topic Re: Formula for forward-inverse RMSE? in ArcGIS Pro Questions

Formula for forward-inverse RMSE?

Carl_Sack — Sat, 08 May 2021 11:02:11 GMT

Hello! I am struggling with understanding the three types of RMS error reported while georeferencing in ArcGIS Pro. All of the documentation seems to include this paragraph (emphasis added):

The forward residual shows you the error in the same units as the data frame spatial reference. The inverse residual shows you the error in the pixel units. The forward-inverse residual is a measure of how close your accuracy is, measured in pixels. All residuals closer to zero are considered more accurate.

OK, so I understand how forward and inverse RMSE are calculated, but what the heck is forward-inverse?! The description is a non-explanation; it sounds exactly the same as inverse RMSE. Obviously it isn't, though, because it is given as a fractional decimal less than 1. Can anyone explain or provide the mathematical formula for forward-inverse RMSE so I can understand what it actually is and why it might be useful to interpret along with the other two?

Re: Formula for forward-inverse RMSE?

BranislavBlagojevic — Mon, 10 May 2021 08:24:31 GMT

It is obvious only that the programmer and the author of the help do not understand what they actually did (formula), i.e. wrote. A more detailed explanation in this regard has already been requested from users, but has not been provided by ESRI.

Re: Formula for forward-inverse RMSE?

JamalNUMAN — Wed, 24 Jul 2024 05:58:36 GMT

I have encountered the same issue. I haven't found a sufficient explanation of how these metrics are calculated. Specifically, I find the difference between the green and red lines vague. How are they determined, and what do they indicate?

Re: Formula for forward-inverse RMSE?

MichaelMorgan4 — Thu, 10 Apr 2025 21:44:14 GMT

I copied the following blurb from Stack Exchange regarding a question about a "reverse root mean square value":

https://stats.stackexchange.com/questions/565724/root-mean-square-value-but-with-reverse-order-of-operation

The 2 formulas on this page seem to show a familiar root-mean-square formula (sqrt (1/N)(sum 1-N xi^2)), followed by what looks like an "inverse" of the same formula (1/N sum 1-N sqrt (|xi|))^2. This might be the difference, I just have not verified this calculating against residuals from my latest georeferencing run.