title: Compute Coordinates of image pixel in new reference frame
body: <p>I have a bunch of images taken at different scales and sizes for each of which a certain number of facial landmarks have been manually annotated. The annotation process returns a matrix with the <code>(x,y)</code> coordinate with respect the the global reference frame of the image.</p>
  
  <p>For the sake of my project I need to normalize all the images to a unique standard size (in particular <code>960 x 1080</code> pixels) and do some processing on them.</p>
  
  <p>My question is:</p>
  
  <ul>
  <li>Given that I know the size of both the old and new image, by means of which equations for <code>TRANSLATION</code>, <code>ROTATION</code> and <code>SCALE</code> will a pixel with coordinates <code>(x1_1,y1_1)</code> in reference frame 1 be mapped into the pixel <code>(x2_1,y2_1)</code> of reference frame 2?</li>
  </ul>
  
  <p>The image below should help clarify what I'm trying to do:</p>
  
  <p><img src="https://i.stack.imgur.com/vSxDh.jpg" alt="enter image description here"></p>
  
  <p>You can see 2 versions of the same image (the original <code>800 x 978</code> and the desired one <code>960 x 1080</code> ) and the positions of the landmarks of interest. Supposing I know the coordinates for all of the landmarks in the figure on the right, how do I get the equivalent coordinates for the figure on the left? (Note that the weird position of the <code>y</code> axis is due to how matlab puts the reference frames)</p>
  
  <p><strong>ADDED PART:</strong></p>
  
  <p>In particular the image was scaled by using <code>matlab's</code> <code>imresize()</code> function as follows:</p>
  
  <pre><code>B = imresize(A, [1080 960])
  </code></pre>
  
  <p>How can I compute what the scale factor was in this case?</p>