Apparent movements induced by luminance modulations: a model study

When the receptive-field profiles of the different units in the primary visual cortex are described by a series of different functions which are given by a Gaussian distribution and its first, second, and so on, spatial derivatives, a full analysis of the input-output processing of these units (under the assumption of linearity for small signals) can be achieved for a wide variety of optical stimuli consisting of closely adjacent fields modulated independently in intensity. Once the input-output relationship for one particular unit has been obtained, it is possible to calculate in a straightforward manner the spatial representation of the stimulus pattern in a two-dimensional distribution of such units. Investigations are reported into how a stimulus pattern (a dark or bright bar between two fields modulated in illuminance) is represented in a hierarchical structure of such layers of units, each layer containing just one type of receptive-field profile from the Gaussian family of derivatives. It is shown that if a visual percept is associated with the behaviour of the extrema or zero-crossings of the representations in the first few layers of such an architecture, a complete description can be given of the experimental results obtained by Gregory and Heard in their psychophysical experiments on illusory movement perception induced by luminance intensity modulations.