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Map Algebra

Contents 1 Background 2 Algebraic Operators 3 Subsections of this Article 4 Information about this article 5 Contact

Background

One of the major strengths of GIS is its analytical capabilities. Map algebra provides tools to perform spatial analysis operations. Map algebra is based on matrix algebra which is the algebraic manipulation of matrices or grid networks. The raster data structures in GIS a particularly suited to algebraic manipulation.

Map algebra creates new features and attribute relations by overlaying the features from two or more input map layers. Features from each input layer are combined to create new output features. Attributes of each input feature are combined from the two input layers to describe each new output feature, thus creating new attribute relationships.

Often, the manipulation of multiple data layers is required to achieve the objective of the overlay operation. This is done in a stepwise fashion - two input layers are combined to form an intermediate layer, this intermediate layer is then combined with a third layer to form another intermediate layer, and so on until the desired resultant map layer is achieved.

Algebraic Operators

Map algebra uses math-like expressions to combine raster layers using operators such as arithmetic, relational, Boolean and logical.

• Arithmetic operators allow addition, subtraction, multiplication, and division. For example, two rasters are added together to produce a third raster. Each cell value from the first raster is added to the corresponding cell value in the second raster to create an analysis raster. In this example two rasters are added together to produce a third raster. Each cell value from the first raster is added to the corresponding cell value in the second raster to create an analysis raster.

• Relational operators allow you to build logical tests, returning values of true (1) and false (0). Use either the Relational Operator (<>,<,>,<=,>=) or the abbreviation (NE, LT, GT, LE, GE).
• Boolean operators such as "and", "or", and "not" allow you to chain logical tests. Like relational operators, Boolean operators return values of true and false.
• Logical operators DIFF, IN, and OVER allow you to build logical tests on a cell-by-cell basis, but are implemented with specific rules.
  • A DIFF B: If a cell value in raster A and raster B are different, the cell value in raster A is returned. If the cell values are the same, the value zero is returned.
  • A IN {value list): If a cell value in raster A is in the value list, the cell value in raster A is returned. Otherwise, No Data is returned.
  • A OVER B: If a cell value in raster A is not equal to zero, the cell value is raster A is returned. Otherwise, the cell value in raster B is returned.
    

Subsections of this Article

No subsections available

Information about this article

Short title: Map Algebra

Description: Map algebra provides tools to perform spatial analysis operations. Map algebra is based on matrix algebra which is the algebraic manipulation of matrices or grid networks

Expertise level: intermediate

Author: Greg Reed

Approval status: approved

Approved by: Greg Reed

Last change: 2010-4-20

Subsection of: Spatial Analysis

Contact

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