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.
Spis treści
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 % Math Type!MTEF!2!1!+- % feaafiart1ev1aaat Cv AUfe BSjuy ZL2yd9gz Lbvy Nv2Caerbu Lw BLn % hiov2DGi1BTf MBae Xafv3y SLgz Gmv ETj2BSbqefm0B1jx ALjhiov2D % aebbnrfif Hh DYfgasaac H8srps0lbbf9q8Wr Ffeu Y-Hhbbf9v8qqaq % Fr0xc9pk0xbba9q8Wq Ffea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq % Q8fr Fve9Fve9Ff0dmeaabaqaci Gaca Gaaeqaba Waaeaaeaaakeaatu % u DJXw AK1uy0Hwmae Hbfv3y SLgz G0uy0Hgip5wza Gqbaiab-9q8qnaa % Caaaleqaba Wex LMBb50ujbqehq0BYng ALnh DLjhitn MCPbh DG0eva G % Gba Kqzaf Gae4NBa4gaaaaa!4FF9! $$/mathcal{P}^n $$ to % Math Type!MTEF!2!1!+- % feaafiart1ev1aaat Cv AUfe BSjuy ZL2yd9gz Lbvy Nv2Caerbu Lw BLn % hiov2DGi1BTf MBae Xafv3y SLgz Gmv ETj2BSbqefm0B1jx ALjhiov2D % aebbnrfif Hh DYfgasaac H8srps0lbbf9q8Wr Ffeu Y-Hhbbf9v8qqaq % Fr0xc9pk0xbba9q8Wq Ffea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq % Q8fr Fve9Fve9Ff0dmeaabaqaci Gaca Gaaeqaba Waaeaaeaaakeaatu % u DJXw AK1uy0Hwmae Hbfv3y SLgz G0uy0Hgip5wza Gqbaiab-9q8qnaa % Caaaleqaba Wex LMBb50ujbqehq0BYng ALnh DLjhitn MCPbh DG0eva G % Gba Kqzaf Gae4NBa4gaaaaa!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.
O autorze
Researcher in geometric computing for cognitive systems
Full Professor at the Computer Science Department of the
Center of Research and Advanced Studies CINVESTAV, Guadalajara, Mexico
Author and editor of books on geometric computing for computer science and engineering, reviewer, chair and active organiser of workshops and conferences on geometric computing for fields related to the design and building of perception action systems. Areas of research interest: pattern recognition, computer vision, neurocomputing, robotics, multidimensional image analysis, applications of Lie algebras and Clifford geometric algebra to cognitive systems.
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