Cross- and auto-correlation in early vision

Abstract

Neurons that respond selectively to the orientation of visual stimuli were discovered in V1 more than 50 years ago, but it is still not fully understood how or why this is brought about. We report experiments planned to show whether human observers use cross-correlation or auto-correlation to detect oriented streaks in arrays of randomly positioned dots, expecting that this would help us to understand what David Marr called the ‘computational goal’ of V1. The streaks were generated by two different methods: either by sinusoidal spatial modulation of the local mean dot density, or by introducing coherent pairs of dots to create moiré patterns, as Leon Glass did. A wide range of dot numbers was used in the randomly positioned arrays, because dot density affects cross- and auto-correlation differently, enabling us to infer which method was used. This difference stems from the fact that the cross-correlation task is limited by random fluctuations in the local mean density of individual dots in the noisy array, whereas the auto-correlation task is limited by fluctuations in the numbers of randomly occurring spurious pairs having the same separation and orientation as the deliberately introduced coherent pairs. After developing a new method using graded dot luminances, we were able to extend the range of dot densities that could be used by a large factor, and convincing results were obtained indicating that the streaks generated by amplitude modulation were discriminated by cross-correlation, while those generated as moiré patterns were discriminated by auto-correlation. Though our current results only apply to orientation selectivity, it is important to know that early vision can do more than simple filtering, for evaluating auto-correlations opens the way to more interesting possibilities, such as the detection of symmetries and suspicious coincidences.