TY - JOUR A1 - Barthelme, Simon A1 - Trukenbrod, Hans Arne A1 - Engbert, Ralf A1 - Wichmann, Felix A. T1 - Modeling fixation locations using spatial point processes JF - Journal of vision N2 - Whenever eye movements are measured, a central part of the analysis has to do with where subjects fixate and why they fixated where they fixated. To a first approximation, a set of fixations can be viewed as a set of points in space; this implies that fixations are spatial data and that the analysis of fixation locations can be beneficially thought of as a spatial statistics problem. We argue that thinking of fixation locations as arising from point processes is a very fruitful framework for eye-movement data, helping turn qualitative questions into quantitative ones. We provide a tutorial introduction to some of the main ideas of the field of spatial statistics, focusing especially on spatial Poisson processes. We show how point processes help relate image properties to fixation locations. In particular we show how point processes naturally express the idea that image features' predictability for fixations may vary from one image to another. We review other methods of analysis used in the literature, show how they relate to point process theory, and argue that thinking in terms of point processes substantially extends the range of analyses that can be performed and clarify their interpretation. KW - eye movements KW - fixation locations KW - saliency KW - modeling KW - point process KW - spatial statistics Y1 - 2013 U6 - https://doi.org/10.1167/13.12.1 SN - 1534-7362 VL - 13 IS - 12 PB - Association for Research in Vision and Opthalmology CY - Rockville ER - TY - JOUR A1 - Engbert, Ralf A1 - Trukenbrod, Hans Arne A1 - Barthelme, Simon A1 - Wichmann, Felix A. T1 - Spatial statistics and attentional dynamics in scene viewing JF - Journal of vision N2 - In humans and in foveated animals visual acuity is highly concentrated at the center of gaze, so that choosing where to look next is an important example of online, rapid decision-making. Computational neuroscientists have developed biologically-inspired models of visual attention, termed saliency maps, which successfully predict where people fixate on average. Using point process theory for spatial statistics, we show that scanpaths contain, however, important statistical structure, such as spatial clustering on top of distributions of gaze positions. Here, we develop a dynamical model of saccadic selection that accurately predicts the distribution of gaze positions as well as spatial clustering along individual scanpaths. Our model relies on activation dynamics via spatially-limited (foveated) access to saliency information, and, second, a leaky memory process controlling the re-inspection of target regions. This theoretical framework models a form of context-dependent decision-making, linking neural dynamics of attention to behavioral gaze data. KW - scene perception KW - eye movements KW - attention KW - saccades KW - modeling KW - spatial statistics Y1 - 2015 U6 - https://doi.org/10.1167/15.1.14 SN - 1534-7362 VL - 15 IS - 1 PB - Association for Research in Vision and Opthalmology CY - Rockville ER - TY - JOUR A1 - Trukenbrod, Hans Arne A1 - Barthelme, Simon A1 - Wichmann, Felix A. A1 - Engbert, Ralf T1 - Spatial statistics for gaze patterns in scene viewing BT - effects of repeated viewing JF - Journal of vision N2 - Scene viewing is used to study attentional selection in complex but still controlled environments. One of the main observations on eye movements during scene viewing is the inhomogeneous distribution of fixation locations: While some parts of an image are fixated by almost all observers and are inspected repeatedly by the same observer, other image parts remain unfixated by observers even after long exploration intervals. Here, we apply spatial point process methods to investigate the relationship between pairs of fixations. More precisely, we use the pair correlation function, a powerful statistical tool, to evaluate dependencies between fixation locations along individual scanpaths. We demonstrate that aggregation of fixation locations within 4 degrees is stronger than expected from chance. Furthermore, the pair correlation function reveals stronger aggregation of fixations when the same image is presented a second time. We use simulations of a dynamical model to show that a narrower spatial attentional span may explain differences in pair correlations between the first and the second inspection of the same image. KW - scene viewing KW - pair correlation function KW - spatial correlations Y1 - 2019 U6 - https://doi.org/10.1167/19.6.5 SN - 1534-7362 VL - 19 IS - 5 SP - 1 EP - 19 PB - Association for Research in Vision and Opthalmology CY - Rockville ER -