## 3 Traffic Model and Knowledge Discovery
Route objects do not merely count the registered transiting vessels, but are also statistically described by the static and kinematic features of the vessels that created or updated them. Specifically, the Route Objects Manager, whose main steps are reported in Algorithm 3--Route Objects Manager in Annex A--deals with the creation of new route objects and with the dynamic  
Figure 2: Stationary points (green dots) incrementally detected during a two-week period over the Strait of Gibraltar, an area characterized by intense traffic. Stationary points are then clustered using incremental Density-Based Spatial Clustering of Applications with Noise (DBSCAN) into port and offshore platform objects, whose concave hulls (right) consistently capture areas where vessels anchor outside ports. management of their features and labels, as resulting from the incremental clustering of the relevant \(WPs\) described in Algorithm 2--_On-Line WPs Clustering_, Annex A. Once a vessel enters the scene, its features are compared with the existing set of routes. If a route already exists, whose positional features are compatible to the vessel features, both the vessel is added to the route list of vessels and, mutually, the route is added to the list of the \(WPs\) transited by the vessel. Otherwise, the vessel contributes to the initialization of a new route, and, when a minimum number of detections (_i.e._, number of transits along the route) is reached, the new route is activated. Each route object has a spatio-temporal sequence of state vectors, facilitating the analysis and classification of activities. The detected routes can be organized in historical atlases, which summarize the maritime traffic in the considered area. As an example, we report the route codebook learned in the North Adriatic Sea in Figure 4. Some of the derived routes are not easy to explain by glancing at the AIS traffic messages reported in Figure 3b. The methodology shows a significant agreement with the traffic schemes in use on nautical charts. In Figure 5, an example of two routes extracted between two detected stationary areas in the Strait of Gibraltar is illustrated. The major east and westbound traffic volumes significantly exceed the traffic flow between the selected ports, making the routes' visual isolation difficult. The two routes adhere to the maritime rules of the road when crossing the main traffic flows: the main traffic in the same direction flow is crossed at a shallow angle (_i.e._, \(20^{\circ}\)-\(30^{\circ}\)), while the opposing traffic flow in each route is cut across at broad angles (_i.e._, \(90^{\circ}\)). The second portion of each route is, therefore, more diffuse, as the ferries maneuver more when crossing the opposing sea lanes compared to overtaking traffic in the same direction. The extracted routes, whose number is not assumed _a priori_, but automatically learned, are characterized also by the information of the entering and exiting time of the registered vessels together with their ship type. Different from live video analysis applications,  
Figure 3: Waypoints detection and characterization over a \(200\times 160\) km area in the North Adriatic Sea (**a**) from March 1 to May 15, 2012. The unsupervised analysis leads to the detection of entry (cyan), exit (magenta) and stationary areas (green) (**b**), one of them being an offshore regasification gateway as confirmed by the ship type distribution analysis (**c**), following the categorization in [39], performed on the Maritime Mobile Service Identity (MMSI) list of registered vessels. this allows the extraction of higher level information, such as the ship type, distribution of the route, its average travel time and the daily/weekly patterns, as shown in Figure 6.  
Anomalies in the traffic schedule can therefore be modeled on vessels that are fully compliant with the route directions, but use them at low-likelihood times.