laser_trace.md

 # Laser Tracking
 
 ---
-### Intensity picture
-The image with the laser path is converted to the grayscale image with the highest proportion to a Red channel. This image is called an intensity picture.
+## Intensity picture
+The image with the laser path is converted to the grayscale picture with the highest proportion to a Red channel. This picture is called an intensity picture.
 
 [//]: # (  ![test](http://gitlab.ciirc.cvut.cz/cmirajak/laser_plane_scanner/uploads/1cececf3a4de9af3a250f479f6e82051/test.jpg) ) 
 
 ## Pixel maximum
 
-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). The laser path tracking direction is the direction of picture rows. The cumulative mean function is used, when multiple maximal values are present in a single direction:
+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). The laser path tracking direction is in the direction of the picture rows. The cumulative mean function is used, when multiple maximal values are present in a single direction:
 
 <img src="http://mathurl.com/jdfae4x.png" />
 
 
 
-A laser light has a normal distribution around its 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. The global maximum of the parabola is:
+A laser light has a normal distribution around its 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, a local maximum  of the parabola is a place with maximal intensity in our specified direction. The global maximum of the parabola is:
 
 <img src="http://mathurl.com/hpbxpbz.png" />
 
-This allows us to find the laser position with a sub-pixel precision.
+This approximation allows us to find the laser position with sub-pixel precision.
 
 [//]: # (For the pixel-precise maximum index we just call maximal index find for the array which returns only the first index. After that, we check if the maximum is larger then selected noise level and if it is not we will start processing next row. Actually, there can be more pixels with the same maximal value following first one. So we use iterative mean to calculate the middle of those pixels.)