deletions | additions       diff --git a/subsection_Approximation_of_probability_distribution__.tex b/subsection_Approximation_of_probability_distribution__.tex  index 1868a1f..d07b6f2 100644  --- a/subsection_Approximation_of_probability_distribution__.tex  +++ b/subsection_Approximation_of_probability_distribution__.tex 
...
\subsection{Approximation of probability distribution based on trajectories}  The approximation of probability distribution of positions or accelerations is a key part of mutual information computing.  To cope with sparcity we used Parzen windowing as it is described in \cite{Pluim_2003} for instance.  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 $W$ is a gaussian kernel. in practice we take a discrete gaussian filter for $W$.