Distributional and Temporal Properties of Eye Movement Trajectories in Scene Perception

Distributional and Temporal Properties of Eye Movement Trajectories in Scene Perception Theo Rhodes (trhodes3@ucmerced.edu) Christopher T. Kello (ckello@ucmerced.edu) Bryan Kerster (bkerster@ucmerced.edu) Cognitive and Information Sciences, University of California Merced, 5200 North Lake Rd., Merced, CA 95343 Abstract Sims et al., 2008). Various land and sea creatures have been tracked while foraging for food, and the lengths of paths from one locale to the next are measured. The probability of observing path length d often goes as P(d) ~ d -β , with β ~ 2. The precise formulation of the distribution is often a matter of dispute, but they are generally agreed to be heavy- tailed. The Levy distribution is part of a broader class of heavy-tailed distributions that indicate multiplicative interactions in generating the observed data (i.e. path lengths in this case; Shlesinger, Zaslavsky & Klafter, 1993). These results are relevant to eye movements because animal foraging and scene perception are both search behaviors. Indeed, even memory search has been shown to result in heavy-tailed distributions of “path lengths”, i.e. time intervals between recall events (Rhodes & Turvey, 2007). These results suggest that eye movement trajectories may also exhibit heavy-tailed path length distributions by virtue of being a kind of search behavior. Consistent with this hypothesis, Stephen and Mirman (2010) found that distances between successive eye tracking samples were lognormally distributed in a “visual world paradigm” task (lognormal distributions are heavy-tailed and also associated with multiplicative interactions). This study alone, however, leaves it unclear whether the observed lognormal distributions were due to characteristics of the tasks or stimuli, such as their constrained, repetitive nature. The second body of research to suggest general properties of eye movement trajectories concerns temporal correlations in neural and behavioral activity. It turns that many different measures of both kinds of activities have been found to contain long-range correlations in their intrinsic fluctuations (Kello et al., 2007). These correlations tend to follow a 1/f scaling relation, and 1/f scaling is also a kind of heavy- tailed distribution associated with multiplicative interactions (Van Orden, Holden & Turvey, 2003). Any time series can be expressed in the frequency domain as a set of sine waves of varying amplitudes (power) and frequencies (phase is discarded for this analysis). 1/f scaling describes a time series for which power is related to frequency as P ~ 1/f α , where ideally α ~ 1. Widespread findings of 1/f scaling, across modalities and levels of analysis, suggest that its origins are task-general and domain-general. 1/f scaling has also been found in eye movements, i.e. in fluctuations of repetitive target fixations (Shelhamer, 2005), and in variations within and across standard visual search tasks (Aks, Zelinsky & Sprott, 2002). However, as with heavy-tailed path lengths, these results on Eye movements gather visual information from the environment for various purposes and goals. Spatial patterns of eye movements vary depending on the layout of visual information, and intentions of the observer. However, despite this variability, basic principles of visual information gathering may be reflected in lawful properties of eye movement trajectories that hold across various stimulus and intentional conditions. Two experiments are presented analyzing eye movement trajectories during scene perception across pictures with varying spatial frequency distributions (Expt 1), and across two different task conditions, finding versus counting tasks (Expt 2). Results show that, in all conditions, distributions of saccade amplitudes are heavy- tailed and nearly identical in shape, and fixation fluctuation series are long-range correlated with nearly identical spectral slopes. While a small effect of task intention was found, the broader conclusion is that eye movements during scene perception exhibit general statistical characteristics that models have yet to address. Keywords: Eye movements, scene perception, lognormal distributions, Levy flights, 1/f scaling, long-range correlation. Introduction Research on visual search and scene perception tends to focus on the effects of stimulus factors on eye movements. For instance, the debate over parallel versus serial search hinges on stimulus characteristics of targets, distractors, and the visual field (Triesman & Gelade, 1980). Models of scene perception relate the saliency of visual features and objects in scenes to probabilities of eye fixations (Itti, Koch & Niebur, 1998). By contrast, the basic character of eye movements is mostly taken for granted in research on scene perception, i.e. there are saccades between fixations, and microsaccades and other more fine-grained movements within fixations (Liversedge & Findlay, 2000). These categories are coarse and describe little about the structure of eye movement trajectories, beyond the fact that trajectories will string together periods of small-scale movements (fixations) interspersed with periods of large-scale movements (saccades and pursuits). One might assume that more quantitative statements about eye movements during scene perception will depend on particularities of scenes and intentions of observers. However, two bodies of research suggest otherwise. First, a large body of research on foraging behaviors has shown that search trajectories are nearly universally characterized by heavy-tailed distributions of path segment lengths (e.g.,