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\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.  \subsubsection{sparcity problem}  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.