# What is some theory on the number of GCP when georeferencing?

Just wondering, is it always better to have more than 3 GCPs? Should the GCPs be spread out evenly? Where can I find some general resources on the theory of this? Other than trial an error, which simply teaches me what works at that moment in time and not what should work in given instances. Not critical, but just interested.

The number of points depends on type of the transformation (and georeferencing is always a transformation) that you need to apply to the image. In the most simple case the transformation is linear and you will need 6 coefficients to perform transformation:

``````x0 = a0 + a1x + a2y
y0 = b0 + b1x + b2y
``````

where x and y - initial coordinates, x0 and y0 - final coordinates, a0... and b0... - are 6 coefficients of the transformation provided by 3 ground control points.

For a nonlinear transformation (polynomial transformation 2, 3 and higher orders) you will need more points. To find minimum number of points needed use this formula:

``````((t+1)(t+2))/2
``````

where t - is the order of the transformation.

To distribute points across the image you should have a clue about locations of the greatest distortions of the image. Points should be denser where greater distortion is expected (e.g. in mountains). The intuitive approach to the points location is to imagine that you use your N fingers (imagine that you have hundreds of them if needed) to move and stretch the image across the flat surface. The locations where you would apply your fingers - have to be georeferenced.

Also you may check out my notes on the georeferencing for some extreme scenarios.

• This is a nice conversationally-phrased answer. And you may have coined a phrase.. now I can't wait to use my N fingers for something. :) For anyone curious what N fingers might look like, check out this guitarist. Apr 5, 2013 at 16:38
• Wow, this is great stuff! I'm checking out your site now - thanks again. Apr 5, 2013 at 17:35
• EDIT: Great read! Exactly the stuff I was wondering about. Apr 5, 2013 at 17:53
• @Chewy, I'm glad I was able to help! Apr 5, 2013 at 17:55
• As a rule of thumb the preferred number of GCPs should be 4 times the order of the transformation. i.e: Linear = 4; 1st order polynomial = 8; 2nd order polynomial = 12; 3rd order polynomial = 16; etc. Apr 11, 2013 at 19:31