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\section{Introduction}  Affordable computing, cheap sensor technology, and mobile computing are transforming the information landscape: big data is changing how we interact with our environment and approach problem solving tasks and this is particularly true in the field of transportation. This should come to no suprise as transportation's complexity and pervasiveness in daily life lends itself naturally to large data sets. End users are being empowered by direct access to navigational information, traffic reports, and incident alerts, not only during the planning stages of a trip, but also, progressively, during the execution of a trip as well. This opens up possibilities for more dynamic traffic load balancing and congestion easing of road networks and in return provides researchers with participatory network usage data collection. Meanwhile, older technology is being repurposed for more inteligent traffic analysis; for example, the onset of computer vision has the potential of transforming the mass surveillance infrastructure into a highly detailed traffic data collection tool to identify and study many different traffic behaviours. One such behavioural study application is in proactive road safety diagnosis. This has been a long-standing goal in the field of transportation safety. Traditional statistical methods applied to accident data require long observation periods, are expensive to organize and come at a price to society: one must wait for (enough) accidents to occur. Beginning in the 1960s, attempts were made to predict collision rates based on observations without a collision rather than historical accident records \cite{Perkins_1968}: these methods are now termed surrogate safety methods. The traffic conflict technique was one of the earliest methods proposed which entailed the observation of quasi-collision events: situations in which road users were exposed to some recognizable risk (probability) of collision, e.g. a “near-miss”. However, several problems limited their adoption: the manual data collection method is costly and may not be reliable, and the definition and objective measurement of these events are difficult \cite{Chin_1997}.  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 \cite{Saunier_2010} 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{Jackson_2013}. 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{saunier07probabilistic}. 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.   This data-driven methodology is applied to a large video dataset collected at more than 20 roundabouts in Quebéc to study road user behaviour and their safety. Camera views record data at more than 40 roundabout weaving zones, an area within the roundabout delimited by an entry and the next following exit. Each camera records 12 to 16 h of video on a given work day, which constitutes a dataset of over 600 hours of video data. Applying the proposed method to this large dataset yields considerable amounts of indicators, from individual road user measurements, e.g.\ speed, to individual interaction measurements, e.g.\ TTC, to aggregated indicators per road user or interaction, to aggregated indicators per site over time and space.  Analyzing such big data is a challenge of a magnitude that has never been undertaken before in driver behaviour and road safety research. It holds the key to understanding the processes that lead road users to collide, and to design and validate safety indicators that do not require accidents to occur. The approach will be demonstrated on this video dataset to identify roundabout characteristics that influence road safety.