estimate_laser_plane.md

@@ -39,13 +39,11 @@ In first, when we want to track a laser path, the image with the laser path is c
 
 As you can see in the picture above, the laser path has slightly higher intensity than anything around. The laser position is given as a pixel with maximal intensity in some direction (i.e., row/column). 
 
-A laser light has a normal distribution around the maximum. This assumption is used to refine laser position to sub-pixel precision. The neighborhood around maximum is chosen and intensities are logarithmized. These logarithms now describe a parabola. Finally, the parabola local maximum is a place with maximal intensity in our specified direction. 
+A laser light has a normal distribution around the maximum. This assumption is used to refine laser position to sub-pixel precision. The neighborhood around maximum is chosen, and intensities are logarithmized. These logarithms now describe a parabola. Finally, the parabola local maximum is a place with maximal intensity in our specified direction. 
 
 ### Estimating Laser Plane Position
 
-As you can see on pictures below, not all laser points are laying on the chessboard, so we select the only the one that does and transforms them from image points to the camera coordinates.
-
-We obtain these points for two different positions of a chessboard and get a set of points, which are laying on the laser plane. After that, we fit plane in-between points using singular value decomposition (svd) and receive the laser plane equation as:
+As you can see on pictures below, not all laser points are laying on the chessboard. The position of the pattern in the image is known, and only points which lay on the patter are chosen. The points in world coordinates are found using the inverse transformation of a pinhole camera with added pattern plane condition. 
 
 <img src="http://mathurl.com/zw2vhdq.png" />