Map algebra


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 which allows two or more raster layers of similar dimensions to produce a new raster layer 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:
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:

  1. demo for Brown's Pond data set
  2. Give layers
  3. altitude
  4. development – 0: vacant, 1: major, 2: minor, 3: houses, 4: buildings, 5 cement
  5. water – 0: dry, 2: wet, 3: pond
  6. calculate the slope at each location based on altitude
slope = IncrementalGradient of altitude
  1. identify the areas that are too steep
toosteep = LocalRating of slope
where 1 replaces 4 5 6
where VOID replaces...
  1. 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...