Map algebra is a set-based algebra for manipulating geographic data, proposed by Dr. Dana Tomlin in the early 1980s. It is a set of primitive operations in a geographic information system (GIS) which allows two or more raster layers ("maps") of similar dimensions to produce a new raster layer (map) using algebraic operations such as addition, subtraction etc.
Depending on the spatial neighborhood, GIS transformations are categorized into four classes: local, focal, global, and zonal. Local operations works on individual raster cells, or pixels. Focal operations work on cells and their neighbors, whereas global operations work on the entire layer. Finally, zonal operations work on areas of cells that share the same value. The input and output for each operator being map, the operators can be combined into a procedure or script, to perform complex tasks.
When map algebra is performed in cells from local operations, different types of operations can be used:
- Arithmetic operations uses basic mathematical functions like addition, subtraction, multiplication and division.
- Statistical operations uses statistical operations such as minimum, maximum, average and median.
- Relational operations compares cells using functions such as greater than, smaller than or equal to.
- Trigonometric operations uses sine, cosine, tangent, arcsine between two or more raster layers.
- Exponential and logarithmic operations use exponent and logarithm functions.
Several major GIS systems use map algebra concepts, including ERDAS Imagine and ArcGIS. ArcGIS 10 implements Map Algebra in Python; functions are imported Python methods and Python's overloading capability is used for operators. For example, rasters can be multiplied using the "*" arithmetic operator.
Here are some examples, in MapBasic:
# demo for Brown's Pond data set # Give layers # altitude # development – 0: vacant, 1: major, 2: minor, 3: houses, 4: buildings, 5 cement # water – 0: dry, 2: wet, 3: pond # calculate the slope at each location based on altitude slope = IncrementalGradient of altitude # identify the areas that are too steep toosteep = LocalRating of slope where 1 replaces 4 5 6 where VOID replaces ... # create layer unifying water and development occupied = LocalRating of development where water replaces VOID notbad = LocalRating of occupied and toosteep where 1 replaces VOID and VOID where VOID replaces ... and ... roads = LocalRating of development where 1 replaces 1 2 where VOID replaces ... nearread = FocalNeighbor of roads at 0 ... 10 aspect = IncrementalAspect of altitude southface = LocalRating of aspect where 1 replaces 135 ... 225 where VOID replaces ... sites = LocalMinimum of nearroad and southface and notbad sitenums = FocalInsularity of sites at 0 ... 1 sitesize = ZonalSum of 1 within sitenums bestsites = LocalRating of sitesize where sitesize replaces 100 ... 300 where VOID replaces ...
- Longley; et al. Geographic Information Systems and Science. John Wiley & Sons, Inc. pp. 414–7. ISBN 978-0-470-72144-5.
- GISGeography. "Map Algebra-Global, Zonal, Focal and Local Functions".
- "3.4. Special method names¶". The Python Language Reference. Retrieved 3 May 2015.
- Esri, Inc. "ArcGIS 10.0 Help".
- B. E. Davis GIS: A Visual Approach (2001 Cengage Learning) pp. 249ff.
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