This repository contain scripts to run the experiment and to do the follow-up analyses. These scripts simulate an observer's forwarding self-motion through a crowd of point-light walkers. In each trial, self-motion simulation has a different velocity and traveled distance. Point-light walkers ressemble a crowd of humans that either approaches, leaves, or remains static. Participants' task is to carefully watch the simulation, and estimate the traveled distance after each trial by placing a walker on a line to the approached distance in the world. The following video shows one trial as example:

These scripts are optimized for MatLab 2021b with Psychtoolbox (http://psychtoolbox.org/download.html) and OpenGL add-on libraries from the Psychtoolbox. So what needs to be installed on you computer are Matlab and Psychtoolbox. If you want to run the analyses for your data, please install R with RStudio and Python with Spyder.

Download all the files and add them to your Matlab folder. Within your Matlab folder, create a subfolder names "functions". Move the script "geFrustum" to this subfolder. Add the Python and R files to your respective folder.

• github_travel_distance_0_16.m: This is the main script creating the scene.
• getFrustum.m: this script generates frustum data. The main script uses this script to do some calculations. No need to adapt this script.
• extrapolatewalkerdata.m: we extrapolated walker motion data (sample_walker3) to generate slightly slower and faster articulating walkers. The matching translation speed is generated in the main script. You do not need to do anything with that script. If you want to, you can extrapolate your own walker motion speeds with that script. The main script does not use this script.
• sample_walker3: motion data for point_light walker with normal speed
• sample_walker_0.8: motion data for point_light walker with slower speed
• sample_walker_1.2: motion data for point_light walker with faster speed
• streifen.rgb.tiff: ground type stripes
• gravel.rgb.tiff: ground type gravel
• leaky fit.py: Python script to model the data according to the leaky path fit by Lappe et al. (2007)
• descriptive analysis distance estimates.R: R script to run descriptive analysis of distance estimates and to create plots
• inferential analysis leaky.R: R script to analyse and plot the leaky model parameters from the leaky fit.py sript.

Open the script in Matlab and click on 'run'. Matlab automatically requires your input in the command line, and subsequently asks questions. Enter the participant id and further information subsequently. When done, Psychtoolbox automatically opens a window and runs the script in that window. You will see the stimulus presentation. After each presentation, you are required to estimate your traveled distance by moving the mouse along the vertical axis. Confirm your answer by pressing the left mouse buttom. Subsequently, the next trial starts. The script finishes when all trials are done.

You want to see the true traveled distance? Just change show_true_distance (line 15) in the script from false to true:

show_true_distance = true; %show true traveled distance. 

We apply point-light walkers to operationalize human motion. These walkers originated from the motion-tracking data of a single walking human (de Lussanet et al., 2008). Each walker consists of 12 points corresponding to the ankles of a human body (knee, hip, hands, elbow, and shoulder joints).

For the experiment, we create a crowd of 30 colored walkers. Each walker starts individually with a random selection starting position in the gait cycle. The group appears collectively as static, approaching or leaving the observer. Because point-light walkers are ambiguous in their facing direction when static, we only show static walkers facing the observer (Vanrie et al., 2004).

In real-life scenarios, humans differ in their translation, and thus, articulation speed (Masselink & Lappe, 2015). To keep the scene close to reality, we manipulate the articulation and translation speed of the walkers. The original motion-tracking data have a matching translation speed of 0.013 (0.6m/s.). By linear interpolation (see Matlab Skript extrapolatewalkerdata.m), we create two more motion files with either 0.8 (slower) or 1.2 times (faster) the original articulation speed. Translation speed is adjusted accordingly. The three different articulation and translation speeds are divided equally among the 30 point-light walkers. The average walker speed remains constant at 0.013 at any trial. Randomized position in depth combined with a randomized starting position in the gait cycle let the crowd appear naturally.

The walkers' positions are uniformly sampled in the frustum. We limit their position in depth to 26 m maximum so that walkers appear at an adequate sight. This limited in-depth position is beneficial for leaving crowds combined with slow observer speeds. When walkers disappear from the frustum, we replace them at 23 m in depth and correct for the movement speed of the observer. To avoid collisions with static or approaching walkers, we place the walkers 1.5 m each left and right past the observer. Such a replacement creates a kind of tunnel to form through the crowd. Shortly before the end of the trial (maximum 600 frames left), walkers disappearing from the frustum can be placed within the tunnel without any risk of collision. This setting does not reveal any information about travel distance or travel velocity. But it makes the scene look realistic. Leaving crowds are located without such replacements within the frustum.

The experimental world spans over 60 m scene depths. We placed a visible ground plane at eye height (1.60 m). Its appearance could either be structured (gravel) or unstructured (stripes in the motion direction). The gravel ground provides independent optic flow, while the stripes ground neither conveys any structure nor optic flow.

We simulate observers' forwarding self-motion towards a crowd of point-light walkers. Travel distances are chosen by Lappe et al. (2007): 4.00 m, 5.66 m, 8.00 m, 11.31 m, 16.00 m, and 22.63 m. All distances are traveled at 0.013, equal to the average translation speed of the crowd. In addition, short distances (4.00 m, 5.66 m, 8.00 m) are simulated more slowly at 0.0104, which is half the crowd's average speed. For long distances (11.31 m, 16.00 m, 22.63 m), we choose a simulation speed of 0.0154, or 1.5 faster than the crowd.

We combine three walker conditions (approaching vs. leaving vs. static), two ground conditions (gravel vs. stripes) with six traveled distances (4.00 m, 5.66 m, 8.00 m, 11.31 m, 16.00 m, 22.63 m), and two different self-motion speeds (equally fast as the walkers vs. unequally fast as the walkers). This combination of variables results in 72 trials. We repeat the stimulus combinations five times giving 360 in total.

Participants' task is to reproduce the traveled distance by placing a point-light walker on a blue line from a red starting line (at 2.624 m) as far as they went before ('adjust-to-target'-paradigm: Lappe et al. 2007; Lappe & Frenz, 2009). Moving the walker in-depth immediately rescales it according to its position in depth. This rescaling should help participants receive a better depth impression, thus, increasing estimation accuracy.

Depending on travel distance and velocity, a trial lasts between 5 and 28 seconds. To avoid fatigue effects we divide the experiment into four sessions on two days. So when entering the session number, make sure to choose a number between 1 and 4. Trials are blocked according to the ground type (gravel vs stripes). We assigned participants alternatingly to start their session with either the gravel or stripes ground type.

The analysis includes descriptive and inferential analysis in R, and computational modeling in Python.

Lappe et al. (2007) developed a path integration model with leaky integration over the spatial motion extent to explain travel distance estimate and its increasing misestimation over long travel distances. According to the leaky path integration model (Lappe et al., 2007), two parameters influence the instantaneous change of distance: the gain factor k and the leak factor α. The gain factor increments the integrated distance proportionally to the distance of motion while the leak rate reduces the perceived distance as the motion goes on. Because of the leak, longer distances lead to more decrease in the current distance estimate such that the extent of underestimation increases.

Leaky integrator model describing the perceived distance p(x) by the gain factor k and α

As our analysis strategy, we decided to fit our data non-linearly and then run traditional inferential analyses with the calculated parameters from our fit. From previous studies (Lappe et al., 2007) we know that there are biases in the path integration of traveled distance and that these biases do not behave linearly. Due to this evidence of non-linear biases, we decided to fit our data non-linearly according to their model. The gain factor k describes to what extent physical and psychological distances are congruent. Values around 1 indicate perfect congruency. Values above 1 indicate distance overestimation while values smaller than 1 denote distance underestimation. The leakage parameter α measures the extent to which the perceived traveled distance is reduced. As a consequence of α larger than 0, the perceived traveled distance while moving becomes disproportionately smaller. Please note that even if data could be fitted normally, the leaky path integration model will set α to 0, resulting in a linear fit. We consider this flexibility a plus to describe and analyze our data as accurately and validly as possible.

The python script now fits the model to the data and calculates α and k per condition. Further, the script creates plots with raw data and their respective leaky model fit. The figure below shows some fitted data as example. The dotted line represents veridical performance:

Descriptive analysis of the distance gauges includes descriptive values (mean, median and standard deviation), several data checks, and plots.

Strategy: The inferential analyses we focussed on the leakage parameter α and gain factor k. The data structure is based on a within-subject design with repeated measurements and two categorical independent variables with several levels. As an appropriate procedure, we perform an analysis of variance by applying a mixed-modeling framework (LMM). LMM benefits from higher flexibility, accurateness, and powerfulness for repeated-measures data (Kristensen & Hansen, 2004; Jaeger, 2008) than traditional variance analyses. 

Procedure: We analyzed separately, whether the magnitude of k or α depends on the walker combinations and the ground types. We fitted LMM (estimated using restricted maximum likelihood criterion (REML) and nloptwrap optimizer) with random intercept and constant slope for participants. This model predicted k respectively α the interaction of ground types and walker combinations.

The R script also plots the magnitude of α and k. The figure below presents the modeled data from python (left) and the visualized inferential analysis of gain parameter and leak rate: