## Focal Operations

Focal operations work on cells and their neighbors. To compute the value at a cell the method uses the cell and its nearest neighbors, and creates a new grid. Examples include Slope and Reflectance (or hillshade), or Filtering.  For this type of operation, missing values for any of the points in the neighborhood will lead to a missing value in the output layer.

 This example uses the SW corner of a grid, with the cells numbered with (0,0) in that corner.  This is a traditional convention of DEMs (it leads to a regular Cartesian grid), but is not what is used for most satellite imagery which uses a computer graphics convention with the origin in the NW corner and values increasing to the right and down.  The principles are the same, just the identification of the grid points.Focal operations pass an operator, generally a square matrix, over the grid, and replace the center value with the computed value. A. Because the operator requires a 3x3 neighborhood, the first computation will be done for cell (1,1).  The operator cannot work on the left column, or the bottom row.  In this case, because cell (0,2) is missing, no value can be computed for (1,1). B. The operator moves to the right, and computes a value for cell (2,1). C. The operator moves to the right, and computes for every cell in the row except the last column on the right, which like the first does not have a complete neighborhood. D.  The operator moves up a row, and repeats the process.  Cell (1,2) is missing two neighbors, so it will be missing data. E. The operator continues to the right. F. The operator continues.  The last row on the top of the grid, like the bottom, cannot be done.

Last revision 3/14/2014