Modelling the spatial tuning of the Hermann grid illusion

Abstract

Does a physiologically plausible model of the retinal ganglion cell (RGC) receptive field (RF) predict the spatial tuning properties of the Hermann Grid Illusion (HGI)? The spatial tuning of a single intersection HGI was measured psychophysically in normal observers using a nulling technique at different vertical grid line luminances. We used a model based upon a standard RGC RF, balanced to produce zero response under uniform illumination, to predict the response of the model cell to the equivalent range of stimulus conditions when placed in either the 'street' or the 'intersection' of a single element of a Hermann grid. We determined the equivalent of the nulling luminance required to balance these responses and minimise the HGI. The model and the psychophysical data demonstrated broad spatial tuning with similarly shaped tuning profiles and similar strengths of illusion. The line width at the peak of the model tuning function was around twice the model RGC RF centre size. Modelling the psychophysical functions gave RF centre sizes smaller than expected from human anatomical evidence but similar to that suggested by primate physiological evidence. In the model and psychophysically the strength of the illusion varied with the luminance of the vertical grid line when HGI strength was expressed as a Michelson nulling contrast, but this effect was smaller when HGI strength was expressed as a nulling luminance. The shape, width, height and position of the spatial tuning function of the HGI can be well modelled by a RGC RF based model. The broad tuning of these functions does not appear to require a broad range of different cell sizes either in the retina or later in the visual pathway.