Abstract
New approaches to processing of dense and point images are presented. They are based on the theory of hypercomplex numbers and make use of simplified but reasonably adequate image models that incur no significant loss of information. The advantage of these approaches consists in increased efficiency of decisions made by machine vision systems and in considerable reduction of time needed to arrive at these decisions. The basics of the theory of complex-valued (contour) and quaternion-valued signals are considered. We show how this theory is related to the theory of real-valued signals and identify the problems where hypercomplex signals have advantages over real-valued ones.
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