Aspects of the analytical formulation and applicability of a three-dimensional shape descriptor function
Chi Jung Hwang · 1987
With the advent and common utilization of computer imaging, the requirement for automated shape analysis is of ever increasing importance. An immediate example of the use of automated shape analysis is in the early screening of cervical cancer, in which cervical malignancies are apparent by the irregular morphology of cervical cells, whereas normal cervical cells are (basically) uniform and rectilinear. This two-dimensional example can be extended to three dimensions. However, the transition of this material from the 2-dimensional world into the (more natural) 3-dimensional world has not always met with success. Under most conditions, the analysis of such 3-dimensional imagery produces information which might adequately describe local aspects of a 3-dimensional surface, but no technique has been successfully proposed to deal with global aspects of the 3-dimensional surface. The importance of global information (as distinct from local information) is readily apparent if one considers such factors as invariance under rotation, translation or changes of parameter (changes of atlas). This dissertation concerns itself with the derivation of a three-dimensional shape descriptor function defined over the surface of an object in such a way as to conform to the following constraints: (1) the shape descriptor function be invariant under the action of the group of rotations in three dimensions SO(3); (2) the shape descriptor function be a continuous function of the object's surface; (3) the shape descriptor function be expressible in a compact form so as to permit comparative analyses of objects to performed in a straightforward manner, thus allowing an object to be recognized simply independent of its orientation.