deletions | additions       diff --git a/subsection_Approximation_of_probability_distribution__.tex b/subsection_Approximation_of_probability_distribution__.tex  index 4d4170d..f5fb8ad 100644  --- a/subsection_Approximation_of_probability_distribution__.tex  +++ b/subsection_Approximation_of_probability_distribution__.tex 
...
Given a trajectory $T$, the probability $p(x,y)$ of $(x,y)$ is the sum of the contribution of each $(x',y')$ in $T$. The contributions are functions of a Gaussian kernel.  Hence the following definition of the probability of $(x,y)$ given $T$:  \[P((x,y),T) = \sum_{(x',y')\in T}K((x,y),(x',y'))\]  where $K$ is a gaussian kernel. in In  practice we take a discrete gaussian kernel filter for $K$. $K$, given by the 3x3 matrix:  \[ K = \left| \begin{array}{ccc}  0.0625 & 0.125 & 0.0625 \\