deletions | additions       diff --git a/Methodology Video Data.tex b/Methodology Video Data.tex  index e062fe0..54a2257 100644  --- a/Methodology Video Data.tex  +++ b/Methodology Video Data.tex 
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It should be noted however that each successive derivation increases pixel precesion error for that measure. A velocity measure requires twice as many pixels as a position measurement. Similarly, an acceleration measurement requires three times as many pixels as a position measurement. This type of error can be compensated for with moving average smoothing over a short window (e.g. 5 frames). At this time, acceleration measurements are still too noisy to be useful for instantaneous observations. Higher camera resolutions sould solve this problem in future applications.  \subsubsection{Size of data} Data}  Feature tracking provides a microscopic level of detail. Individual observations measured at a single site over the course of a normal day typically register in the tens of millions. The sample size (number) of individual tracking  measurements (positions, velocities, etc.) per hour $n$ can be estimated with the equation \begin{equation} \label{eqn:data-size} n = fQd \end{equation}  where $f$ is the number of frames per second of the video, $Q$ is the average hourly flowrate, and $d$ is the average dwell time of each vehicle in the scene (excluding full stops). Dwell time is affected by the size of the analysis area in the scenery scene  and the average speed. As such, the size of the analysis area needs to be carefully selected, and selected. Furthermore,  overrepresentation of objects traveling below the average speed needs to be accounted for in all calculations. One option is to sample data per object with, for example, a simple mean, or alternatively to resample observations by position instead of time. For a series of equally spaced points in a grid, hex map, or along a spline the resampled value $m'_j$ at the point $p_j$ is the average   \begin{equation} \label{eqn:resampling} m'_j = \frac{\sum_{i=1}^{n}{m_i} }{n} \end{equation}  where $m_i$ is the measure of a series of points $i=1..n$ satisfying the constraint   \begin{equation} \label{eqn:resampling-constraint-map} [(mx_i-px_j)^2+(my_i-py_j)^2 < (px_{j+1}-px_j)^2+(py_{j+1}-py_j)^2] \end{equation}  for a grid or hex map and the constraint   \begin{equation} \label{eqn:resampling-constraint-spline} [(mS_i-pS_j) < (pS_{j+1}-pS_j)] \end{equation}  for a spline. This choice of resampling will vary from one context to the next.