  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.
