Bayesian Modeling of Motion Perception using Dynamical Stochastic Textures

TL;DR

This paper develops a biologically plausible Bayesian model of motion perception using dynamic textures, deriving multiple formulations including solutions to stochastic PDEs, and validates it through psychophysical experiments on human speed perception.

Contribution

It introduces a comprehensive Bayesian framework for motion perception based on dynamic textures, with novel formulations and real-time synthesis capabilities.

Findings

Perceived speed is positively biased by spatial frequency increments.

Bayesian observer model accounts for perceptual biases with a frequency-dependent likelihood width.

Dynamic texture likelihood width decreases with increasing spatial frequency.

Abstract

A common practice to account for psychophysical biases in vision is to frame them as consequences of a dynamic process relying on optimal inference with respect to a generative model. The present study details the complete formulation of such a generative model intended to probe visual motion perception with a dynamic texture model. It is first derived in a set of axiomatic steps constrained by biological plausibility. We extend previous contributions by detailing three equivalent formulations of this texture model. First, the composite dynamic textures are constructed by the random aggregation of warped patterns, which can be viewed as 3D Gaussian fields. Secondly, these textures are cast as solutions to a stochastic partial differential equation (sPDE). This essential step enables real time, on-the-fly texture synthesis using time-discretized auto-regressive processes. It also allows for the derivation of a local motion-energy model, which corresponds to the log-likelihood of the probability density. The log-likelihoods are essential for the construction of a Bayesian inference framework. We use the dynamic texture model to psychophysically probe speed perception in humans using zoom-like changes in the spatial frequency content of the stimulus. The human data replicates previous findings showing perceived speed to be positively biased by spatial frequency increments. A Bayesian observer who combines a Gaussian likelihood centered at the true speed and a spatial frequency dependent width with a "slow speed prior" successfully accounts for the perceptual bias. More precisely, the bias arises from a decrease in the observer's likelihood width estimated from the experiments as the spatial frequency increases. Such a trend is compatible with the trend of the dynamic texture likelihood width.