Book contents
- Frontmatter
- Contents
- List of contributors
- Preface
- Acknowledgments
- Part one Theoretical considerations
- Part two Applications of Fourier descriptors
- 6 Closed-form Fourier analysis: A procedure for extraction of ecological information about foraminiferal test morphology
- 7 Fourier descriptors and shape differences: Studies on the upper vertebral column of the mouse
- 8 Application of the Fourier method on genetic studies of dentofacial morphology
- 9 Fourier analysis of size and shape changes in the Japanese skull
- 10 Craniofacial variability in the hominoidea
- 11 Heuristic adequacy of Fourier descriptors: Methodologic aspects and applications in Morphological
- 12 Analyzing human gait with Fourier descriptors
- 13 Elliptic Fourier descriptors of cell and nuclear shapes
- 14 Cranial base changes in shunt-treated hydrocephalics: Fourier descriptors
- 15 A numerical and visual approach for measuring the effects of functional appliance therapy: Fourier descriptors
- 16 Size and shape of the rabbit orbit: 3-D Fourier descriptors
- 17 From optical to computational Fourier transforms: The natural history of an investigation of the cancellous structure of bone
- 18 Epilogue: Fourier methods and shape analysis
- Appendix
- Glossary
- Index
18 - Epilogue: Fourier methods and shape analysis
Published online by Cambridge University Press: 14 September 2009
- Frontmatter
- Contents
- List of contributors
- Preface
- Acknowledgments
- Part one Theoretical considerations
- Part two Applications of Fourier descriptors
- 6 Closed-form Fourier analysis: A procedure for extraction of ecological information about foraminiferal test morphology
- 7 Fourier descriptors and shape differences: Studies on the upper vertebral column of the mouse
- 8 Application of the Fourier method on genetic studies of dentofacial morphology
- 9 Fourier analysis of size and shape changes in the Japanese skull
- 10 Craniofacial variability in the hominoidea
- 11 Heuristic adequacy of Fourier descriptors: Methodologic aspects and applications in Morphological
- 12 Analyzing human gait with Fourier descriptors
- 13 Elliptic Fourier descriptors of cell and nuclear shapes
- 14 Cranial base changes in shunt-treated hydrocephalics: Fourier descriptors
- 15 A numerical and visual approach for measuring the effects of functional appliance therapy: Fourier descriptors
- 16 Size and shape of the rabbit orbit: 3-D Fourier descriptors
- 17 From optical to computational Fourier transforms: The natural history of an investigation of the cancellous structure of bone
- 18 Epilogue: Fourier methods and shape analysis
- Appendix
- Glossary
- Index
Summary
Introduction
The previous chapters have dealt with some of the theoretical aspects of the development of Fourier descriptors (FDs) as well as numerous applications reflecting very diverse research areas. They give the reader a sense of the complexities attendant to the numerical characterization of form as well as indicating the relative infancy of these research methods. Although the basic mathematical underpinnings of FDs have been available for over 150 years, significant practical developments and applications in biology have only begun to appear in the last thirty-five years. One feels that there is increasing interest as well as tremendous potential in the use of these methods. However, major breakthroughs in Fourier techniques and applications have been made by individual investigators working in the frontiers of their respective fields. Previously little effort has been made to communicate their findings, techniques, and problems across these specialization boundaries. This book represents the first attempt to do so.
It is interesting to note that many of the authors in this volume exploring Fourier analysis for evaluation of aspects of form have had to develop their own methods and computer programs in the process of trying to answer specific research questions. In fact, the time line for the increase in interest and use of these methods closely parallels the broader capabilities now available to researchers in all fields with respect to computer programming and processing power, which are critical for the practical use of these computationally intensive techniques.
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- Fourier Descriptors and their Applications in Biology , pp. 409 - 414Publisher: Cambridge University PressPrint publication year: 1997