deletions | additions       diff --git a/subsection_Approximation_of_probability_distribution__.tex b/subsection_Approximation_of_probability_distribution__.tex  index 1f59b88..4bcbb40 100644  --- a/subsection_Approximation_of_probability_distribution__.tex  +++ b/subsection_Approximation_of_probability_distribution__.tex 
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The approximation of probability distribution of positions or accelerations is a key part of mutual information computing.  \subsubsection{sparcity \subsubsection{sparsity  problem} To cope with sparcity sparsity  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 $T$: