Rolling Motion Along an Incline: Visual Sensitivity to the Relation Between Acceleration and Slope

Abstract

People easily intercept a ball rolling down an incline, despite its acceleration varies with the slope in a complex manner. Apparently, however, they are poor at detecting anomalies when asked to judge artificial animations of descending motion. Since the perceptual deficiencies have been reported in studies involving a limited visual context, here we tested the hypothesis that judgments of naturalness of rolling motion are consistent with physics when the visual scene incorporates sufficient cues about environmental reference and metric scale, roughly comparable to those present when intercepting a ball. Participants viewed a sphere rolling down an incline located in the median sagittal plane, presented in 3D wide-field virtual reality. In different experiments, either the slope of the plane or the sphere acceleration were changed in arbitrary combinations, resulting in a kinematics that was either consistent or inconsistent with physics. In Experiment 1 (slope adjustment), participants were asked to modify the slope angle until the resulting motion looked natural for a given ball acceleration. In Experiment 2 (acceleration adjustment), instead, they were asked to modify the acceleration until the motion on a given slope looked natural. No feedback about performance was provided. For both experiments, we found that participants were rather accurate at finding the match between slope angle and ball acceleration congruent with physics, but there was a systematic effect of the initial conditions: accuracy was higher when the participants started the exploration from the combination of slope and acceleration corresponding to the congruent conditions than when they started far away from the congruent conditions. In Experiment 3, participants modified the slope angle based on an adaptive staircase, but the target never coincided with the starting condition. Here we found a generally accurate performance, irrespective of the target slope. We suggest that, provided the visual scene includes sufficient cues about environmental reference and metric scale, joint processing of slope and acceleration may facilitate the detection of natural motion. Perception of rolling motion may rely on the kind of approximate, probabilistic simulations of Newtonian mechanics that have previously been called into play to explain complex inferences in rich visual scenes.

Keywords: Bayesian; gravity; internal models; mental simulations; virtual reality.

FIGURE 1

Experimental set-up and 3D visual scenario.

FIGURE 2

Experimental design for Experiment 1 and 2.

FIGURE 3

Experiment 1: Incline tilt progression from the starting incline tilt 𝜃_i,s to the chosen incline tilt in a representative subject (D.P.) as a function of the number of steps in each condition. Colored traces in each panel are the 15 repetitions × 3 motion durations of each condition.

FIGURE 4

Sagittal view of the inclined plane (long black line) and ball (in green) in all experimental conditions for ball motion duration equal to 0.6 s. The ball is represented twice on the incline, at start position and at incline end. The black ball diameter is orthogonal to the line between ball center and the midpoint between the eyes. Blue and red lines delimit the angular diameter of the ball in the start position and at incline end, respectively, when the viewpoint is the midpoint between participant’s eyes.

FIGURE 5

Time derivative of the angular gap ψ between the instantaneous position of ball center, the midpoint between the eyes and ball center at incline end for all experimental conditions and motion durations. Blue, red and yellow traces denote ψ derivatives (multiplied by –1) for motion duration equal to 0.5, 0.6, and 0.7 s respectively.

FIGURE 6

Dilation speed (rate of ball image expansion) for all experimental conditions and motion durations (blue, red, and yellow traces denote dilation speed for motion duration equal to 0.5, 0.6, and 0.7 s respectively). γ is the angle the rolling ball subtends at the midpoints between participant’s eyes (i.e., the angular diameter of the ball when the viewpoint is the midpoint between participant’s eyes).

FIGURE 7

Experiment 1: Distribution histograms of the responses provided after exploration (pooled over participants) for each ball acceleration a_b (i.e., slope 𝜃_b). Abscissae: incline tilt 𝜃_i for which motion appeared as the most natural for a given a_b (or slope 𝜃_b). Ordinates: number of responses. Red bars: distribution medians; blue bars: ideal correct response. In left, middle, right panels the data are plotted for slope 𝜃_b (TARGET incline) equal to 19°, 39°, or 60°, respectively.

FIGURE 8

Experiment 1: CDFs estimated by the GLMM for each participant (gray) and for the population (red). The blue bar represents the distance between the PSE and the ideal correct response.

FIGURE 9

Experiment 2: Progression from the START condition to the chosen motion in a representative subject (C.C.). Colored traces in each panel are the 15 repetitions × 3 motion durations of each condition.

FIGURE 10

Experiment 2: Distribution histograms of the responses (pooled over participants) for each incline tilt 𝜃. Abscissae: 𝜃_b for which motion appeared as the most natural for the given incline tilt 𝜃_i (TARGET incline). Ordinates: number of responses. Red bars: ideal distribution medians; blue bars: correct response.

FIGURE 11

Experiment 2: CDFs estimated by the GLMM for each participant (gray) and for the population (red). The blue bar represents the distance between the PSE and the ideal correct response.

FIGURE 12

Experiment 3: Distribution histograms of the responses (pooled over participants) for each ball acceleration a_b (i.e., slope 𝜃_b). Abscissae: incline tilt for which motion appeared as correct for a given a_b (i.e., slope 𝜃_b). Ordinates: number of responses. Red bars: distribution medians; blue bars: ideal correct response.

FIGURE 13

Experiment 3: Box-and-whisker plots of all subject responses. Bottom and top of the boxes correspond to the lower and upper quartile, respectively, and define the IQR. The red line in each box is the median between subjects’ median response. Results from all repetitions of any subjects have been pooled for each condition. The lower and upper ends of the whiskers correspond to the smallest and largest datum within 1.5 IQR.