[Qgis-user] Fwd: Georeferencer Plugin Help - QGIS

[Alexandre Neto]

Hi,

As far as I know, the residual column represents the difference (distance
in map units) between the GCP coordinates and the place where that image
position ended up after the georeferencing process. So, yes, it represents
the error for each GCP.

To calculate the total RMSE, I think you have the formula wrong. According
to Wikipedia:

The RMSD of predicted values {\displaystyle {\hat {y}}_{t}}[image:
\hat y_t] for
times *t* of a regression's
<https://en.wikipedia.org/wiki/Regression_analysis> dependent variable
<https://en.wikipedia.org/wiki/Dependent_variable> {\displaystyle
y_{t},}[image:
{\displaystyle y_{t},}] with variables observed over *T* times, is computed
for *T* different predictions as the square root of the mean of the squares
of the deviations:
{\displaystyle \operatorname {RMSD} ={\sqrt {\frac {\sum _{t=1}^{T}({\hat
{y}}_{t}-y_{t})^{2}}{T}}}.}[image: {\displaystyle \operatorname {RMSD}
={\sqrt {\frac {\sum _{t=1}^{T}({\hat {y}}_{t}-y_{t})^{2}}{T}}}.}]
So, I think you need to sum the squares of each GCP residual, divide it by
the number of GCP, and then get the Square root of the result.
If we look at an example, imagine you have 10 GCP, each with a residual of
2 m.
Your suggested formula:
Sqrt (20) = 4,47 m

Following Wikipedia suggestion:

Sqrt (10 * (2^2) / 10 ) = 2 m

Hope it helps.

Alexandre Neto
QGIS Support
www.qcooperative.net

On Mon, Nov 2, 2020 at 9:43 PM Alexis R.L. <alroyliz0 at gmail.com> wrote:

> Greetings,
>
> The relevant code is located here
> https://github.com/qgis/QGIS/blob/master/src/app/georeferencer/qgsleastsquares.cpp
>
> Hope this helps.
>
> Alex
>
>
> Le lun. 2 nov. 2020 à 16:18, Randal Hale <rjhale at northrivergeographic.com>
> a écrit :
>
>> Good afternoon QGIS People
>>
>> I received a question on RMSE errors in georeferencer and after talking
>> to Ethan about it I realized I have no clue what I'm talking about. How
>> would we go about calculating an RMSE for a rectified image in QGIS?
>>
>> I've cc'd ethan on this so he can chime in also.
>>
>> Thanks
>>
>> Randy
>>
>>
>> -------- Forwarded Message --------
>> Subject: Georeferencer Plugin Help - QGIS
>> Date: Fri, 2 Oct 2020 15:27:13 +0000
>> From: Ethan Cissell <ecissell at bio.fsu.edu> <ecissell at bio.fsu.edu>
>> To: info at northrivergeographic.com <info at northrivergeographic.com>
>> <info at northrivergeographic.com>
>>
>> Hi Randal,
>>
>> I have a question about the usage and outputs of the Georeferencer Plugin
>> in QGIS, and thought, given your expertise, you might be able to directly
>> help, or point me in the right direction.
>>
>> I am a Ph.D. candidate in Ecology and Evolution at Florida State
>> University applying spatial techniques to study the dynamics of benthic
>> cyanobacterial mats on coral reefs. This past summer, I photographically
>> tracked individual cyanobacterial mats in which I had placed plastic stakes
>> as ground control points for later image rectification. I am trying to
>> essentially create image stacks, so that I can parameterize a generalized
>> additive mixed effects model that accounts for the inherent spatial
>> autocorrelation and includes a parameter with occupation at the previous
>> time-point explicitly included to hopefully model the population dynamics
>> of this system.
>>
>> Thus, a quantitative understanding of the error in my alignment is
>> absolutely critical to the downstream conclusions (especially for informing
>> my resampling to larger grid size to account for error in my alignments).
>> I am using QGIS for obtaining all raw data from these photos (scaling,
>> rectification, classification, resampling), but I am stuck at the
>> rectification step. I am using the “Georeferencer” plugin to accomplish my
>> alignments, but I have received mixed advice on how to interpret the
>> residuals output on the GCP table in the Georeferencer window (screenshot
>> below). The documentation for this plugin seems to indicate that the far
>> right column (Residual) is actually a per GCP RMS error.
>>
>> Can you tell me how to interpret these errors/how to obtain a total RMSE
>> error for the image alignment (i.e. not just per GCP error, but total error
>> for each image)? I have been told to sum all of the values from the
>> residuals column and take the square root of that raw summation. Is this
>> correct?
>>
>> Many thanks in advance. I apologize for the lengthy email, but I wanted
>> to establish the motivations for this project so that you would have more
>> context for the goals of the alignment.
>> Any and all help here is greatly appreciated.
>>
>>
>>
>>
>> Best,
>>
>> Ethan C Cissell
>> ——————————————
>> Ph.D. Candidate - McCoy Lab
>> National Science Foundation Graduate Research Fellow
>> Florida State University
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