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

16 2. Background and Related Work
The definition domain of an array is expressed as a multidimensional interval by its
lower and upper bounds, l i and u i respectively, along each direction l i of the domain,
denoted as D = [l 1 : u 1 ; ...; l d : u d ], where l i < u i , i = 1, ..., d, and l i , u i ∈ S i .
Figure 2.1(a) shows the constituents of a sample 3D array.
Figure 2.1. 3D Array
The following subsections provide a brief summary of the main contributions of
data modeling and query languages that support array data in GIS and remote-sensing
imaging applications.
2.1.2 2D Data Models
A uniform representation and algebraic notation for manipulating image-based data
structures known as map algebra was first advanced by Tomlin and Berry [56]. While
not the first ones to describe this type of spatial data processing, Tomlin and Berry put
forward the methodological basis for the organization of this form of geographical
data analysis. Map algebra represents a method of treating individual rasters or array
layers as members of algebraic equations. Map algebra functions are grouped into the
following categories:
• Local functions create outputs in which output cell values are determined on a
cell-by-cell basis without regard for the value of neighboring cells.
• Focal functions create outputs in which the value of the output grid is affected by
the value of neighboring cells. Low-pass filters are commonly used to smooth
out data.
• Zonal functions create outputs in which the values of output cells are determined
in part by the spatial association between cells in the input grids.
• Global functions compute an output raster where the value for each output cell
is potentially a function of all of the input cell values.