Visualization techniques are of increasing importance in exploring and analyzing large amounts of multidimensional information. One important class of visualization techniques which is particularly interesting for visualizing very large multidimensional data sets is the class of pixel-oriented techniques. The basic idea of pixel-oriented visualization techniques is to represent as many data objects as possible on the screen at the same time by mapping each data value to a pixel of the screen and arranging the pixels adequately. A number of different pixel-oriented visualization techniques have been proposed in recent years and it has been shown that the techniques are useful for visual data exploration in a number of different application contexts. In this paper, we discuss a number of issues which are important in developing pixel-oriented visualization techniques. The major goal of this article is to provide a formal basis of pixel-oriented visualization techniques and show that the design decisions in developing them can be seen as solutions of well-defined optimization problems. This is true for the mapping of the data values to colors, the arrangement of pixels inside the subwindows, the shape of the subwindows, and the ordering of the dimension subwindows. The paper also discusses the design issues of special variants of pixel-oriented techniques for visualizing large spatial data sets.
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