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Boundary Morphometrics: Some Theoretical Issues and Some Data Based Applications
Keynote Address
P. E. LESTREL1, 2
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.
INTRODUCTION
Mathematics is the door and key to the sciences. Roger Bacon (ca. 1214-1294)
No human investigation can be called a real science if it cannot
be demonstrated mathematically. Leonardo da Vinci (1452-1519)
ā¦the universeā¦cannot be understood unless one learns to
comprehendā¦the language of mathematics. Galileo Galilei (1564-1642)
I often say that when you can measure what you are speaking about,
and express it in numbers, you know something about it; but when you
cannot measure it, when you cannot express it in numbers, your knowledge
is of a meagre and unsatisfactory kind. Lord Kelvin (1824-1907)
The purpose of this address delivered at the opening of the third ISBSA held at the University of Tokyo, Yayoi Campus on June 14-17, 2013, is two-fold. It is intended to: (1) introduce the participants and guests to the symposium and (2) stress the fundamental importance of the biological form, which is considered central to any assessment of biological processes such as growth and development or evolution.
First, I want to extend a warm welcome to you all for coming to the Third International Symposium of Biological Shape Analysis being held here at the University of Tokyo. This is the third time that we are meeting and this is the largest group so far. Speaking for the organizers, I want to especially thank those of you who have had to travel a long way to get here. This symposium is truly international. The initial idea of the organizers was to try to keep the size fairly small so that everyone can get to know everyone else in an informal setting. The ISBSA is a very unusual group in that it is composed of researchers from very diverse disciplines. These include agricultural genetics, botany, entomology, dentistry, physical anthropology, paleontology, zoology to name a few. What makes this symposium possible is a common interest in the biological form and how best describe it in quantitative terms.
In very general terms, this then leads to two aspects, which are: (1) how is the biological form perceived and once perceived (2) how is the biological form best described. The first part deals with the act of seeing and the second part deals with how to quantify what is being perceived. In an attempt to speak briefly to these two major issues, the following topics, considered of particular relevance, will be addressed:
Part one consists of:
(1)Visual perception and the role it plays in recognizing forms,
(2)Evolution of vision and the structure of the eye,
(3)Some recent quantitative applications of vision,
Part two deals with:
(4)The role that form plays in biological processes,
(5)Models viewed as representations of form,
(6)Computational Shape Analysis
Because the literature on vision, visual perception, structures of the eye, and more recently on the evolutionary and molecular physiology of the eye is extensive, it is only possible here to touch briefly on some these issues. The material here is divided into two parts. Part 1, deals with visual perception; that is, how the visual system is constructed, and how is this visual information transferred from the retina to the brain. This section ends with the quantification of aspects of the retina/brain relationship. The second part, Part 2, shifts the discussion from the visual system per-se to the analysis of forms as apprehended by the visual system. Discussion of the latter material will be followed by some examples of models of shape. Finally, the discussion concludes with the presentation of a Fourier-wavelet model. This last model joins the shape or boundary (global aspects) of a form with local changes (localized features) along the boundary contour. It is termed Computational Shape Analysis.
Vision has been considered as an information processor, analogous to a computer with a central processing unit (CPU) and memory and in that sense, the vision system can be viewed as consisting of an input that leads to a cascade of events that eventually produces a behaviorally appropriate response as an output [1].
PART 1: THE VISUAL SYSTEM
Vision as an Information System
With respect to humans, it can be argued that the most important basis for acquiring knowledge about the external world is the visual system [2]. The question that then arises (even if it cannot be satisfactorily answered in all aspects) is as follows. How can the normal brain process visual information from cues in the external environment to produce precise behaviors?
For example, consider the skull specimen displayed in Fig. 1 [3], viewed from the side (lateral view). Most reasonably educated nonprofessionals, would in all probability, identify it a human-looking skull based on their experience and education. However, if prompted to provide further details, they would probably be unable to do so. A physical anthropologist, on the other hand, would be able to readily identify it and describe it with a wealth of details. For example, that it is a Neanderthal specimen called La Ferrassie 1, discovered in 1909 by Denis Peyrony and Louis Capitan in a cave near the Dordogne region of France. It is an adult male of roughly 40-55 years of age. It is dated to roughly between 50,000 and 70,000 years ago. Associated faunal evidence indicates the presence of glacial cold conditions associated with the last glacial period. Archeological evidence suggests that La Ferrassie was an intentional burial. La Ferrassie had excessively worn teeth, giving hints as to the nature of the diet of Neanderthals.
This specimen also raises the interesting question of what, if any, is its relationship is to modern man (Homo sapiens)? This continues to be a hotly debated issue. Neanderthals are currently considered as a separate lineage from modern humans due to its distinct morphology. Whether it is a totally separate species has become increasingly unlikely as interbreeding with Homo sapiens appears to have occurred prior to Homo neanderthalensis disappearing from the fossil record. We will briefly return to this debate and the relationship between Homo neanderthalensis and Homo sapiens later in this address.
Returning to the issue here of vision as an information system, it can be reasonably presumed that both the educated individual and the anthropologist are viewing the same skull image. Further, neither observation (of the educated individual or the anthropologist), can be considered right or wrong. That is, one can assume that both visual assessments are closely similar, although perhaps n...
