This book introduces readers to the latest exciting advances in human motion sensing and recognition, from the theoretical development of fuzzy approaches to their applications. The topics covered include human motion recognition in 2D and 3D, hand motion analysis with contact sensors, and vision-based view-invariant motion recognition, especially from the perspective of Fuzzy Qualitative techniques.Â
With the rapid development of technologies in microelectronics, computers, networks, and robotics over the last decade, increasing attention has been focused on human motion sensing and recognition in many emerging and active disciplines where human motions need to be automatically tracked, analyzed or understood, such as smart surveillance, intelligent human-computer interaction, robot motion learning, and interactive gaming. Â Current challenges mainly stem from the dynamic environment, data multi-modality, uncertain sensory information, and real-time issues.
Just suppose, for a moment, that all rings of integers in algebraic number fields were unique factorization domains, then it would be fairly easy to produce a proof of Fermat's Last Theorem, fitting, say, in the margin of this page. Unfortunately however, rings of integers are not that nice in general, so that, for centuries, mathÂ ematicians had to search for alternative proofs, a quest which culminated finally in Wiles' marvelous results - but this is history. The fact remains that modern algebraic number theory really started off with inÂ vestigating the problem which rings of integers actually are unique factorization domains. The best approach to this question is, of course, through the general theÂ ory of Dedekind rings, using the full power of their class group, whose vanishing is, by its very definition, equivalent to the unique factorization property. Using the fact that a Dedekind ring is essentially just a one-dimensional global version of discrete valuation rings, one easily verifies that the class group of a Dedekind ring coincides with its Picard group, thus making it into a nice, functorial invariant, which may be studied and calculated through algebraic, geometric and co homological methods. In view of the success of the use of the class group within the framework of Dedekind rings, one may wonder whether it may be applied in other contexts as well. However, for more general rings, even the definition of the class group itself causes problems.
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