This handbook brings together the most recent advances in the application of geometric computing to the most important fields related to the endeavor of building perception action systems: computer vision, robotics, image processing and understanding, pattern recognition, computer graphics, quantum computers, brain theory and neural networks. Coverage introduces diverse, powerful geometric methods in a unified manner, covering geometry theory and geometric computing methods related to the design of perception and action systems, intelligent autonomous systems and intelligent machines. It is aimed at a broad audience of applied mathematicians, physicists, computer scientists, and engineers. The book is ideal for specialists working in a particular field or for those who are interested in procedures for dealing with concurrent techniques of different fields such as the design of perception action systems.