Stimulus orientation in the primary visual cortex of primates and carnivores is mapped as iso-orientation domains radiating from pinwheel centres, where orientation preferences of neighbouring cells change circularly. Whether this orientation map has a function is currently debated, because many mammals, such as rodents, do not have such maps. Here we show that two fundamental properties of visual cortical responses, contrast saturation and cross-orientation suppression, are stronger within cat iso-orientation domains than at pinwheel centres. These differences develop when excitation (not normalization) from neighbouring oriented neurons is applied to different cortical orientation domains and then balanced by inhibition from un-oriented neurons. The functions of the pinwheel mosaic emerge from these local intra-cortical computations: Narrower tuning, greater cross-orientation suppression and higher contrast gain of iso-orientation cells facilitate extraction of object contours from images, whereas broader tuning, greater linearity and less suppression of pinwheel cells generate selectivity for surface patterns and textures.