Linking minds and brains.

When I first came across William James' dictum that " … this sense of sameness is the very keel and backbone of our thinking," I thought he had foreseen the importance of cross-correlation in the brain, and told myself to find out how he had reached this conclusion. When I finally did this a year or two ago, I slowly came to realize that I had completely misunderstood him; from the full quote it is absolutely clear that his dictum cannot be referring to the process by which a cortical simple cell responds selectively to the orientation of features in a visual image, as I had originally supposed. If one translates the original dictum into two more prosaic modern versions, his version would say: "Our minds could not think at all without neural circuits in our brains that compute auto-correlations," but in my mistaken interpretation the last word would be "cross-correlations.

Perceived motion is influenced by random dynamic information.

Distortions of the local spatial-frequency power spectrum caused by motion blur may be used by the visual system to improve motion analysis (e.g., Barlow and Olshausen, 2004 Journal of Vision 4415-426).

Cross- and auto-correlation in early vision.

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.

Convergent evidence for the visual analysis of optic flow through anisotropic attenuation of high spatial frequencies.

Photoreceptors strongly attenuate high temporal frequencies. Hence when an image moves, high spatial frequency components are lost if their direction of modulation coincides with the direction of movement, but not if it is orthogonal. The power spectra of natural images are remarkably consistent in having a 1/f 2 falloff in power in all directions.