deletions | additions       diff --git a/Methodolofy Measurement Definitions.tex b/Methodolofy Measurement Definitions.tex  index a7c7f16..3a6504a 100644  --- a/Methodolofy Measurement Definitions.tex  +++ b/Methodolofy Measurement Definitions.tex 
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An interaction quantifies the spatial relationship between moving objects in a scene. At the most fundamental level, an interaction is defined as a pair of moving objects simultaneously present in a scene over a common time interval (also reffered to as a user pair). We further define an instantaneous observation (i.e. in a give video frame) within this time interval as an interaction-instant.  This interaction definition is generic, if not naive, as the quality depends largely on how the scene is constructed. For example, the significance of an interaction between two vehicles seperated from each other physically (e.g. via a median or a large building) may not be comparable to an interaction between two vehicles merely seperated by a painted line because the risk probability  that one of the vehicles comes into contact with the other vehicle is reduced in the case of the median. This may skew interfere with  collision prediction attempts, particularly if scenes are not consistently selected and geometry is not  controlled. One solution is to perform a triage of user pairs based on physical access and proximity. A network topology coupled with a driving distance horizon is proposed. This is not a perfect solution, however, as physical access isn't necessarily a binary option. In our median example, it is still physically possible, although less likely, for vehicles to cross-over into an opposing lane and cause a collision, although this is something that could be modeled.  \subsubsection{Motion Prediction}  \label{motion-prediction}  While vehicle trajectories offer a rich set of observed behavioural data, they do not provide much collision data; this is by design of the proactive road safety approach: predicting collisions should be performed without observing them directly. In order to study collisions, they need to be extrapolated from traffic events with potential for collision. This potential is modeled by predicting future positions of vehicles using motion prediction at every instant in time and examining i) situations of particular risk probability of collision  (i.e. threshold) or ii) evolution of the risk. probability of collision over a timeseries.  Several motion prediction models are proposed for study \cite{Mohamed_2013}: \begin{itemize}  \item \textbf{Constant velocity} is the classic motion prediction model, wherein vehicles are projected along straight paths at a constant speed and heading using the velocity vector at that moment in time. This model is the simplest but also makes the most assumptions: only one movement is predicted at every instant, both users do not enter evasive action in the event of a collision course, and the natural (non-reacting) motion of a moving object is a straight path (not always true). These assumptions may be adequate for specific applications of the methodology, e.g. highways \cite{St_Aubin_2013}. The current implementation is based off of \cite{Laureshyn_2010}.