Title: Radial growth models for geometric objects
Authors: John Kent - University of Leeds (United Kingdom) [presenting]
Abstract: Consider an object in two or three dimensions evolving through time. For example, the head of a child changes in shape and size as it grows into an adult. Various radial growth models have been proposed in the literature to give a simplified description of growth, notably the cardioid strain models of Todd and Mark. These models involve a ``seed'', typically interior to the object, such that (a) growth occurs along rays emanating from the seed, and (b) the magnitude of growth depends on the distance from the seed. Modified versions of these models, based on linear regression and directional statistics, are developed here to facilitate the estimation of the growth parameters. To fit such models in practice, suppose that a set of landmarks has been identified on the object and that the object has been observed at two distinct ages. The hardest part of fitting these growth models is the estimation of the seeds. For planar objects it is possible, given the seeds, to write the maximized log-likelihood over the remaining parameters in closed form. Hence it is possible to examine the goodness-of-fit of the model, especially how well-determined the seeds are, through a numerical grid search in four dimensions. Some examples will be given to illustrate the strengths and limitations of these radial growth models.