deletions | additions       diff --git a/Methodology Measurements TTC.tex b/Methodology Measurements TTC.tex  index 706d1f3..638c1de 100644  --- a/Methodology Measurements TTC.tex  +++ b/Methodology Measurements TTC.tex 
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Time-to-collision (TTC) is one of the most popular surrogate safety measures. It is a method of quantifying proximity to danger. Time-to-collision measures the time, at a given interaction-instant $t_0$, until two road users collide, if they collide, based on the motion prediction model. In the simplest form, e.g. constant velocity, time-to-collision is the ratio of differential velocity and differential distance. A TTC value of 0 seconds is, by definition, a collision. TTC is particularly useful as it has the same dimensions as some important traffic accident factors such as user perception and reaction time and breaking time. Larger values of observed TTC thus provide greater factors of safety for these driving tasks.  Time-to-collision is measured instantaneously: a new value of TTC may be computed for every interaction-instant. Thus, a pair of users may have a time series of TTC observations evolving over time. Some efforts have been made to study these evolutions microscopically over time series  [CITE]. Other approaches focus on minima or quantile observations [CITE], while others still attempt to examine step-by-step instantaneous  risk. TTC distributions are generally gamma-like-shaped across the literature. Quantifying collision risk based on TTC is the remaining puzzle piece. TTC thresholds have been popular, though are subject to arbitrary selection. One recent approach proposed a shifted gamma-generalised pareto distribution model \cite{Zheng_2014}. In the meantime, some qualitative analysis is possible in some circumstances, for example when shifts in center of mass of distributions are clear as demonstrated in Figure~\ref{fig:distro-comparison}. This approach has been tried in some early applications of the methodology, e.g. in \cite{Autey_2012} and in \cite{St_Aubin_2013}.