Discriminant operators: emulation of visual receptive fields for the extraction of transitions in signals and images

The theory of discriminant operators, a robust mathematical framework for the extraction of transitions, gradients, and edges from signals and images in the presence of noise, is introduced. The discriminant operator, which is briefly introduced, is an attempt to emulate the robust information extraction properties of the receptive fields found in the retina and the visual channel leading to the visual cortex. The discriminant operator (or the Θ operator) has differential properties with inherent aggregation. The differentiation properties help to extract the transition and edge information while the aggregation operation provides noise immunity. Also introduced is the differential operator, and then the Θ operator is used in both the continuous and discrete domains. The robustness of the theory is illustrated by means of a set of simulation studies on one-dimensional signals. This theory will be used in the development of robust algorithms for robotics and feedback control problems