Mathematical modeling and computer simulation of the early vision processing stages: a theoretical frame work

This work presents and discusses a series of related mathematical models of the primary visual cortex (V1). The aim is to describe several steps of visual processing in V1, within a unified theoretical framework. The proposed models analyse specific phenomena, both physiological and perceptive, and use different levels of detail in the physiological description, according to the particular cognitive purpose and respecting the modular organization of the visual system. The work starts from the study of visual information processing at a single point of the retina, hypercolumn, (section 2, 3 and 4) and then evolves toward the study of intracortical connectivity in order to process the image in an entire portion of the visual space (section 5, 6, 7 and 8). All models respect the physiological fundamental properties characterizing V1, still providing a good compromise between mathematical/computational simplicity and physiological reliability. First, a model of orientation selectivity, representing a single hypercolumn is presented to understand the characteristic of simple cells to respond preferentially to elongated visual stimuli of a particular orientation. The model is then used to investigate the phenomenon of “Tilt Aftereffect” (TAE): prolonged viewing of an oriented stimulus (adaptation) makes a subsequently viewed stimulus of similar orientation to appear tilted away from the adapting stimulus. Subsequently, the model is temporally characterized in order to explain the direction and velocity selectivity in simple cells, i.e., their preference to respond to stimuli moving to a particular direction with a given velocity. The next step is to extend the model to scrutinize a region of the visual space by handling more hypercolumns and introducing an original model of cortical circuitry. Synapses among hypercolumns are then included in the model to critically approach the genesis of complex cells as well as to assess the role of intracortical synapses in the discrimination between simple and complex cells. In the last step, the proposed architecture is further improved assuming synaptic fields, on the basis of some Gestalt perceptual criteria (contiguity and continuity) to investigate the role of the primary visual cortex in contour extraction and perceptual grouping. The model is finally related with activity from higher visual centres, including two fundamental additional aspects, i.e., multi-scale decomposition and attention. Attention from higher hierarchical levels selects the portion of the image to be scrutinized and sets the appropriate scale. This allows an image to be scrutinized at different levels of detail.