A linear sensorimotor transformation accounts for response range-dependent biases in human heading estimation
Authors: Sun Qi , Xu Ling-Hao , Stocker Alan A 
Published: May 2024

Accurate estimation of heading direction from optic flow is a crucial aspect of human spatial perception. Previous 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. Rather we found that they 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 derived a Bayesian observer model to quantitatively account for participants’ estimation behavior. The model assumes an efficient sensory encoding of heading direction according to the natural prior of freely behaving humans. In addition, the model incorporates a response mapping that linearly maps the percept to the reported estimate with a scaling factor that depends on the size of the response range. This perception-action model accurately predicts participants’ estimates both in terms of mean and variance. Our findings underscore that human heading perception follows efficient Bayesian inference; differences in participants reported estimates can be solely attributed to differences in linear mapping from percept to probe response.

Author summary

Humans can estimate the direction of their self-motion (heading) from the visual motion pattern (optic flow) on their retinae generated by their movement. 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 significantly attributed to differences in the response range within which participants were able to move their cursor to report their estimates. Additionally, we introduce a quantitative, Bayesian observer model that accounts for these conflicting bias patterns. The model assumes that perceived heading direction is identical for identical optical flow patterns, yet the reported heading directions are the result of a sensorimotor transformation that linearly maps the percept to the reported estimate. Our results show that participants reported perceptual estimates can be severely affected by sensorimotor 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 sensorimotor transformations that describe the mapping from perception to action.