deletions | additions       diff --git a/Methodology Flow.tex b/Methodology Flow.tex  index 2d35bf2..c289417 100644  --- a/Methodology Flow.tex  +++ b/Methodology Flow.tex 
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Traffic flow data is obtained from the automated analysis video data: vehicle trajectories extracted from video data using computer vision techniques built for traffic analysis applications. In this case, the computer vision tool used is the Traffic-Intelligence project, an open-source traffic-analysis software \cite{Jackson_2013}. See section \ref{data-size} for more details on the source and size of the data.  Trajectory data is formed from the tracking of moving features within camera space. These feature tracks are a series of continuously measured positionsand derived velocity vectors  mapped to real coordinates using a scene projection transformation by way of a homography matrix. These features are continuous, forming a path (trajectory) moving through space and time representing the a road user's movement through the scene. Features are grouped together into objects using specifically calibrated algorithms for the task of identifying individual road users in the a scene (though context-insensitive classification is still a work in progress). Some secondary filtering techniques were developed to automate validation and error correction \cite{Jackson_2013, St_Aubin_2014}. Traffic flow and flow ratios can be obtained by performing counts on these objects according to the context of the specific metric. In this case we collect per-lane per-hour counts over the time of the study. Flow ratio is calculated as follows: 
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\subsubsection{Speed}  Speed is similarly obtained from trajectory data. It is derived from position observations between successive frames. It should be noted that a moving average filter with a half window  ofroughly  5 frames is applied to this data to correct for inaccuracies introduced by the pixels, reduce tracking noise,  but this still corresponds to speed measurements performed several times per second per object. \subsubsection{Time-to-collision}  Time-to-collision (TTC)  is the surrogate measure of safety of choice for its relative maturity, simplicity, and transferability properties. Time-to-collision TTC  measures the time remaining, at any instant in time before two road users on a potential collision course collide: higher values are better for safety. It doesn't have the same level of validation as speed does in the literature, but while speed is a good predictor of collision severity, TTC promises to be a good predictor of collision probability, a property which is arguably lacking with speed \cite{Hauer_2009}. Therefore, modelling the two together should give a good overall coverage of collision risk. The constant velocity motion prediction model is deemed inadequate for TTC measurement in roundabouts however, as road users in roundabouts rarely follow straight trajectories. Fortunately, some more sophisticated naturalistic motion prediction models have been developped to overcome this shortcoming: motion patterns are used for their ability to learn normal movement within a traffic scene. A discretised motion pattern matrix method developed specifically for roundabouts \cite{St_Aubin_2014} is used for this study. We also elect to model all traffic events, use no minimum detection probability, and use the indicator aggregation by the  15th percentile unique per  user pairindicator aggregation  as is described in \cite{St_Aubin_2015}. \subsection{Site Selection}  Site selection was performed according to a number of criteria including practical constraints and statistical representation. Data collection feasibility was scored on a five-point scale measuring data collection cost and quality and sorted to generate a feasibility rank. Among a population of nearly one hundred candidate roundabouts in the province of Québec, starting from the most feasible, thirty sites were chosen to provide a good representation of design and land use characteristics, knowing that a fraction of these sites would have to be rejected due to logistical issues (e.g. adverse weather, road closures, or equipment failure hampering data collection efforts). In particular:  \begin{itemize}  \item An adequate geographical coverage of the province of Québec and land use representation types  was desired. Sites were selected throughout all but one of the the major populated regions of Québec, as well as some of the more rural areas to provide regional representation. As listed in Table~\ref{tab:be_fac}, representation of the built environment factors is adequate though with a few exceptions. Notably, roundabouts on private roads are difficult to access for data collection and, in any case, provides little safety information as traffic flows are too small. Also, while roundabouts can often be found in school or commercial zones, these roundabouts did not serve through-traffic, serving instead as limited  accessgentrified  points for parking lots or campus roads. These sites were rejected. \item Roundabouts located on the territory of the provincial transportation agency are all built to very similar specifications and are significantly more consistent in design than municipal roundabouts. However, provincial roundabouts tend to serve more network classes than municipal roundabouts which serve collector roads for the most part. 40\% 40~\%  of the sites were located on provincial territory while the remainder were strewn across seven different municipalities. \end{itemize}  \subsection{Modelling}  Mean speed Speed  can be nicely averaged as it is generally normally distributed. TTC however is not alwaysnicely distributed,  so nicely distributed:  different aggregation methods may should therefore  be used. Instead this data will be analysed in a disaggregated manner. The data is thus effectively unbalanced panel data, where sites are the panels containing individual observations of behaviour (speed, TTC indicators, gap acceptance). Random effects modelling is chosen for the analysis using the formula \begin{equation} \label{eqn:rextreg_model} ln(Y_{ij}) = \mu + {\sum}^{n}_{k=1} \beta_k X_{kij} + u_{ij} + \epsilon_{ij} \end{equation}