Yoann raised an interesting question about errors when georeferencing and carrying out a rectification of an image. You should start by reading the GEOM guide to GIS, watching Kamel's video and reading his 'Questions diverses' post. They provide the conceptual background, I'm just adding a bit more about the practical side of things. You clearly need to distinguish two very different cases when thinking about georeferencing, rectification and errors
Georeferencing images that have already been rectified (i.e., have no geometric distortion):
- This includes things like images and maps from Google Earth or Geoportail (not including aerial photos from "Remonter le temps" and very poorly georeferenced maps like the Carte d'Etat Major). These images either never had much distortion (e.g., topographic maps, satellite images) or someone went to a lot of trouble to remove distortions (e.g., from aerial photos).
- As Kamel noted these images do not require rectification. This means that i) you need relatively few reference Ground Control Points (GCPs) and corresponding locations on your image and ii) a linear statistical model (affine) should work extremely well fitting the relationship between the GCPs from your reference source (Geoportail or another georeferenced map) and the corresponding locations in your image. Indeed errors, which are derived from the fit of the statistical model, should not exceed the size of a couple of pixels. In this case, if you have large errors it's because you screwed up with your GCPs or with locating them on the image. This will cause unwanted distortion in your image. Go back and check your work.
Georeferencing and rectifying mages with substantial distortion:
- Aerial photos nearly always have significant distortion due to oblique view angles - this creates distortion due to the angle of view and due to topography. This distortions can be relatively linear if due to angle of view or highly non-linear if due to topography.
- As Kamel noted, you will need quite a few GCPs that are well distributed across the entire image to rectify these images .
- You may need to use a polynomial fit (2nd or even 3rd order) to remove non-linear distortions.
- Errors will usually be substantially higher than with rectified images. In the case of aerial photos or old maps that you will be using for GEOM projects you should try to get errors below about 15-20 m.
- Errors will be smaller as you go from linear to 2nd order to 3rd order polynomials. This is because it's easier to fit a a higher order statistical model to relationship between the reference GCPs and the corresponding locations in your image. THIS DOES NOT NECESSARILY MEAN that the distortion has been properly removed with higher order polynomials. Indeed, you may increase distortion even though the errors go down due to "overfitting" of the statistical model.
- As a result, it's difficult to decide whether you have a good fit and which type of statistical model to use. Use your best judgement, ask your instructor and be very careful about the quality of your work!