estimate_laser_plane.md

@@ -16,22 +16,18 @@ The inverse transformation for picture coordinates ![alt text](http://mathurl.co
 
 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" />.
-
-Now we have to obtain a normal of plane and its translation:
-
 <img src="http://mathurl.com/h23dwzm.png" /> ,
 <img src="http://mathurl.com/hxa6ykl.png" /> ,
 <img src="http://mathurl.com/j7y8cdf.png" /> , 
 
 so the <img src="http://mathurl.com/j865cst.png" />.
-
-We can add this condition to the pinhole camera model equation, where [**R**|t] matrix is an identity matrix and <img src="http://mathurl.com/j7ltgkr.png" />, we end up with:
+This condition is added to the pinhole camera model:
 
 <img src="http://mathurl.com/jzqcmgq.png" />
 
-Thereafter, we can make inverse transformation from ![alt text](http://mathurl.com/hw2kh9a.png) to ![alt text](http://mathurl.com/hj835tq.png) as following:
+, where [**R**|t] matrix is an identity matrix and <img src="http://mathurl.com/j7ltgkr.png" />.
+
+The inverse transformation from ![alt text](http://mathurl.com/hw2kh9a.png) to ![alt text](http://mathurl.com/hj835tq.png) writes:
 
 <img src="http://mathurl.com/zv29thy.png" />