# Focal Operation

**Focal Operations**, sometimes referred to as neighborhood operations, is a function type of Map Algebra. A focal operation produces a new raster data set where each cell value is a product of a function involving multiple cells of the input raster.^{[1]} The value of each new raster cell is determined using a group or neighborhood of cells. The value of these cells would be used in a mathematical function to produce a value for the new cell.^{[2]} This neighborhood of cells operates as window, moving to each and every cell, performing the function and assigning the value to the cell. Most common window or neighborhood shape consists of a 3x3 square as seen in the figure to the right.

## Example

An example of a focal operation would be determining the slope of the terrain. The neighborhood would consist of a 3x3 square around the cell in question. Taking the values of each of those cells and averaging them together, you are able to produce a value for the cell in question.

Common applications include terrain analysis, image processing, site analysis or data simplification.

## Reference

- ↑ ESRI, "The types of operations in Spatial Analyst," http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#//005900000017000000 , Accessed on September 10, 2013
- ↑ University of Washington, "Introduction to Geographic Information Systems in Forest Resources," http://courses.washington.edu/gis250/lessons/raster_analysis1/#focal Accessed on September 10, 2013