Quantitative Bayesian model of human visual motion perception

A A Stocker and E P Simoncelli

Published in Computational and Systems Neuroscience (CoSyNe), Mar 2004.

This paper has been superseded by:
Noise characteristics and prior expectations in human visual speed perception
A A Stocker and E P Simoncelli.
Nature Neuroscience, vol.9(4), pp. 578--585, Apr 2006.

Human visual motion perception has been demonstrated to be non-veridical. Psychophysical experiments have shown that the perceived motion of visual stimuli clearly depends on their contrast, with low contrast stimuli being perceived to move slower than high contrast ones. A probabilistic Bayesian model has been proposed that qualitatively accounts for a large amount of the reported data in the literature [Weiss, Simoncelli and Adelson; Motion illusions as optimal percepts; Nature Neuroscience 5(6):598-604, 2002]. Formulated as the maximum a posterior estimate $\hat{\vec{v}}$ of visual motion $\vec{v}$ given its measurement $\vec{m}$, \begin{equation} \hat{\vec{v}}\ = \ \mbox{max}[\underbrace{p(\vec{v}|\vec{m})}_{posterior}\ \propto \ \underbrace{p(\vec{m}|\vec{v})}_{likelihood} \ \underbrace{p(\vec{v})}_{prior}]\ , \end{equation} the prior reflects the model's assumption that humans apply a priori information to estimate visual motion, namely that they encounter slow visual motion more often than fast one. Clearly, the model's prediction depends crucially on the exact form of the likelihood and the prior. Unfortunately, it is very difficult to measure the prior or the system's likelihood directly. Thus in principle, many different combinations of likelihood and prior could explain the same motion estimate. However, here we show that with an appropriate psychophysical experiment we are able to constrain the form of the likelihood and the prior individually.

We measured the \emph{contrast dependent shift of perceived speed} and \emph{speed discrimination thresholds} with a simple speed-matching experiment. While the shift of perceived speed is determined by the shift of the maximum of the posterior, the discrimination threshold is dominantly dertermined by the width of the posterior. Width and shift are differently affected by the prior and the likelihood from which we can conclude that

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