Gathering and Retaining Visual Information Over Recurring Fixations: A Model

Abstract

We construct a mathematical model indicating the information available to the observer regarding each item in a spatial unit in the visual scene, at any given moment, dependant on previous fixations and eye movement scanpath. Dividing the items in the visual scene into discrete units, two processes affect the amount of information available about each unit at each time: an incremental component and a memory decay component. We assume that extracted information is incremented for a scene unit each time the fixation falls on it and increases as a sigmoid or exponential growth function with subsequent fixations and that information decays exponentially between recurring fixations on a unit. Results show that the amount of available information grows and fluctuates stochastically, varying from unit to unit and from time to time, so that complete information is never reached for the entire scene. Simulations show that the larger the scene, the less information is available, on average, for each scene unit, though more may be available in total, as well as more for favored units. The resulting dynamics of this local available information measure might predict the probability of perceiving a change in stimulation at a corresponding visual unit or its complementary, the probability of change blindness.

Appendices

Appendix 1: Algorithmic Representation of the Model

The principal algorithm of the proposed model is described below. Each variation in the simulation, such as biased probability of fixations and biased decay rate, would impose an appropriate variation on the algorithm.

Appendix 2: Algorithm for Determining Model Parameters Following a Change Detection/Change Blindness Experiment

The following algorithm is designed to output the optimal parameters of the model, which best fit change detection experimental data. The algorithm is based on the observation that the result of each experimental trial is a dichotomy, either detection or miss, while the model predicts the available information, which we assume is directly related to the detection probability. The available information is related to the probability of change detection by some transformation, which is here considered included in the formula for available information so that the available information is measured in units of predicted detection probability. Hence, to compare the experimental results with the model predictions, the algorithm suggests grouping trials according to their ranges of predicted detection probability as obtained by the model, allowing calculation of a single detection probability for the trials in each range (by averaging their results) and comparing this probability with the model predictions. The match between experimental and predicted values will indicate degree of fit of the parameters.

The algorithm works as follows: Part I outputs the detection probabilities for each trial, as calculated by the model (on the basis of the fixation sequence of these trials), corresponding to all permutations of parameters. Part II, the core of the algorithm, calculates the experimental detection probability for the trials that fall in a certain probability range obtained by the model (in Part I) and then calculates the deviations between the experimental results and the model predictions, for each set of parameter permutations and for each bin of probability range. It then calculates the norms of the deviation vectors and outputs the optimal parameters, those with the minimal deviation. This is the output of the algorithm. Actually, Part II could be merged into Part I, but is shown separately for clarity. In general, the algorithm can either be applied separately for each individual observer using only his/her results or applied over all subjects together, pooling all trials. Note also that the parameter bins could be assigned finer values for more precise results.