Fractional discriminant functions: emulation of real-index-order receptive fields for vision systems

Extraction of transitions and edge information from signals and visual images in the presence of noise is an important class of problems in image processing. Biological visual systems posses some robust neuro-morphological functions for information abstraction. The complex architecture of the neural elements from the retina to the visual cortex are organized into receptive fields. Discriminant functions are further extended into a family of fractional discriminant functions based on the notion of fractional D operators. This paper presents the theory of fractional discriminant functions Θ^ν[ξ] which attempt to emulate the biological receptive field functionality. It employs Θ[ξ] functions for the enhancement of various attributes of images which require human intervention