Studies have shown that the perception of self-motion direction (i.e., heading) from optic flow is consistent with a Bayesian inference account when all attentional resources are allocated to this perception process. These studies generally proposed that the heading perception was a sensory-information driven process. Sun et al. (2024) were the first to demonstrate that attention affected the perception process. Specifically, when the attentional resources allocated to the heading estimation and discrimination task were reduced, both the estimation accuracy and discrimination sensitivity were reduced; additionally, when the attentional focus was biased towards one side of the center of the computer display, the heading estimates were systematically biased towards the attentional focus. Therefore, Sun et al. (2024) demonstrated that heading perception from optic flow was sensory-information and cognition driven process. However, no study was conducted to explore the computational mechanism underlying the effects of attention on the heading estimation from optic flow.
To address the above question, the current study developed a Bayesian inference model to explain the effects of attention on the heading perception from optic flow behaviorally observed in Sun et al. (2024). In the model, we proposed that participants’ heading estimates were derived from a posterior distribution ($p\left(\theta_{l} \mid M\right)$) that is the optimal combination between the prior ($p\left(M \mid 0\right)$) and the likelihood ($p\left(M \mid \theta_{l}\right)$), given as:
$p\left(\theta_{l} \mid M\right) \propto p(M \mid 0) \times p\left(M \mid \theta_{l}\right)$ Equation 1.
where M represents the heading estimate, is the actual heading. According to the previous studies (Saunders & Niehorster, 2010; Xing & Saunders, 2016; Xu et al., 2022), we propose that the likelihood distributions follow a Gaussian distribution, given as:
$p(M \mid 0)=\frac{1}{\sqrt{2 \pi} \sigma_{p}} e^{-\left(\frac{M-0}{\sqrt{2} \sigma_{p}}\right)^{2}}$ Equation 2.
$p\left(M \mid \theta_{l}\right)=\frac{1}{\sqrt{2 \pi} \sigma_{l}} e^{-\left(\frac{M-\theta_{l}}{\sqrt{2} \sigma_{l}}\right)^{2}},$ Equation 3.
In Equations 2 and 3, σp is the standard deviation of prior distribution. σl is the standard deviation of likelihood distribution. Previous studies typically took the discrimination threshold as the standard deviation of likelihood distribution (σl ) (Xing & Saunders, 2016). In Experiment 3 of Sun et al. (2024), they directly evaluated the σl s in the baseline and attention load conditions with the heading discrimination task. Therefore, only the standard deviation of prior distribution σp was free. We firstly developed a Bayesian inference model with the σl given by Experiment 3 to test the efficiency of the model. Following this step, we then set the σl to be free to predict the finding of Experiments 1b, 2a, and 2b in Sun et al. (2024). A Markov Chain, the Monte Carlo (MCMC) sampling method was employed to determine the best value of parameters.
The results showed that our model well explained the effects of attention on heading estimation from optic flow revealed in Sun et al. (2024). Meanwhile, the standard deviation of the likelihood distributions increased with the attentional load and was shifted by the attentional focus: the standard deviations were smaller for the headings close to the attentional focus than those far away from the attentional focus. These were all consistent with the behavioral findings of Sun et al. (2024).
In summary, the current study reveals that the effects of attention on heading estimation from optic flow can be predicted by the Bayesian inference model and attention affects heading perception by potentially modulating the certainties of headings’ internal representations, which increases our understanding of the computational process underlying heading perception from optic flow. It should be noted that our model is developed based on the fact that attention affects the activity of sensory neurons Dubin and Duffy (2007, 2009) that are positively correlated with the likelihood distributions. Next, we should directly build the likelihood distribution based on the tuning function of populational neurons to uncover the neural basis of the computational process, which will help us to understand the heading estimation mechanisms comprehensively.
Key words
attention /
heading perception /
optic flow /
bayesian inference model
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