This volume represents an ongoing series entitled Biological Shape Analysis, of which this is the 4th Edition. These proceedings represent state-of-the-art research in the field of biology, broadly-based, that deal with the quantitative analysis of the shape of the biological form. These numerical analyses include Fourier analytic methods, wavelets, neural networks, machine vision, machine learning, median axis transforms, spectral clustering, genome-wide association studies, 3D surface mapping, as well as more traditional morphometric approaches. Studies included are drawn from research in agricultural genetics, anatomy, anthropology, botany, dentistry, entomology, forensics, human evolution, paleontology, primatology, to name a few.The shape of forms can be considered of central importance in terms of identification, comparison, and classification of biological organisms. These proceedings, of which this is the fourth one, are unique in that they deal extensively with a wide range of organisms in biology, including both fauna and flora. They bring together diverse practitioners from a wide variety of disciplines. This represents a major departure from the current emphasis on specialization in the biological sciences. It is of particular importance to note that these issues dealing with shape analysis of biological structures are found to be common across very diverse disciplines and these proceedings are the first ones to highlight this.There are no volumes currently available that are as broadly-based as these proceedings in dealing with the quantification of shape analysis. (1) These volumes are unique in their diversity in covering the biological disciplines; (2) The emphasis on numerical approaches; and (3) the numerous state-of-the-art research papers.

The proceedings were designed to bring together researchers who share a common interest in the quantitative description of the biological form. Participants came from very diverse disciplines such as agricultural genetics, botany, entomology, forensics, human anatomy, paleontology, human evolution, primatology, dentistry, etc. The participants applied various methodological approaches that are being increasingly used to describe aspects of the biological form. These techniques include neural networks, Fourier descriptors, shape mapping, genome-wide association studies (GWAS), Riemann curves, surface mapping, etc. A number of the contributions in the proceedings represent state of the art research that reflects advances in that discipline.

This proceedings volume describes the current state of research dealing with biological shape analysis. The quantitative analysis of the shape of biological organisms represents a challenge that has now seen breakthroughs with new methodologies such as elliptical Fourier analysis, quantitative trait loci analysis (QTLs), thin plate splines, etc. The volume also illustrates the diversity of disciplines that are actively involved in the characterization and analysis of the biological shape. Some of the papers deal with the need to relate the underlying genome responsible for the actual observed characteristics of form. Moreover, many of the papers focus on the relationship of the shape to the processes that determine the biological form, an issue of major continuing concern in biology.This volume brings together for the second time practitioners from a variety of disciplines who have been concerned with the necessity of applying new methods to the analysis of biological shape. Previous methodologies based on the conventional metrical approach (distances, angles and ratios), have not been able to adequately capture - in quantitative terms - the subtleties and complexities of biological form due to its irregularity. This volume represents an initial attempt to quantitatively characterize the biological form in both two- and three-dimensions, as it is actually perceived.There is no volume available that deals with the subject matter of these Proceedings. The papers represent, as in the first proceedings, a unique look at: (1) new methodologies developed and used quantitatively describe the biological form; (2) the need to relate the observed biological shape to the underlying processes that determine the shape; and (3) the tremendous diversity of disciplines actively involved in the characterization and analysis of biological shapes. These range from physical anthropology, anatomy, genetics, botany, entomology, forensics, to applied mathematics, etc.

The Proceedings describe the current state of research dealing with biological shape analysis. The quantitative analysis of the shape of biological organisms represents a challenge that has now seen breakthroughs with new methodologies such as elliptical Fourier analysis, quantitative trait loci analysis (QTLs), chromosome segment substitution lines (CSSLs), thin plate splines, etc. The Proceedings also illustrate the diversity of disciplines that are actively involved in the characterization and analysis of biological shape. Moreover, many of the papers focus on the relationship of the shape to the processes that determine the biological form, an issue of major continuing concern in biology.

The purpose of this book is to introduce Fourier descriptors as a method for measuring the shape of whole, or parts of, organisms. Fourier descriptors refers to the utilization of Fourier analysis, primarily the Fourier series as a curve fitting technique, that can numerically describe the shape of irregular structures such as are commonly found in living organisms. The quantitative characterization of irregular forms is often the first step toward elucidation of the underlying biological processes, whether they be genetic, evolutionary, or functional. The first five chapters discuss the theory behind the use of Fourier descriptors and the remaining chapters show case studies of how they can be used in various fields of biology such as anatomy, cell biology, medicine and dentistry. This is the first book solely devoted to this subject.

The purpose of this book is to introduce Fourier descriptors as a method for measuring the shape of whole or parts of organisms. Fourier descriptors refer to the utilization of Fourier analysis, primarily the Fourier series as a curve-fitting technique, that can numerically describe the outline (shape) of irregular structures such as are commonly found in living organisms. The quantitative characterization of irregular forms is often a first step towards elucidation of the underlying biological processes, whether they be genetic, evolutionary, or functional. The first five chapters discuss the theory behind the use of Fourier descriptors and the remaining chapters show case studies of how they can be used in various fields of biology such as anatomy, cell biology, medicine and dentistry. This book is solely devoted to this subject and will be of interest to all those interested in biological morphometrics.