title: Calculate distance between two points in a perpective image
body: <p>I want to verify the distance between two points C and D (CD) in a perpective image.</p>
  
  <p>The picture is taken in my living room. Dimension of each tiles is 0.6x0.6 (in meters).</p>
  
  <p><a href="https://i.stack.imgur.com/AMXU1.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/AMXU1.jpg" alt="enter image description here"></a></p>
  
  <p><strong>Real world measurements:</strong></p>
  
  <p>Distance between point A and point D (AD) = 1.8 meters.
  Distance between point A and point B (AB) = 0.6 meters</p>
  
  <p><strong>Image plane coordinates:</strong></p>
  
  <p>A' = (232, 613)</p>
  
  <p>B' = (221, 341)</p>
  
  <p>C' = (215, 189)</p>
  
  <p>D' = (210, 98)</p>
  
  <p><a href="https://i.stack.imgur.com/Ts3ss.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/Ts3ss.png" alt="enter image description here"></a></p>
  
  <p>I used cross ratios to calculate CD.</p>
  
  <p>R{A', B', C', D'} = 1.316</p>
  
  <p>and</p>
  
  <p>R{A,B,C,D} = (AC * BD)/(AD * BC)</p>
  
  <p>After calculation, CD is 0.584m (Instead of 0.6m)</p>
  
  <p><strong>Questions:</strong></p>
  
  <p>1) Is the method I'm following to verify CD correct?</p>
  
  <p>2) Should I consider the angle between A and D (which is not 90 deg)</p>
  
  <p>3) Should I look into vanishing points here?</p>
  
  <p>4) If we don't know the real world distance between A and B and know only AC and AD, is it possible to calculate 
  the distance between either B and A or B and D?</p>
  
  <p>5) The difference 0.016m in the above calculation, is it acceptable?</p>
  
  <p>I'm newbie to Projective geometry. Please let me know if I'm doing anything wrong.</p>