Fig 1.
Schematic representation of multiple object tracking task.
(a) Multiple object tracking. Subjects tracked three indicated objects before responding whether or not a probed object was a target. (b) Example trajectories of four objects through virtual space. Dashed lines indicate object trajectories over 1.5s, disks indicate trajectory start and the grey plane indicates the screen. The blue and red lines represent part of the 2D and 3D trajectories, respectively. Trajectories were taken from trials with σx = 4° and σv = 0.2° per frame.
Table 1.
Experimental sessions with σx, σv, and depth conditions.
Fig 2.
Schematic representation of ideal observer MOT model.
White circles indicate the model’s estimate of an object state; black circles indicate their noisy perceptual measurements (indicated by σm). Grey squares indicate the predictions of their future state. represents the process noise variance used for prediction. The initial model estimates are set to the objects’ start position. The model proceeds to track the objects for the duration of the trial. This is accomplished by predicting the future state using the process dynamics and combing this with noisy perceptual measurements to determine the measurement assignments. The assignments are used to estimate the objects’ state. The estimates are used to generate predictions and the process is repeated until the end of a trial. At the end of a trial the model is probed to test if objects were correctly tracked. This was done by drawing a random sample from the position of one object and calculating the probability this sample came from a target or non-target.
Fig 3.
Simplified model illustration.
(A) NE-cd model run on object trajectories for two objects, including confusion of objects. The red and blue dashed lines represent the actual trajectory for two different objects, the green line indicates the model’s position estimate of one object. The vertical black line indicates the time point of the data used in B. (B) Likelihood of a measurement coming from object 1 (blue) and object 2 (red) in the 2D case (left) and 3D case (right). Contour plots represent four slices of the two-dimensional likelihood function, evenly spread from the minimum to maximum likelihoods. Similar likelihoods in one dimension can be disambiguated in the other dimension. (C) Contour plots of predicted state and covariance given the posterior distribution of previous time step (black) for FE (magenta) and NE-cd (cyan) model, NE-cd does not use velocity information in the prediction, leading to biases towards zero velocity and position. Data was generated with σx = 2° and σv = 0.2° per frame using the best fit parameters from the NE-cd model (see Table 2).
Fig 4.
Accuracy data from tracking experiment.
Data and fitted psychometric curves for a single subject (left) and group data (right). Data points indicate percentage of correct responses. Error bars indicate 1 standard error calculated across subjects. Shaded areas indicate 1 standard error of psychometric curves across subjects. Dashed lines indicate σv value for 75% correct performance used for comparison across conditions.
Fig 5.
Distance and depth interaction.
Interaction between depth and distance for the σv value required for 75% correct performance in 2D and 3D conditions for the different models. Solid lines indicate 3D conditions, dashed lines the 2D conditions, black lines indicate data and the colors represent model predictions (Blue: FE, green: NE-cd, orange: NE-id and yellow: NV). Error bars indicate one standard error.
Fig 6.
Data points indicate percentage of correct responses for this stimulus combination. FE is full extrapolation model, NE-cd is the no extrapolation with correct dynamics model, NE-id is the no extrapolation with incorrect dynamics model and NV is no velocity model. Blue and red lines indicate percentage correct predictions for 2D and 3D conditions, respectively. Error bars indicate one standard error.
Table 2.
Maximum Likelihood parameters and quality of fit for the four models.