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A linear perception-action mapping accounts for response range-dependent biases in heading estimation from optic flow

Qi Sun,Ling-Hao Xu,Alan A. Stocker

Published 2025 in bioRxiv

ABSTRACT

Accurate estimation of heading direction from optic flow is a crucial aspect of human spatial perception. Previous psychophysical studies have shown that humans are typically biased in their estimates of heading directions, but the reported results are inconsistent. While some studies found that humans generally underestimate heading direction (central bias), others find the opposite, an overestimation of heading direction (peripheral bias). We conducted three psychophysical experiments showing that these conflicting findings do not reflect inherent differences in heading perception but are caused by the different sizes of the response range that participants were allowed to utilize when reporting their estimates. Notably, we show that participants’ heading estimates monotonically scale with the size of the response range, leading to underestimation for small and overestimation for large response ranges. Additionally, neither the speed profile of the optic flow pattern nor the response method (mouse vs. keyboard) significantly affected participants’ estimates. Furthermore, we introduce a Bayesian heading estimation model that can quantitatively account for participants’ heading reports. The model assumes an efficient sensory encoding of heading direction according to a prior inferred from human heading discrimination data. In addition, the model assumes a response mapping that linearly scales the perceptual estimate with a scaling factor that monotonically depends on the size of the response range. This simple perception-action model accurately predicts participants’ estimates both in terms of mean and variance across all experimental conditions. Our findings underscore that human heading perception follows efficient Bayesian inference; differences in participants reported estimates can be parsimoniously explained as differences in mapping percept to probe response. Author summary Humans can estimate the direction of their self-motion (heading) from the associated visual motion pattern (optic flow) on their retinae. While these heading estimates are typically biased, previous studies have found quite conflicting bias patterns despite using very similar optic flow stimuli. Our findings demonstrate that these differences in participants’ reported estimates can be attributed to differences in the response range within which participants were able to move their cursor to report their estimates. We introduce an efficient Bayesian observer model to quantitatively analyze these conflicting bias patterns. The model assumes that perceived heading directions are identical for identical optical flow patterns, yet the reported heading directions are the result of an additional response mapping that linearly maps the percept to the reported estimate. This model fits the data well and demonstrate that participants reported perceptual estimates can be substantially modulated by post-perceptual response transformations, in particular under conditions where they do not receive feedback. Our study is a reminder that psychophysical measurements necessarily provide only an indirect account of perception. Full explanations of such data require the inclusion of appropriate post-perceptual transformations that describe the mapping from perception to action.

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