There are two prevailing explanations for the foveal deficit in texture segmentation reported in previous works. One is based on the spatial and temporal properties of the stimuli, which means in terms of physiology a strong contribution of the Magno-channel. The other one is purely spatial and assigns filters of different bandwidths to each eccentricity in the visual field. We have challenged the first explanation experimentally by using isoluminant stimuli. The central performance drop persisted although the Magno-channel is known to respond weakly to stimuli with low luminance contrast. Therefore, we agreed with the spatial explanation. But instead of the abstract filter theories from previous works we propose a computational neural model assuming local lateral interactions in a cortical map model. The psychophysical performance measures could be directly related to geometric properties of the primary visual cortex concerning its mapping geometry and its intrinsic interaction width. Our model accounts quantitatively for our own psychophysical data as well as for others from literature. In general, we claim that the high foveal retino-cortical magnification maps texture elements too far away from each other for being compared by local processes.