title: Calculating camera coordinates from single img with marker
body: <p>My goal is calculating camera's world coordinates using flat marker.<br> 
  I have calibrated the camera and studied all the internal parameters.<br>
  The marker is a square. <br>
  Look my <a href="http://www.zoomex.org/stuff/marker.bmp" rel="nofollow">illustration</a> (unfortunately I can not post it here yet).</p>
  
  <p>{Xc,Yc,Zc} - camera-basis coordinates <br>
  {Xw,Yx,Zw} - world coordinates</p>
  
  <p>My task is calculating the camera's coordinates in {Xw,Yw,Zw}-basis.<br>
  I need to do this using just one photo. <br>
  Actually I need to do it for every photo from my collection.<br></p>
  
  <p>I have learned projective geometry theory. <br>
  I also implemented homography calculation.<br> 
  Using intrinsic camera matrix which I know after calibration I have solved the system of linear equations
  and found extrinsic matrix. And it's inverse matrix.
  The inverse matrix allowed me to find my camera's {Xw,Yw}-coordinates. The solution looks right. I have tryed several photos made from different angles.
  But I can not calculate Zw.</p>
  
  <p>Now I'm not shure that the problem has a solution.
  But augmented reality applications solve the similar problem.
  They calculates the marker vertexes' coordinates in {Xc,Yc,Zc}-basis.
  If I could do this I would be able to resolve my question too.</p>
  
  <p>I tried to investigate the ARToolKit implementation, but I did not overcome it. 
  I want to understand the substance, not to use any library or ready solution.</p>