I have written an image rectification function which allows a user to select 2 points on an image and 2 points on a map. The function will then rectify the image so it is translated, scaled and rotated to fit the two points on the map.

The code I have written works perfectly along the equator. However this function 'breaks' when moving further north or south. The rotation and the scale are both wrong. I believe this is because of the Mercator projection I use which stretches along the latitude axis.

I am unsure how to proceed. Is there a bit of math I am unaware of which will compensate for the stretching along the latitude? Or am I wrong in my assumption this is because of the Mercator projection?

Below you will find the code I use:

// transformFromPoints is an array with the two coordinates on the image
// They are in lat long
var fromPointA = this.transformFromPoints[0];
var fromPointB = this.transformFromPoints[1];

// transformToPoints is an array with the two coordinates on the map
// They are in lat long
var toPointA = this.transformToPoints[0];
var toPointB = this.transformToPoints[1];

// This is the img we want to transform
var img = this.activeBaseMapImg;

// First update the anchor so the anchor is exactly at fromPointA
// The anchor defines the point around which the image will be drawn
// This is also the point around which the image is rotated.
var cornerPoints = img.getCornerPoints();
var xAnchorPos = M.Math.projectPointOnLine(fromPointA, cornerPoints[0], cornerPoints[1]);
var yAnchorPos = M.Math.projectPointOnLine(fromPointA, cornerPoints[0], cornerPoints[3]);

var xAnchorDir = M.Math.subVector2(xAnchorPos, cornerPoints[0]);
var xLineDir = M.Math.subVector2(cornerPoints[1], cornerPoints[0]);
var yAnchorDir = M.Math.subVector2(yAnchorPos, cornerPoints[0]);
var yLineDir = M.Math.subVector2(cornerPoints[3], cornerPoints[0]);

var xAnchor = xAnchorDir.x / xLineDir.x;
var yAnchor = yAnchorDir.y / yLineDir.y;

// Set the anchor at the fromPointA location
img.setAnchor({x: xAnchor, y: yAnchor});

// Move the image to the toPointA location

var fromDirection = M.Math.subVector2(fromPointB, fromPointA);
var toDirection = M.Math.subVector2(toPointB, toPointA);

// Determine scale
var scale = toDirection.length() / fromDirection.length();

// Determine rotation
var fromAngle = Math.atan2(fromDirection.y, fromDirection.x);
var toAngle = Math.atan2(toDirection.y, toDirection.x);

var angle = fromAngle - toAngle;

// Perform rotation and scale
img.setRotation(img.rotation + angle);
img.setSize({width: img.size.width * scale, height: img.size.height * scale});

If you need any more information to help in answering this question, please let me know.

  • is this python ? I also don't see any spatial reference object in the code which I think could be relevant. Jul 24, 2014 at 12:51
  • Hello jbchurcill, thank you for your reply. The code is Javascript not Python. What do you mean with spatial reference object? I am sorry I am still very new to this field. Should I add some more information to my original question?
    – Mathyn
    Jul 24, 2014 at 14:15
  • You may get more eyes on this if you tag with the term "javascript". I was referring to arcpy.SpatialReference in python. This is probably out of my depth if using javascript for this type of thing. I would have probably pursued something like this with a Geoprocessing tool in ArcGIS server but I don't have a lot of experience with that yet either. Jul 24, 2014 at 16:12
  • I've added the Javascript tag, thank you for the suggestion.
    – Mathyn
    Jul 25, 2014 at 7:44

1 Answer 1


I believe you need a minimum of 3 points to translate, scale, and rotate. The procedure and open source code for doing this is explained here: http://docs.opencv.org/doc/tutorials/imgproc/imgtrans/warp_affine/warp_affine.html I'm assuming your images are not georeferenced, so it should not matter what your map projection is since the user only has to match 3 points on the image to 3 map coordinates.

  • I agree with the above. Also, you should generally try to rectify the image with a basemap in the same projection as the image. Aug 5, 2014 at 23:27
  • 1
    Would you be able to expand upon your very brief answer perhaps by referring to some relevant documentation, please?
    – PolyGeo
    Aug 5, 2014 at 23:35
  • 1
    If the scale is a single scale, aka this is a 2D conformal transformation, then the minimum is 2 points. A 2D affine transformation needs 3 points. Perhaps expand your answer that the OP will get better results if he implements an affine tfm instead?
    – mkennedy
    Aug 5, 2014 at 23:55
  • Thank you for the explanation and link. I have successfully implemented an image rectification function using 2 points. I believe this works because the image will remain a rectangle. Looking at the link you have given me I believe using 3 points might give better results, so I'll look into that. Thanks.
    – Mathyn
    Aug 6, 2014 at 7:58

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