%\subsubsection{Post-encroachment time}

%While prediction models and TTCs relate to the collision potential, other surrogate safety measures aim to measure collision proximity from crossing, but not necessarily colliding movements. Trajectory data is detailed enough to provide gap acceptance time (GT) and post-encroachment times (PET). These are measures that broadly characterize how aggressively and close in space and time merging and crossing tasks, respectively, are performed. As such, there is generally only one of these measures for the entire common time interval of a pair of road users. Gap acceptance time and PET fall under the category of high-level interpretation measures as the calculation of these measures cannot be generalized for all traffic studies, in part because the behaviour does not apply to all types of traffic interactions, and, in the case of gap acceptance time, because the measuring method may vary from one type of geometry to another.

%For the crossing zone defined by the intersection of the two trajectories of a pair of road users, the post-encroachment time measures the time between complete departure of the first arriving vehicle, and first arrival of the next arriving vehicle. If $PET = 0$, a collision has occurred. As such, higher PETs should demonstrate safer behaviour, although not necessarily linearly. An alternative to PET is predicted PET (pPET) which is measured from motion prediction instead of direct observation \cite{Mohamed_2013}. PET is, along with divergence, the complement to situations involving a TTC for any type of interaction.

%Gap acceptance time similarly measures arrival and departure of a road user at a common crossing zone, but in this case, the crossing zone occurs in-line during a merging task, usually followed by following behaviour.

\subsection{Indicator aggregation over time and space}

Instantaneous surrogate safety indicators such as speed and TTC are observed continuously. Currently, there is a lack of consensus in the literature on how to interpret continuous measures in terms of safety besides the event-based \cite{Hyden_1987,Svensson_2006} or safety continuum \cite{Zheng_2014} paradigms. One qualitative approach used in the literature has been to compare shifts in the probability distributions of these indicators when the magnitude of impact of individual indicators has no bearing on the overall direction of shift of safety risk \cite{Ismail_2010,Autey_2012,St_Aubin_2013}. For example, as illustrated in Figure~\ref{fig:distro-comparison} c) and d) it's unclear if converting "high and low risk" events into "medium risk" events is beneficial, but converting "high risk" events into "low risk" events is always beneficial as illustrated in a) and b). Still, there may be more complex interpretations related to driver awareness and learning as a function of perceived danger as described in \cite{Svensson_2006}. Alternatively, changes in frequency of events meeting a given threshold may yield similar results. While traffic event conversion factors have been developed and used in the past \cite{Hyden_1987,Svensson_2006}, transferability of validated conversion factors has been cited as problematic \cite{Mohamed_2013}. Indeed, while the shape of probability distributions of TTC has generally been characterized as Gamma-like in the literature \cite{Ismail_2010,Autey_2012}, variations or compound effects can be found, particularly when traffic streams become mixed \cite{St_Aubin_2013}. One recent approach proposed a shifted gamma-generalized Pareto distribution model \cite{Zheng_2014}.

Indicator interpretation may depend on the precise definition of what constitutes a "traffic interaction". The disaggregated interaction approach treats indicators as a representation of incremental risk which add up over time, but it tends to bias slower moving objects which dwell in the scene longer and complicates conditional probability calculations. The user-pair aggregated approach solves these problems but is sensitive to how the analysis area is defined and which users pairs are defined as interacting. Overall, a more detailed interaction exposure framework is still needed in the literature. Some simplifications have been made in the meantime. The traditional TCT methodology frequently represented user pair interactions using a single value of TTC, the minimum TTC ($TTC_{min}$). In practice, due to the imperfect nature of automated video data extraction, minimum values tend to oversample instantaneous tracking errors, and so a 15th percentile approach is preferred \cite{St_Aubin_2015_TRBa}.