In a local function, the value at each location on the output raster is a function of the input values at that location. When computing a local function, you can combine input rasters, calculate a statistic, or evaluate a criterion for each cell in an output raster based on the values of each cell from multiple input rasters.
For example, by using cell-based statistics, the user can visualize where a desert may spread over a 10-year period. Based on this information, a developer may choose an alternate location for a new golf course because of the decreased water supply that will occur in the near future for this area.
Neighbourhood functions create output values for each cell location based on the value for that location and the values identified in a neighbourhood specified by the user. The statistics calculated for the neighbourhood act as a moving window that scans across the data. Neighbourhood statistics can be overlapping or nonoverlapping. Overlapping neighbourhood functions, or focal functions, generally calculate a specified statistic within the neighbourhood. For example, you may want to find the mean or maximum value in a three-by-three-cell neighbourhood. Variations of the overlapping neighbourhood statistics function are the high- and low-pass filter functions to smooth and accentuate data.
The nonoverlapping neighbourhood functions, or block functions, allow statistics to be calculated in a specified nonoverlapping neighbourhood. The block functions are commonly used for aggregating raster data to a coarser cell size. The values assigned to the coarser cells can be based on some other calculation, such as the maximum value in the coarser cell, as opposed to using the default nearest-neighbour interpolation.
In addition to the predefined statistics and filters, you can also create your own custom filters by specifying neighbourhoods and weight values such as edge detection filters.
Zonal Overlay Statistics
Zonal Statistics tools calculate a statistic for each zone of a zone dataset based on values from another dataset. The zonal functions are grouped by how the zones are specified, either by a single input value raster or by a second zone raster.
Zonal functions in which the zones are defined by a single input value raster either calculate statistics or quantify the characteristics of the geometry of the input zones. Zonal functions in which the zones are defined by a second zone raster either calculate statistics or fill specified zones with values from the input value raster.
Using zonal statistics, you can calculate the mean elevation for each forest zone or the number of accidents along each of the roads in a town. You can also determine how many different types of vegetation there are in each elevation zone.
The Multivariate Statistics tools allow exploration of relationships between many different data layers or types of attributes. This collection of tools supports supervised and unsupervised classification and principal component analysis. These tools can be used not only for traditional image processing applications, such as transforming a multispectral image into a categorized land-cover map, but also for other statistical analyses of multivariate data, such as terrain stratification or habitat analyses.