deletions | additions       diff --git a/res_pre.md b/res_pre.md  index dd19b62..32bc7ec 100644  --- a/res_pre.md  +++ b/res_pre.md 
...
### Image preprocessing  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 \(1/(8k\cdot(n+1))\). \(^1/_{(8k\cdot(n+1))}\).  For example, when n=1 the kernel would be \[  \left( \begin{array}{ccc}  ^1/_{16} & ^1/_{16} & ^1/_{16}\\\\