Eduardo Bayro Corrochano Knihy

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.

The book explores the construction of Perception Action Cycles (PAC) as a method for developing intelligent systems, emphasizing the application of geometric algebra over traditional matrix algebra. It argues that geometric algebra simplifies complex calculations, enhancing the efficiency and accuracy of cognitive system algorithms. The initial chapters introduce the foundational concepts of geometric algebra, while later sections demonstrate its practical applications in cognitive systems. This approach aims to unify and clarify the challenges faced in artificial intelligence development.

The 14th Iberoamerican Congress on Pattern Recognition (CIARP 2009, C- gresoIberoAmericanodeReconocimientodePatrones)formedthelatestofanow longseriesofsuccessfulmeetingsarrangedbytherapidlygrowingIberoamerican pattern recognition community. The conference was held in Guadalajara, Jalisco, Mexico and organized by the Mexican Association for Computer Vision, Neural Computing and Robotics (MACVNR). It was sponsodred by MACVNR and ? ve other Iberoamerican PR societies. CIARP 2009 was like the previous conferences in the series supported by the International Association for Pattern Recognition (IAPR). CIARP 2009 attracted participants from all over the world presenting sta- of-the-artresearchon mathematical methods and computing techniques for p- tern recognition, computer vision, image and signal analysis, robot vision, and speech recognition, as well as on a wide range of their applications. This time the conference attracted participants from 23 countries,9 in Ibe- america, and 14 from other parts of the world. The total number of submitted papers was 187, and after a serious review process 108 papers were accepted, all of them with a scienti? c quality above overall mean rating. Sixty-four were selected as oral presentations and 44 as posters. Since 2008 the conference is almost single track, and therefore there was no real grading in quality between oral and poster papers. As an acknowledgment that CIARP has established itself as a high-quality conference, its proceedings appear in the Lecture Notes in Computer Science series. Moreover, its visibility is further enhanced by a selection of a set of papers that will be published in a special issue of the journal Pattern Recognition Letters.

After an introduction to geometric algebra, and the necessary math concepts that are needed, the book examines a variety of applications in the field of cognitive systems using geometric algebra as the mathematical system. There is strong evidence that geobetric albegra can be used to carry out efficient computations at all levels in the cognitive system. Geometric algebra reduces the complexity of algebraic expressions and as a result, it improves algorithms both in speed and accuracy. The book is addressed to a broad audience of computer scientists, cyberneticists, and engineers. It contains computer programs to clarify and demonstrate the importance of geometric algebra in cognitive systems.