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\section{Literature Review}  The capture of high-resolution data permits the measurement of precisely defined instantaneous surrogate safety measures for the purpose of identifying potential for collision. One such measure is Time-to-Collision (TTC), first proposed by \cite{Hayward_1971}, which measures the time remaining, at any given instant and for any potential collision course with another road user or a stationary obstacle, before the collision occurs. This measure is useful as it provides a minimum reaction time required for drivers to react to and avoid a potential collisions, typically set at the critical value of 1.5 seconds \cite{Hyden_1987, Green_2000}. Higher TTCs are generally considered safer, though the precise link has yet to be validated in part because the potential for collision is poorly established and defined in the literature. In fact, this measure relies on motion prediction hypotheses to identify potential collision courses. The traditional approach is to use constant velocity projection \cite{Amundsen_1977, Laureshyn_2010} (situations in which road users fail to correct their course for some reason or another and are subject to Newton's first law of motion), which is the motion prediction method most frequently used, often without further justification. This approach does not natively provide a collision course probability, and it is not be suitable in situations where observed trajectories do no include constant velocity displacements: for example, turning lanes in an intersection and movements in a roundabout.  More advanced collision course modelling efforts have being developed, including motion patterns which represent naturalistic (expected) driving behaviour learnt from all other road users of a particular scene with corresponding initial conditions. This probabilistic approach provides a continuum of potential collision points. Motion patterns may be described discretely over time and space \cite{St_Aubin_2014} or with prototype trajectories \cite{saunier07probabilistic}. Some disadvantages of motion patterns are that they are limited in usable time-horizon (maximum predictable TTC) and are computationally intensive as they explore, for each pair of road users, at each point in time, all future positions in time and space subject to the time horizon. Furthermore, interaction complexity and exposure tend to increase exponentially as the number of simultaneous road users in a scene increases varying anywhere from hundreds to millions of interactions per hour.   diff --git a/layout.md b/layout.md  index 9d8695f..9217930 100644  --- a/layout.md  +++ b/layout.md 
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Abstract.tex  Introduction.tex  LitRev.tex  Methodology.tex  figures/Overview1/Overview.png  Methodology Video Data.tex