Boundary Morphometrics: Some Theoretical Issues and Some Data Based Applications

Abstract

Of the five senses, hearing, tasting, smelling, touching and seeing; vision is the predominant sense among primates, including humans. Humans rely almost exclusively on sight. It is via the visual system that we interact and make sense of the world around us. With the vision system as a starting point, the focus here will be primarily on three issues: (1) The role that visual perception plays in recognizing the biological form, (2) the function that form plays in biological processes, and (3) models as representations of form. The visual system can be considered as a part of the central nervous system (CNS) and acts as a major influence on other systems such as locomotion. However, more important, is the fact that it allows the brain to interact with the external environment. The human visual system is endowed with special qualities such as binocular vision allowing both eyes to look straight ahead facilitating 3D vision. Moreover, the vision system provides the ability to distinguish between different, often closely related forms, as well as allowing for the tracking of movement. All visual information entering the eyes is focused by the eye lens onto the retina. From the retina, it is transferred along the optic nerve to the visual cortex. The visual cortex lies at the posterior aspect of the brain. Sensory signals of objects are only recognized because similar experiences are stored in the brain as memories. Biological forms as perceived by the visual system are quite complex and attempts to characterize them can be accomplished by using models. Three such models are: (1) physical models, (2) heuristic models, and (3) mathematical models. For purposes here, the emphasis is on mathematical models; that is, to generate a mathematical representation of the biological form. More specifically, the focus here is on shape. Shape is defined as the outline of a biological form. It can be viewed in 2D or 3D terms. A mathematical model termed Computerized Shape Analysis is briefly presented here. It is composed of two aspects. Elliptical Fourier Descriptors (EFFs) to assess the boundary outline of a form and the Continuous wavelet transform (CWT) to extract localized features. This Fourier-wavelet model is intended as a model that generates substantially more of the visual information that is always present in the biological form. 1 Formerly, Sections of Orthodontics and Oral Biology, UCLA School of Dentistry, Los Angeles, CA 90024-1668, USA, plestrel@earthlink.net or peter.lestrel@gmail.com. 2 This chapter is a greatly enlarged version of the keynote address delivered at the 3 ISBSA at the University of Tokyo, Yayoi campus.