deletions | additions       diff --git a/res_pre.md b/res_pre.md  index 3970022..dd19b62 100644  --- a/res_pre.md  +++ b/res_pre.md 
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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   \[  \left( \begin{array}{ccc}  ^1/_{16} & ^1/_{16} & \^1/_{16}\\\\ ^1/_{16}\\\\  ^1/_{16} & ^1/_{2}& ^1/_{16}\\\\  ^1/_{16} & ^1/_{16} & ^1/_{16} \end{array} \right)  \]