Geometric Computing

This book offers a gentle introduction to Clifford geometric algebra, an advanced mathematical framework, for applications in perception action systems. Part I, is written in an accessible way allowing readers to easily grasp the mathematical system of Clifford algebra. Part II presents related topics. While Part 3 features practical applications for Computer Vision, Robotics, Image Processing and Neural Computing.

Topics and Features include: theory and application of the quaternion Fourier and wavelet transforms, thorough discussion on geometric computing under uncertainty, an entire chapter devoted to the useful conformal geometric algebra, presents examples and hints for the use of public domain computer programs for geometric algebra.

The modern framework for geometric computing highlighted will be of great use for communities working on image processing, computer vision, artificial intelligence, neural networks, neuroscience, robotics, control engineering, human and robot interfaces, haptics and humanoids.

From the reviews:

“This book presents the theory and engineering applications of geometric algebra, a very powerful mathematical system. … The results highlight that geometric algebra is a mathematical tool that can be used very advantageously in many engineering scenarios. … has a real potential to convince a big audience of the benefits of using geometric algebra in engineering applications, and I hope that it will be successful.” (Dietmar Hildenbrand, IAPR Newsletter, Vol. 33 (3), July, 2011)

“The theory and applications of geometric algebra (Clifford algebra), an advanced mathematical language, are addressed in this book. … The book is aimed at a graduate-level audience … . it can also be well suited for teaching a course or for self-study at the postgraduate level. Each chapter is accompanied by numerous examples and figures … . also be useful to scientists and engineers who are working in various areas related to the development and building of intelligent machines. I really enjoyed reading it.” (George K. Adam, ACM Computing Reviews, October, 2010)

“The subject of this interesting book is the application of geometric algebra to image processing, computer vision, neurocomputing and robotics. … A notation table, a list of useful formulas, a bibliography and an index conclude the book. The book is well structured, rich in data, and it contains many exercises; it is aimed at graduate students.” (Patrizio Frosini, Zentralblatt MATH, Vol. 1211, 2011)