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where $f$ is the number of frames per second of the video.  \item \textbf{Motion patterns} are a family of models which use machine learning to calculate future position likelihoods from past behaviour \cite{Saunier}. behaviour\cite{Saunier}.  This type of model is the most promising as motion prediction is probabilistic in nature and inherently models naturalistic behaviour. However, they may not be able to model erratic behaviour such as roadway departures. Motion patterns are also complex to implement and expensive to process. The type of motion pattern being studied for implementation is a discretised motion pattern \cite{St_Aubin_2014}. \end{itemize}  As illustrated in Figure~\ref{fig:prob-collision-space}, motion prediction is performed for each user pair over each interaction-instant $t_0$ for a number of timesteps of size $\Delta t$ between $t_0$ and some chosen timehorizon. Each motion prediction may generate for two road users a series or a matrix of collision points with a sum of probabilities inferior or equal to 1. This is significantly larger and more difficult to handle than trajectory data, and currently cannot be performed in real time.