Converting Total RMS Error into meters

Question

I'm wanting to georeference an old chart in the same manner described in a published article:

"All charts were transformed to the British National Grid. The 1904 chart was georeferenced using nine fixed landmarks such as church spires, of which the National Grid coordinates were known. Errors due to georeferencing were <0.01 cm, corresponding to a maximum positioning error of 7.5 m on 1:75,000 maps. The accuracy of the digitizer itself was claimed to be +/- 0.127 mm."

My own image has a cell size of 22, has a scale of approx. 1:127,000 and was georeferenced onto a map of scale 1:25,000 using 10 evenly-distributed GCPs. My Total RMS Error is 36.

How do I identify the maximum positioning error as described in the article? I.e. can I convert RMS Error into meters?

Interpretation of RMS Error is well described in this thread: Generally accepted root mean square (RMS) error for rectifying topographic maps. However, I'm not sure how the author obtains an "RMS of 5 m". Is the RMS Error expressed in meters, or is there an additional conversion needed?

Answer 1

With most softwares, the RMSE is computed either in input coordinates or in output coordinates.

For on screen georeferencing, input coordinates are usually expressed in pixels. If the pixels are used, you need to multiply this value with the size of your pixel in meter (which can be found in your image properties). In the article that you mention, this looks like manual georeferencing using a digitizing board, so that the conversion factor from the XY system of the board and the XY system of their coordinate system is the scale factor of the paper map.

With most softwares, the RMSE is now directly provided in the unit of the coordinate system. Just check in what unit is your CRS to make the appropriate correction.

As a last notice, the author of the post mentioned in your question is talking about how to define a reasonable RMSE target for quality control. His 5 m RMSE is not the RMSE of the model but a QC target estimated based on a specific context. In your case, I guess that your pixel size and your RMSE are both in meters. As your reference data is more precise than your map, you could expect a smaller RMSE if your image is a scanned map with visible features. For a satellite or aerial image, selecting a more complex model (e.g ideally orthorectification with a DEM) could improve your RMSE, especially if you work on a rugged terrain.