GDAL setgeotransform() - c++

Question

I have been trying to use GDAL library to add geoinformation to an image. From the documentation from GDAL web page I could find that I could use GDAlSetGeotransform(), for that I need a six parameters GDAL transformation information. Among the six parameters, the x-rotation and y rotation are considered 0 for north up image. But in my case I don't have north up image. So how could I get these rotation values if I have four corner coordinates of the image.
Or there is any other technique to add geoinformation to my image if I have four corner coordinates of the image.

Answer 1

The best way that I found is to estimate a transform matrix using least squares. This takes the following form.
Given N (4+) sets of pixel values and their matching world coordinates, build a pair of transforms. Then solve for the transforms. The following example is shown in octave. If using C++, just use Eigen or OpenCV and build a Moore-Penrose SVD Pseudo-Inverse Solver.
#!/usr/bin/env octave -qf
% Apply Geo Transform
function [Wx, Wy] = Apply_GeoTransform( Px, Py, adfGeoTransform )
% Multiply
Wx = adfGeoTransform(1,2) * Px + adfGeoTransform(1,3) * Py + adfGeoTransform(1,1);
Wy = adfGeoTransform(1,5) * Px + adfGeoTransform(1,6) * Py + adfGeoTransform(1,4);
endfunction
%
% Main Function
%
% Create Sample Inputs
W = [ 0, 50;
50, 0;
0,-50;
-50, 0];
P = [ 0, 0;
10, 0;
10,10;
0,10];
% Build Input Transform (A)
Ai = [P(1,1), P(1,2), 1;
P(2,1), P(2,2), 1;
P(3,1), P(3,2), 1;
P(4,1), P(4,2), 1];
% Build Output Solution Pairs
Bx = [W(1,1);
W(2,1);
W(3,1);
W(4,1)];
By = [W(1,2);
W(2,2);
W(3,2);
W(4,2)];
% Solve For Inverse x and y
Xi = Ai \ Bx;
Yi = Ai \ By;
% Construct Actual Transform
adfGeoTransform = [Xi(3,1), Xi(1,1), Xi(2,1), Yi(3,1), Yi(1,1), Yi(2,1)];
% Test Result
[Wx1, Wy1] = Apply_GeoTransform( 0, 0, adfGeoTransform );
[Wx2, Wy2] = Apply_GeoTransform(10, 0, adfGeoTransform );
[Wx3, Wy3] = Apply_GeoTransform(10,10, adfGeoTransform );
[Wx4, Wy4] = Apply_GeoTransform( 0,10, adfGeoTransform );
[Wx5, Wy5] = Apply_GeoTransform( 5, 5, adfGeoTransform );
printf('W1: %d, %d\n', Wx1, Wy1);
printf('W2: %d, %d\n', Wx2, Wy2);
printf('W3: %d, %d\n', Wx3, Wy3);
printf('W4: %d, %d\n', Wx4, Wy4);
printf('W5: %d, %d\n', Wx5, Wy5);