Causal Inference in the Perception of Verticality

Abstract

The perceptual upright is thought to be constructed by the central nervous system (CNS) as a vector sum; by combining estimates on the upright provided by the visual system and the body’s inertial sensors with prior knowledge that upright is usually above the head. Recent findings furthermore show that the weighting of the respective sensory signals is proportional to their reliability, consistent with a Bayesian interpretation of a vector sum (Forced Fusion, FF). However, violations of FF have also been reported, suggesting that the CNS may rely on a single sensory system (Cue Capture, CC), or choose to process sensory signals based on inferred signal causality (Causal Inference, CI). We developed a novel alternative-reality system to manipulate visual and physical tilt independently. We tasked participants (n = 36) to indicate the perceived upright for various (in-)congruent combinations of visual-inertial stimuli, and compared models based on their agreement with the data. The results favor the CI model over FF, although this effect became unambiguous only for large discrepancies (±60°). We conclude that the notion of a vector sum does not provide a comprehensive explanation of the perception of the upright, and that CI offers a better alternative.

An assessment of Causal Inference in visual-inertial traveled distance estimation

“…This variability could be interpreted as a sign that individuals are wired differently with respect to processes governing the formation of perceptions. However, we believe this to be unlikely: a similar variability has been reported in recent studies on the applicability of CI for perception of heading [20,21] and verticality [22]. As in the present study, it was found that different models were preferred over CI in individual cases, although in these studies the FF model was preferred in the majority of cases.…”

“…This formulation reflects the Model Averaging CI strategy (e.g., [18,28,29]). It is similar to earlier work by our group on heading estimation [20,30,21] and the perception of verticality [22]. The probability of a common cause given the sensory estimates is .…”

“…In previous work, we obtained evidence that the CNS performs CI in the estimation of heading of visual-inertial horizontal linear translations [20,21], and in the estimation of verticality [22]. Here, we extend the assessment of the applicability of the CI model from the qualitative domain of heading and orientation [23] to the quantitative domain of traveled distance.…”

“…The models presented here are Bayesian formulations of prominent theories on how responses arise from multisensory stimulation. The models and their descriptions are adapted from [22], but include different models of sensory estimates and are expanded to more explicitly address the different stages of response generation. We postulate that stimuli s yield sensory estimates e according to estimate generating functions (EGF); percepts p are constructed from these estimates according to percept generating functions (PGF); and the percepts are subsequently converted into responses r via response generating functions (RGF).…”

“…Due to the expression for Pr(C | e V , e I ) in A(e V , e I ) and B(e V , e I ), there is no closed-form solution to (50). This can be dealt with by linearizing A(e V , e I ) and B(e V , e I ) at e V = e V 0 =s V , e I = e I0 = µ I (s I ), as described in [22]:…”