Body-relative horizontal-vertical anisotropy in human representations of traveled distances

Abstract

A growing number of studies investigated anisotropies in representations of horizontal and vertical spaces. In humans, compelling evidence for such anisotropies exists for representations of multi-floor buildings. In contrast, evidence regarding open spaces is indecisive. Our study aimed at further enhancing the understanding of horizontal and vertical spatial representations in open spaces utilizing a simple traveled distance estimation paradigm. Blindfolded participants were moved along various directions in the sagittal plane. Subsequently, participants passively reproduced the traveled distance from memory. Participants performed this task in an upright and in a 30° backward-pitch orientation. The accuracy of distance estimates in the upright orientation showed a horizontal-vertical anisotropy, with higher accuracy along the horizontal axis compared with the vertical axis. The backward-pitch orientation enabled us to investigate whether this anisotropy was body or earth-centered. The accuracy patterns of the upright condition were positively correlated with the body-relative (not the earth-relative) coordinate mapping of the backward-pitch condition, suggesting a body-centered anisotropy. Overall, this is consistent with findings on motion perception. It suggests that the distance estimation sub-process of path integration is subject to horizontal-vertical anisotropy. Based on the previous studies that showed isotropy in open spaces, we speculate that real physical self-movements or categorical versus isometric encoding are crucial factors for (an)isotropies in spatial representations.

Keywords: Anisotropy; Body-centered; Horizontal; Motion simulator; Traveled distances; Vertical.

Fig. 1

a Traveled distance estimation task was used in this experiment. Participants perceived two consecutive translational movements (target and test). The task was to indicate with a button press during the test translation when the participants perceived themselves to have traveled the same distance of the target translation. Participants heard sound beeps indicating the start of the target and test translation as well as the button press and the end of the trial. b Motion profiles for the target and test translations of Experiment 1. The left plot shows an example profile for a target distance of 1.1 m. The right plot shows the profile that was used for all the test translations

Fig. 2

Experiment used two body orientations: upright and 30° backward-pitch (depicted by the tilted cabin and the dashed arrow in the right panel). In each condition, we used 12 different translation directions in the sagittal plane, varying from 0° (forward translation) to ± 180°, in ± 30° steps, as depicted at the periphery of the circle. The solid arrows represent the  earth-centered coordinate system. Participants carried out all trials for one body orientation condition first, before moving to the respective other condition

Fig. 3

a MPI Cable Robot Simulator. b Participants were sitting in the seat mounted on top of the cabin platform. Participants were blindfolded and secured with seat belts. White noise played through the built-in speakers in the helmet masked auditory cues from the simulator, a taped ski-mask prevented visual motion cues. Fans mounted to the cabin were used to mask the airstream cues on hand, arm, and face caused by the motions. A HANS device protected participants from head and neck injuries. Participants held a button device, which they used to indicate traveled distances

Fig. 4

Panels show exemplary accuracy patterns for the isotropy model (a) and the four anisotropy models (b–e) tested in this study. The distance of the dots from the center of the plot represents the magnitude of estimation error. Smaller errors are shown for forward/backward translations, larger errors for upward and downward translations. The arrows represent the increase in the number of parameters and how the models are based on each other

Fig. 5

Example of body-centered (right panel) and earth-centered (middle panel) error patterns as a function of translation direction. In the left panel, in which the posture is upright, an exemplary horizontal–vertical anisotropy error pattern is shown. In the right panel, an exemplary body-centered pattern for the backward-pitch orientation is shown. The pattern is the same as in the upright condition but rotated by 30° (as the body). Hence, less error is shown for body-related forward translations. In contrast, in the middle panel, the pattern did not rotate with the body (the error pattern is earth-centered regardless of the body orientation), and therefore, less error is shown for the earth-centered forward translation

Fig. 6

Absolute error (in meter) in the traveled distance estimation task as a function of translation direction in the sagittal plane (12 directions between − 150° and 180° meter in 30° steps). Zero degrees was a forward translation, 90° an upward translation. Error bars display standard errors of the mean

Fig. 7

Absolute error (in meter) in the traveled distance estimation task as a function of body orientation (upright and backward-pitch) and translation direction in the sagittal plane. The left plot shows the same data as presented in Fig. 6. The data for the 30° backward-pitch condition are displayed twice. In the middle plot, it is shown in an earth-centered coordinate system. In the right plot, the same data are presented in a body-centered reference frame (the data points were simply rotated counterclockwise by − 30°). Both types of encoding of the data acquired in the backward-pitch condition were correlated with the data of the upright condition to test for a body or earth-centered anisotropy

Fig. 8

a Signal-to-noise ratios for the target and test translations of the experimental trials for both body orientations as a function of translation direction. b Absolute difference in RMS of the stimulus noise between the target and test translations across translation directions. The solid line indicates the lowest calculated differential threshold for accelerations in the current literature across the translation directions (obtained from Naseri and Grant ; Nesti et al. 2014a)