee absolute uniqueness. Our setting is a wide class of three-dimensional (polyhedral) objects drawn from such datasets as the visible human datasets and the CAESAR/CARDLab anthropometric datasets. In this short paper we describe the formal definition of a set of vectorial spherical shape descriptors, and give preliminary indications of their role in shape description in anthropometry.