deletions | additions       diff --git a/res_pre.md b/res_pre.md  index d06693c..b543d41 100644  --- a/res_pre.md  +++ b/res_pre.md 
...
The only preprocessing step used is convolving the image with a \((2n+1)\times(2n+1)\) kernel where the center element is \(1/(n+1)\) and the k-th layer surrounding the center is made up of values \(1/(8k\cdot(n+1))\). For example, when n=1 the kernel would be   \[  \left( \begin{array}{ccc}  ^1/_16 ^1\!,/_{16}  & \tfrac{1}{16} & \tfrac{1}{16}\\\\ \tfrac{1}{16} & \tfrac{1}{2}& \tfrac{1}{16}\\\\  \tfrac{1}{16} & \tfrac{1}{16} & \tfrac{1}{16} \end{array} \right)  \]