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When georeferencing a raster image of a long corridor, why do collinear ground control points cause larger residuals?

Say I am using the georeference function in ArcMap, and I have 6 ground control points on a site that is is shaped like an L. Three ground control points are close to collinear on the long end. I find that if I use just 4 of the points (exclude the 2 of the 3 collinear points) I get a lower root mean square.

Why are collinear points giving me a worse root mean square?

  • Some more details would be helpful. Are you using an affine transformation or some higher-order function, such as a polynomial or a projective transformation? Are you reporting the RMS or the adjusted RMS? Are the points perfectly collinear or only approximately so? – whuber Jan 27 '16 at 15:58
  • Points are approximately collinear. I think this is adjusted RMS. I am using an affine transformation. – user66009 Jan 29 '16 at 0:14
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This is just my thoughts as I think about the problem. Unless you are georeferencing to a very high level of accuracy (I don't just mean zooming really far into ArcMap because even your GPS co-ordinates will have error etc), in order to fit that extra point on the co-linear line the data will be warped by a more complex algorithm that can't fit exactly through all of those points. When you only have two, it's easy to fit an algorithm to fit the raster accurately through both data points. When you add the third it will generate small residuals at each point to fit.

Something like this quick conceptual sketch - maybe could have exaggerated it a bit. http://s27.postimg.org/x08pgkaxf/colinear.png

In reality the second line would be curved but it still wouldn't pass precisely through all three points.

What exactly are you georeferencing? Some control points that are not in a line would probably be a good idea. A nice big convex hull of control points and some fill is what you want.

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  • The GPS used to survey the control points is sub-centimeter. Ideally, I am aiming for 10cm residuals horizontally. I am wondering if there is a problem with strength of figure. Would a flat angle caused by 3 approximately collinear points cause a distortion when trying to correct an image? – user66009 Jan 29 '16 at 0:15
  • I am georeferencing imagery of a riverbed, approximately 900m in length. There are some points that are not approximately collinear with the others. – user66009 Jan 29 '16 at 0:35

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