Everyone knows what is meant by ‘shape’. However, it is not a trivial matter to define shape in a manner that is susceptible to mathematical and statistical analysis and it is only over the last two or three decades that appropriate definitions have been developed and studied. In this book we assume that the shape of an object is essentially captured by the shape of a finite subset of its points and, for the latter, we carry out much of the fundamental analysis that is likely to lie at the heart of further progress. Although this may seem a severe restriction, there is no theoretical limit to the number of points we consider and it has the significant advantage that the dimensions of the resulting shape spaces are always finite and only increase linearly with the number of points.
CONTENTS
Preface
1. Shapes and Shape Spaces
2. The Global Structure of Shape Spaces
3. Computing the Homology of Cell Complexes
4. A Chain Complex for Shape Spaces
5. The Homology Groups of Shape Spaces
6. Geodesics in Shape Spaces
7. The Riemannian Structure of Shape Spaces
8. Induced Shape-Measures
9. Mean Shapes and The Shape of the\Means
10. Visualising The Higher Dimensional Shape Spaces
11. General Shape Spaces
Appendix
Bibliography
Index
CONTENTS
Preface
1. Shapes and Shape Spaces
2. The Global Structure of Shape Spaces
3. Computing the Homology of Cell Complexes
4. A Chain Complex for Shape Spaces
5. The Homology Groups of Shape Spaces
6. Geodesics in Shape Spaces
7. The Riemannian Structure of Shape Spaces
8. Induced Shape-Measures
9. Mean Shapes and The Shape of the\Means
10. Visualising The Higher Dimensional Shape Spaces
11. General Shape Spaces
Appendix
Bibliography
Index
Páginas : 318
Peso : 13mb.
Formato : PDF.
Edición : 1 edition
Año de Publicación :1999
ISBN : 978-0471968238
Editorial : Wiley
Autor: D. G. Kendall, D. Barden, T. K. Carne
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