Distance Raster

[Jefferson Ferreira-Ferreira]

Hi dear listers!

I have an open question on GIS StackExchange: Is there any difference between gdal_proximity.py and ArcGIS Euclidean Distance?

I would like to know if someone can help to answer it. Any comments or clues will be appreciated.

Thanks a lot.

Jefferson Ferreira-Ferreira, PhD Candidate 

Geographer

Ecosystem Dynamics Observatory - EcoDyn/UNESP

Department of Geography 

Institute of Geosciences and Exact Sciences (IGCE)

São Paulo State University (UNESP)

Rio Claro, SP - Brazil

[GIS in Ecology]

Hi Jefferson,

This is a very interesting question! Looking at the help files for the Gdal Proximity tool, it seems it seems to function in the same way as the ArcGIS Euclidean Distance tool (and indeed the GRASS R.Grow.Distance tool which you can access through QGIS). This is by calculating a radial distance between the centre off a cell which distances are measured to, and every other cell in the raster data layer using the formula:

d(dx,dy) = sqrt(dx^2 + dy^2)

This is the standard trigonometry formula based on Pythagoras' Theorem, where the hypotenuse is the square root of the sum of squares of the other two edges of a triangle. By definition, this is a Euclidean calculation (i.e. it assumes a flat surface).

However, the Gdal Proximity tool does not specify that it does its calculation based on Pythagoras' Theorem and a flat surface, but I am assuming that it does because it offers to calculate the distance in Pixels as well as Geographic units.

Similarly, the ArcGIS Euclidean Distance tool does not provide the formula for its calculations, but as it states that it is a Euclidean distance calculation, I'm assuming that it must use the above formula.

So, in conclusion, the only proximity tool that clearly explains how the proximities are calculated is the GRASS one (Go GRASS!), but I think it would be reasonable to assume that they are all using the same mathematical approach to calculate the distance between the centres of different grid cells in a raster, as this hasn't really changed since the time of Pythagoras and Euclid. 

I would, however, recommend running a test to check this as it is still only an assumption. This could be done by running the calculation in both ArcGIS and  using the Gdal tool, or you could do it by using the Gdal tool and then using a measure tool in QGIS to manually compare the distance calculated by the Gdal tool to the Euclidean distance measured with the measure tool.

I hope this helps, and sorry not to be able to provide a clear-cut answer.

All the best,

Colin