Abstract
Motivation for the ideas developed in this contribution arise from the perception that the important tasks of object representation, classification and recognition in machine vision need to be released from the strictures inherent in a discrete modeling domain. To this end, a formal language for describing object represented as edges in terms of arcs, parametrized by knot angle, curvature and length, developed earlier (Hadingham, 1988a, 1988b), is now expressed in the context of a novel structure referred to as the arc space. This topological space is shown to have properties important in supporting the above-mentioned machine vision tasks efficiently with respect to both time and space factors. As an example, object generalization/specialization as well as multiscaling operations, which are generally regarded as being crucial to machine vision tasks, are supported in a natural way.
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