title: Camera pixels to planar world points given 4 known points
body: <p>My problem I am assuming is easy, but I still haven't been able to solve it due to my experience in linear algebra a while ago. I have read presentations published from several universities but I just can't seem to follow the somewhat non-standardized notation. If anyone has a better example it would be much appreciated...</p>
  
  <p><strong>Problem:</strong> 
  The camera is angled down facing the floor. Given a pixel coordinate, I want to be able to get the respective 3D world coordinate on the plane of the floor.</p>
  
  <p><strong>Known:</strong></p>
  
  <ul>
  <li>4 dots on the floor where I know the Pixel(x,y) coordinates and the associated World(X,Y,Z=0) coordinates.</li>
  <li>The camera's position is fixed and I know the displacement in the X,Y,Z directions of the camera.</li>
  </ul>
  
  <p><strong>Unknown:</strong></p>
  
  <ul>
  <li>The camera's rotations about the x,y,z axis. Primarily, the camera is rotated just about the X axis with Y &amp; Z being minimal rotations but I think should be taken into account.</li>
  <li>Distortion coefficients, however there is minimal bending of images in the lines and would much prefer to not bring in the checkerboard calibration procedure. Some error as a result of this is not a deal breaker.</li>
  </ul>
  
  <p><strong>What I've looked into</strong>
  A phenomenal example is found <a href="https://stackoverflow.com/questions/12299870/computing-x-y-coordinate-3d-from-image-point?rq=1"><strong>here.</strong></a> In essence it's the exact same problem, but some follow up questions:</p>
  
  <p>SolvePnP looks to be my friend, but I'm not too sure what to do about the Camera Matrix or the distCoefficients. Is there some way I can avoid the camera matrix and dist coefficients calibration steps, which is done I think with the checkerboard process (maybe at the cost of some accuracy)? Or is there some simpler way to do this?</p>
  
  <p>Much appreciate your input!</p>