Applying OLAP Pre-Aggregation Techniques to ... - Jacobs University

Chapter 3
Fundamental Geo-Raster Operations
in GIS and Remote-sensing
Applications
This chapter describes a set of fundamental operations in GIS and remote-sensing
imaging applications. For rigid comparison and classification, these operations are
discussed by means of a sound mathematical framework. The aim is to identify those
operations requiring data summarization that may benefit from a pre-aggregation approach.
To that end, we use Array Algebra as our modeling framework.
3.1 Array Algebra
The rationale behind the selection of Array Algebra as the modeling framework is
grounded in the following observations:
• It is oriented towards multidimensional data in a variety of applications including
imaging.
• It provides the means to formulate a wide variety of operations on multidimensional
arrays.
• There are commercial and open-source implementations of Array Algebra that
show the soundness and maturity of the framework.
The expressive power of Array Algebra, the simplicity of its operators, and its successful
implementation in both commercial and scientific applications make it suitable
for our investigation.
Essentially, the algebra consists of three operators: an array constructor, a generalized
aggregation, and a multi-dimensional sorter [75, 76]. Array algebra is minimal
in the sense that no subset of its operations exhibits the same expressive power. It is
safe in evaluation: every formula can be evaluated in a finite number of steps. It is
closed in its application: any resulting expression is either a scalar or an array.
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