Characterizing and modeling visual persistence, search strategies and fixation times

Abstract

To gather information from the world around us, we move our eyes constantly. In different occasions we find ourselves performing visual searches, such as trying to find someone in a crowd or a book in a shelf. While searching, our eyes “jump” from one location to another giving rise to a wide repertoire of patterns, exhibiting distinctive persistent behaviors. Initially, by focusing on saccadic directions and intersaccadic angles, we disclose that the probability distributions of these measures show a clear preference of participants towards a reading-like mechanism (geometrical persistence), whose features and potential advantages for searching/foraging are discussed.We then perform a Multifractal Detrended Fluctuation Analysis (MF-DFA) over the time series of jump magnitudes in the eye trajectory and find that it exhibits a typical multifractal behavior arising from the sequential combination of saccades and fixations. By inspecting the time series composed of only fixational movements, our results reveal instead a monofractal behavior with a Hurst exponent H ∼ 0.7, which indicates the presence of long-range power-law positive correlations (statistical persistence). Motivated by the experimental findings from the study of the distribution of the intersaccadic angles, we developed a simple visual search model that quantifies the wide variety of possible search strategies. From our experiments we know that when searching a target within an image our brain can adopt different strategies. The question then is which one does it choose? We present a simple two-parameter visual search model (VSM) based on a persistent random walk and the experimental inter-saccadic angle distribution. The model captures the basic observed visual search strategies that range from systematic or reading-like to completely random. We compare the results of the model to the experimental data by measuring the space-filling efficiency of the searches. Within the parameter space of the model, we are able to quantify the strategies used by different individuals for three searching tasks and show how the average search strategy changes along these three groups. Even though participants tend to explore a vast range of parameters, when all the items are placed on a regular lattice, participants are more likely to perform a systematic search, whereas in a more complex field, the search trajectories resemble a random walk. In this way we can discern with high sensitivity the relation between the visual landscape and the average strategy, disclosing how small variations in the image induce strategy changes. Finally, we move beyond visual search and study the fixation time distributions across different visual tasks. Fixation times are commonly associated to some cognitive process, as it is in this instances where most of the visual information is gathered. However, the distribution for the fixation durations exhibits certain similarities across a wide range of visual tasks and foveated species. We studied how similar these distributions are, and found that, even though they share some common properties, such as similar mean values, most of them are statistically different. Because fixations durations can be controlled by two different mechanisms: cognitive or ocular, we focus our research into finding a model for the fixation times distribution flexible enough to capture the observed behaviors in experiments that tested these concepts. At the same time, the candidate function to model the distribution needs to be the response of some very robust inner mechanism found in all the aforementioned scenarios. Hence, we discuss the idea of a model based on the microsacaddic inter event time statistics, resulting in the sum of Gamma distributions, each of these related to the presence of a distinctive number of microsaccades in a fixation.