deletions | additions       diff --git a/Methodology Video Data.tex b/Methodology Video Data.tex  index 7caf0fb..ac904be 100644  --- a/Methodology Video Data.tex  +++ b/Methodology Video Data.tex 
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\subsubsection{Trajectories: Positions in Space and Time (x,y,t)}  Trajectories are, at the simplest level, a series of points in cartesian space representing the position of (the center of) a moving object at time $t$ on a planar syrface (height surface. Height  $z$ is ignored). assumed insignificant.  Points are evenly spaced in time with a consistent $\delta $\Delta  t$ equivalent to the inverse of the framerate of the video. Typical framerates for video are between 15 to 30 frames per second, or 15 to 30 observations per moving object per second, after feature grouping. The object itself is represented by a mass of charicteristic features closely spaced and moving in unison. Three potential sources of error exist: paralax, pixel resolution, and tracking errors. Paralax error is mitigated by maximising the subtending angle between the camera and the hight of tracked objects. In practical terms this requires a high view or ideally a bird's eye view, tracking objects with a small height to base ratio. Passenger cars are generally more forgiving in this respect than trucks or pedestrians. Pixel resolution determines measurement precision. Objects further away from the camera experience lower tracking precision than objects near the camera. Error due to pixel resolution is mitigated by using high-resolution cameras and observing objects near the camera. Finally, tracking errors may occur with scene visibility issues or due to current limits with computer vision. These observations have to be rejected. [CITE]  \subsubsection{Derived Data: Velocity & Acceleration}  Velocity and acceleration measures  are derived from position over time and velocity over time measures  respectively. These are vectors with a magnitude (speed) and a heading. The heading of the velocity vector is typically used to determine the orientation of the vehicle. It should be noted that velocities and accelerations are smoothed over a window of 5 to ten 10  frames. This is necessary as  As such, acceleration measures can be problematic to measure. \subsubsection{Size of data (hours, GB, framerate, resolution)}