title: Trying to derive a 2D transformation matrix using only the images
body: <p>I dunno if this should go in a Math forum or a Programming forums, but I'll post it in both and see where I get.</p>
  
  <p>I have two computer images... one of them is an "original" image (a large TIF file). The other one is a transformed version of the original image... it's been rotated, sheared and translated in a software program. I need to do some work on the transformed image, but I need the (x-y) coordinates of each pixel in the original image to finish my calculations.</p>
  
  <p>I know that the image was rotated and sheared with a 3x3 Transformation matrix. If I had the matrix, I could derive the second image from the first (or vice-versa) myself.  I don't know exactly how much it was rotated, sheared, or translated, so I can't just derive the matrices from a set of known transformations. What I do have is a set of corresponding points (the corners, et al) in each image, and their corresponding (x,y) coordinates. So here's my dilemma:</p>
  
  <p>Using a set of corresponding transformed points ((x,y) -> (x',y'), three or more of them), can I derive the Transformation matrix that was used to turn one image into the other? If I can derive the matrix, I can solve for the original coordinates of all the pixels (all 18-million of 'em) and get the calculations done that I need to do.</p>
  
  <p>Can anyone help? I'm familiar with linear algebra... just not familiar enough to derive this without a whole lotta head scratching. Anything is appreciated!</p>
  
  <ul>
  <li>Mike</li>
  </ul>