A Sampler of Useful Computational Tools for Applied Geometry, Computer Graphics, and Image Processing: Foundations for Computer Graphics, Vision, and Image Processing

A Sampler of Useful Computational Tools for Applied Geometry, Computer Graphics, and Image Processing shows how to use a collection of mathematical techniques to solve important problems in applied mathematics and computer science areas. The book discusses fundamental tools in analytical geometry and linear algebra. It covers a wide range of topics, from matrix decomposition to curvature analysis and principal component analysis to dimensionality reduction. Written by a team of highly respected professors, the book can be used in a one-semester, intermediate-level course in computer science. It takes a practical problem-solving approach, avoiding detailed proofs and analysis. Suitable for readers without a deep academic background in mathematics, the text explains how to solve non-trivial geometric problems. It quickly gets readers up to speed on a variety of tools employed in visual computing and applied geometry Chapter 1. Analytical geometry / Olga Sorkine-Hornung and Daniel Cohen-Or -- chapter 2. Linear algebra? / Daniel Cohen-Or, Olga Sorkine-Hornung and Chen Greif -- chapter 3. Least-squares solutions / Niloy J. Mitra -- chapter 4. PCA and SVD / Olga Sorkine-Hornung -- chapter 5. Spectral transform / Hao (Richard) Zhang -- chapter 6. Solution of linear systems / Chen Greif -- chapter 7. Laplace and Poisson / Daniel Cohen-Or and Gil Hoffer -- chapter 8. Curvatures : a differential geometry tool / Niloy J. Mitra and Daniel Cohen-Or -- chapter 9. Dimensionality reduction / Hao (Richard) Zhang and Daniel Cohen-Or -- chapter 10. Scattered data interpolation / Tao Ju -- chapter 11. Topology : how are objects connected? / Niloy J. Mitra -- chapter 12. Graphs and images / Ariel Shamir -- chapter 13. Skewing scheme / Daniel Cohen-Or