estimate_laser_plane.md

@@ -12,7 +12,9 @@ Courtesy [there](http://docs.opencv.org/2.4/modules/calib3d/doc/camera_calibrati
 
 
 ### Inverse transformation of pinhole camera equation
-The inverse transformation for picture coordinates to world one is under-determined. One more condition must be added to estimate the position ![alt text](http://mathurl.com/hj835tq.png) using only projection coordinates ![alt text](http://mathurl.com/hw2kh9a.png). OpenCV can find the transformation between the chessboard coordinates and the camera coordinates. Hence, we use chessboard plane. Furthermore, we can say that in chessboard coordinates all points are laying on plane described as z = 0. We can transform this plane to the camera coordinates like:
+The inverse transformation for picture coordinates ![alt text](http://mathurl.com/hw2kh9a.png) to world one ![alt text](http://mathurl.com/hj835tq.png) is under-determined. One more equation must be added to the system.
+
+OpenCV can find the transformation between the chessboard coordinates and the camera coordinates by solving P-n-P problem. Hence, the chessboard plane can be used. Chessboard z-axis is facing away from camera, and x-axis and y-axis lay on chessboard. The chessborad plane is desribed as  z=0. The transfromation of plane after solving the P-n-P problem writes:
 
 <img src="http://mathurl.com/gw8dwdp.png" /> ,
 <img src="http://mathurl.com/zwt5qhc.png" />.