  In this article we revisit the concept of abstraction as it is used in
visualization and put it on a solid formal footing. While the term
\emph{abstraction} is utilized in many scientific disciplines, arts, as well as
everyday life, visualization inherits the notion of data abstraction or class
abstraction from computer science, topological abstraction from mathematics,
and visual abstraction from arts. All these notions have a lot in common, yet
there is a major discrepancy in the terminology and basic understanding about
visual abstraction in the context of visualization. We thus root the notion of
abstraction in the philosophy of science, clarify the basic terminology, and
provide crisp definitions of visual abstraction as a process. Furthermore, we
clarify how it relates to similar terms often used interchangeably in the field
of visualization. Visual abstraction is characterized by a conceptual space
where this process exists, by the purpose it should serve, and by the
perceptual and cognitive qualities of the beholder. These characteristics can
be used to control the process of visual abstraction to produce effective and
informative visual representations.
