arcgis desktop - Calculate radius of gyration (average distance between cell and centroid cell)?

Radius of gyration (in the field of ecology) is a measure of the spatial extent of a habitat patch, and is defined as the mean distance between each cell in the patch and the patch centroid (cell-center to cell-center distance).

Can anyone suggest an efficient way to calculate this metric from a raster where patches have a value 1 and the background has a value of 0?

My current model uses the following series of processes, but is clunky and requires a hefty processing time. See below:

1. Convert raster layer to polygon to find the centroid of each patch (Raster to Polygon, Feature to Point.


2. Convert raster layer to point to find cell centers of each cell (Raster to Point).


3. Find the cell center that is closest to the centroid (Near).


4. Calculate distance between the cell center closest to the centroid and every other cell center in the patch (Point Distance).



5. Calculate mean of the resulting table of distances (Summary Statistics)

This is all very clunky and time-consuming given the multiple conversions necessary and the number of patches I need to calculate. I am guessing there is a faster and more efficient way to perform this calculation, as other programs like FragStats can do it very rapidly.

Answer

The workflow below:

• is super fast, because it is raster based


• unlike vector approach, that you are using, it will handle the situation with biggie sitting next to a small patch, when cells of the former are closer to centre of small pacth

INPUT BINARY RASTER:

Note: I removed background values of 0.

WORKFLOW:

arcpy.gp.RegionGroup_sa("binary","C:/FELIX_DATA/SCRARCH/GROUPS","EIGHT","WITHIN","NO_LINK","#")
arcpy.gp.SingleOutputMapAlgebra_sa("$$XMAP","C:/FELIX_DATA/SCRARCH/X","#")
arcpy.gp.SingleOutputMapAlgebra_sa("$$YMAP","C:/FELIX_DATA/SCRARCH/Y","#")
arcpy.gp.ZonalStatistics_sa("GROUPS","VALUE","X","C:/FELIX_DATA/SCRARCH/xMean","MEAN","DATA")
arcpy.gp.ZonalStatistics_sa("GROUPS","VALUE","Y","C:/FELIX_DATA/SCRARCH/yMean","MEAN","DATA")
arcpy.gp.RasterCalculator_sa("""Power(("X" - "xMean")*("X" - "xMean")+("Y" - "yMean")*("Y" - "yMean"),0.5)""","C:/FELIX_DATA/SCRARCH/distance")
arcpy.gp.ZonalStatisticsAsTable_sa("GROUPS","VALUE","distance","C:/FELIX_DATA/SCRARCH/stats.dbf","DATA","MEAN")

arcpy.RasterToPolygon_conversion("GROUPS","C:/FELIX_DATA/SCRARCH/polygons.shp","SIMPLIFY","VALUE")
arcpy.AddField_management("POLYGONS","R_GYR","FLOAT","#","#","#","#","NULLABLE","NON_REQUIRED","#")
arcpy.AddJoin_management("POLYGONS","GRIDCODE","stats","VALUE","KEEP_ALL")
arcpy.CalculateField_management("POLYGONS","polygons.R_GYR","[stats.MEAN]","VB","#")

OUTPUT PATCHES WITH COMPUTED RADIUS:

Very little efforts required to bring it to Python, where by importing spatial analyst tools one can use in memory rasters, e.g. first line will look something like this:

outRegionGrp = RegionGroup(binary, "EIGHT")

If you have to repeat this process, I suggest scripting it.