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.
Table of Contents
Analytical Geometry Olga Sorkine-Hornung and Daniel Cohen-Or
Linear Algebra Daniel Cohen-Or, Olga Sorkine-Hornung, and Chen Greif
Least Squares Solutions Niloy J. Mitra
PCA and SVD Olga Sorkine-Hornung
Spectral Transform Hao (Richard) Zhang
Solution of Linear Systems Chen Greif
Laplace and Poisson Daniel Cohen-Or and Gil Hoffer
Curvatures: A Differential Geometry Tool Niloy J. Mitra and Daniel Cohen-Or
Dimensionality Reduction Hao (Richard) Zhang and Daniel Cohen-Or
Scattered Data Interpolation Tao Ju
Topology: How Are Objects Connected? Niloy J. Mitra
Graphs and Images Ariel Shamir
Skewing Scheme Daniel Cohen-Or
Daniel Cohen-Or, Chen Grief, Tao Ju, Niloy J. Mitra, Ariel Shamir, Olga Sorkine-Hornung, Hao (Richard) Zhang
"… a useful book (the title is correct!) that covers a wealth of processing tools in a single volume accessible to experts and novices alike. … Each chapter is stand-alone, so the reader can learn the material quickly without the need to study earlier chapters. … The text is lucid and easy to read, and follows a logical progression. Equations are explained, and the authors provide ample figures and pictures to illustrate the concepts and discussions. … this book is a good collection of algorithms and tools for computer graphics. The topics are useful, well presented, and collected in a single book for easy access. If you work in this area, you’ll find this book beneficial."
—MAA Reviews, April 2016
"This book presents solutions to many commonly used computational problems in applied geometry, computer graphics, and image processing. It covers a wide range of mathematics in a practical and useful way. … the content is easy to follow even for readers without a good mathematical backgound. … The book is a good starting point for those who want to become familiar with a wide area of applications of mathematical tools in computer graphics and image processing. It can be used as a semester textbook or for self-study. It is intended for practitioners who want to learn the most commonly used methods in the mentioned scientific area."
—Zentralblatt MATH 1322
"This is the book I really missed and was thinking of authoring myself for my students. This book did it perfectly. It compactly and beautifully explains important mathematical tools for problem solving in geometry and image processing. A must-read for practitioners, researchers, and students in graphics."
—Takeo Igarashi, The University of Tokyo
"An intuitive quick tour of many important topics in geometry and image processing, showing insightful associations between concepts in geometry and algebra. It is illustrated using practical examples and is a fun refresher even for those already familiar with the topics."
—Hugues Hoppe, Microsoft Research
"The book provides clear and intuitive coverage of important mathematical tools for graphics and image processing. Covered topics are useful for practitioners and students in the field, with carefully selected eye-opening examples. It will be enjoyed by beginners and experienced alike, improving everyone’s ability for analysis and problem solving."
—Shmuel Peleg, The Hebrew University of Jerusalem