deletions | additions       diff --git a/Introduction Road Safety.tex b/Introduction Road Safety.tex  index 62c64be..569834d 100644  --- a/Introduction Road Safety.tex  +++ b/Introduction Road Safety.tex 
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Today, with technological improvements in computing power, data storage, sensor technologies, and advances in artificial intelligence, these issues are quickly being addressed. This research presents the application of a video-based automated trajectory analysis solution which combines the latest advances in high-resolution traffic data acquisition and machine learning methods to model and predict collision potential from relatively short, but extremely rich traffic data. This data is typically obtained from ordinary video data via computer vision from a camera situated at 10 m or more above the roadway \cite{Saunier_2010}. This trajectory data consists of position and velocity measurements of road users captured 15 to 30 times per second to a relatively high degree of accuracy. This amounts to several million individual instantaneous measurements over the period of one day at a typical site.  This high-resolution data permits the measurement of precisely defined instantaneous surrogate safety measures identifying collision probability. One such measure is time-to-collision (TTC) which measures the time remaining at any given instant to some collision point in the future defined by a collision course with another road user. This measure is useful as it provides the remaining time road users have to react to and avoid potential collisions. Higher TTCs are generally considered safer, though the precise link has yet to be validated. However, this measure relies on motion prediction hypotheses to identify collision courses. The traditional approach is to use constant velocity projection \cite{Amundsen_1977} \cite{Laureshyn_2010}  (situations in which road users fail to correct their course), which is the motion prediction method most frequently used, without a justification. This approach does not natively provide a collision course probability, and it will 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 are underway, including motion patterns which represent naturalistic (expected) driving behaviour learnt from the same data set. This procedure provides several potential collision points and their probability as a function of both the characteristics of the specific site and the behaviour of the road users. The motion patterns, or the distribution of trajectories at a site and their probabilities, may be described discretely over time and space \cite{St_Aubin_2014} or with prototype trajectories [CITE]. The motion and collision predictions are computationally intensive as they explore, for each pair of road users, at each point in time, all future positions in time and space (typically subject to a time horizon). Furthermore, interaction complexity and exposure increases exponentially with increases in the number of simultaneous road users in a scene. For example, over the course of one day, a typical intersection can experience between 100 thousands and 100 millions of these instantaneous interactions, depending on the intersection complexity.