Spectral Geometry of Shapes: Principles and Applications

Spectral Geometry of Shapes presents unique shape analysis approaches based on shape spectrum in differential geometry. It provides insights on how to develop geometry-based methods for 3D shape analysis. The book is an ideal learning resource for graduate students and researchers in computer science, computer engineering and applied mathematics who have an interest in 3D shape analysis, shape motion analysis, image analysis, medical image analysis, computer vision and computer graphics. Due to the rapid advancement of 3D acquisition technologies there has been a big increase in 3D shape data that requires a variety of shape analysis methods, hence the need for this comprehensive resource.

Presents the latest advances in spectral geometric processing for 3D shape analysis applications, such as shape classification, shape matching, medical imaging, etc.Provides intuitive links between fundamental geometric theories and real-world applications, thus bridging the gap between theory and practiceDescribes new theoretical breakthroughs in applying spectral methods for non-isometric motion analysisGives insights for developing spectral geometry-based approaches for 3D shape analysis and deep learning of shape geometry

1. Introduction 2. Spectral Geometry Operation 3. Spectral Geometric Features for Shapes 4. Isometric Shape Analysis Using Spectral Geometry 5. Near Isometric Shape Motion Analysis Using Spectral Geometry 6. Non-Isometric Shape Motion Analysis by Variation of Shape Spectrum 7. Machine Learning of Spectral Geometry 8. Conclusions