Neuroscience -- Spatiotemporal Dynamics of Visual Perception Across Neural Maps and Pathways -- Symmetry, Features, and Information -- Neural Networks -- Geometric Approach to Multilayer Perceptrons -- A Lattice Algebraic Approach to Neural Computation -- Eigenproblems in Pattern Recognition -- Image Processing -- Geometric Framework for Image Processing -- Geometric Filters, Diffusion Flows, and Kernels in Image Processing -- Chaos-Based Image Encryption -- Computer Vision -- One-Dimensional Retinae Vision -- Three-Dimensional Geometric Computer Vision -- Dynamic % MathType!MTEF!2!1!+- % feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D % aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq % Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq % Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaatu % uDJXwAK1uy0HwmaeHbfv3ySLgzG0uy0Hgip5wzaGqbaiab-9q8qnaa % CaaaleqabaWexLMBb50ujbqehq0BYngALnhDLjhitnMCPbhDG0evaG % GbaKqzafGae4NBa4gaaaaa!4FF9! $$\mathcal{P}^n $$ to % MathType!MTEF!2!1!+- % feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D % aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq % Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq % Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaatu % uDJXwAK1uy0HwmaeHbfv3ySLgzG0uy0Hgip5wzaGqbaiab-9q8qnaa % CaaaleqabaWexLMBb50ujbqehq0BYngALnhDLjhitnMCPbhDG0evaG % GbaKqzafGae4NBa4gaaaaa!4FF9! $$\mathcal{P}^n $$ Alignment -- Detecting Independent 3D Movement -- Perception and Action -- Robot Perception and Action Using Conformal Geometric Algebra -- Uncertainty in Geometric Computations -- Uncertainty Modeling and Geometric Inference -- Uncertainty and Projective Geometry -- The Tensor Voting Framework -- Computer Graphics and Visualization -- Methods for Nonrigid Image Registration -- The Design of Implicit Functions for Computer Graphics -- Geometry and Robotics -- Grassmann-Cayley Algebra and Robotics Applications -- Clifford Algebra and Robot Dynamics -- Geometric Methods for Multirobot Optimal Motion Planning -- Reaching and Motion Planning -- The Computation of Reachable Surfaces for a Specified Set of Spatial Displacements -- Planning Collision-Free Paths Using Probabilistic Roadmaps.Many computer scientists, engineers, applied mathematicians, and physicists use geometry theory and geometric computing methods in the design of perception-action systems, intelligent autonomous systems, and man-machine interfaces. This handbook brings together the most recent advances in the application of geometric computing for building such systems, with contributions from leading experts in the important fields of neuroscience, neural networks, image processing, pattern recognition, computer vision, uncertainty in geometric computations, conformal computational geometry, computer graphics and visualization, medical imagery, geometry and robotics, and reaching and motion planning. For the first time, the various methods are presented in a comprehensive, unified manner. This handbook is highly recommended for postgraduate students and researchers working on applications such as automated learning; geometric and fuzzy reasoning; human-like artificial vision; tele-operation; space maneuvering; haptics; rescue robots; man-machine interfaces; tele-immersion; computer- and robotics-aided neurosurgery or orthopedics; the assembly and design of humanoids; and systems for metalevel reasoning.