Question

MATLAB:

Attempting to use the inverse mapping approach and take a 3x3 matrix that will rotate an image. The image is 540 x 420. attempting to write DOUBLE FOR LOOPS that will step through each and every pixel location. I cannot use any Toolbox Functions. Please write a double for loop that will allow this to happen!

[xold,yold,k] = size(A);

Rotation = [cosd(angle) -sind(angle) 0 ; sin(angle) cos(angle) 0; 0 0 1];

InverseRotation = double(inv(Rotation));

Answer 1

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• You're not multiplying the inverse rotation matrix by the image, you're multiplying it by the homogeneous coordinates of a point in the new image to get the corresponding homogeneous coordinates in the original image.

newpt = [xnew ynew 1].';
origpt = InverseRot*newpt;
xold = origpt(1);
yold = origpt(2);

• Your rotation matrix mixes the degree and radian versions of the trig functions. That will mess up your results.
• Rotations without translations are about the origin. Your image is not centered at the origin. You'll need to do something about that.
• The inverse of a rotation matrix is the same as its transpose. If you fix the note above, you'll end up with an affine transformation matrix rather than a straight rotation matrix. This also has an easier way to calculate the inverse. If the affine transformation matrix is [R | t; 0 | 1], the inverse is [RT | -RT*t; 0 | 1] where RT is the transpose of R.
• ​The coordinates in the original image that you get after transformation are not likely to be integers, so you won't be able to simply assign the value of a pixel in the old image to a pixel in the new image. As you said, you'll have to find some way to interpolate the value and assign that to the point in the new image.