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Nicolas Saunier edited section_Methodology_The_approach_proposed__.tex
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TODO This section still needs to be filled: perhaps a figure showing some of the errors? Discuss what each of them does
\subsection{Tracking \subsection{Optimizing Tracking Accuracy}
TODO define MOTA (with matching distance)
A genetic algorithm with the chosen parameters is then run on 5 minutes of each video sequence with a corresponding ground truth. Computer vision is used to create files containing the trajectory information which is then run through the Pvatools filtering functions. The optimization process searches for the tracking parameters $\theta$ that maximize the performance of the of the tracked trajectories compared to the ground truth inventory. The evaluation metric used to rank performance is the Multiple Object Tracking Accuracy (MOTA) as described in \cite{Bernardin_2008}. It is the most common metric for tracking accuracy used in computer vision. Once the genetic algorithm finds a local maximum, the resulting set of parameters is applied to the other video sequences to determine the performance of the tracking parameters under different conditions.
Table~\ref{tab:parameters} is an overview of the tracking parameters optimized by the genetic algorithm.
\begin{table}
\caption{Tracking
Parameters Used in Optimization Process} parameters considered for tracking accuracy optimization}
\label{tab:parameters}
\begin{tabular}{llll}
\hline
...
\end{tabular}
\end{table}
\subsection{Performance Results} The tracking parameters listed in TABLE~\label{tab:parameters} are optimized using a genetic algorithm that aims to improve tracking accuracy, comparing the tracker output to the ground truth for a video sequence (see overview in FIGURE~\ref{fig:optimization_overview}. At each iteration of the genetic algorithm corresponds a set (population) of tracking parameters $\theta$: the tracker and filtering routines are run on the video sequence for tracking parameters $\theta$. The tracker output and the ground annotations are compared in the analysis zone and the genetic algorithm will generate a new population of tracking parameters by favoring and mixing the best tracking parameters of the previous population.
The metric of tracking performance is the Multiple Object Tracking Accuracy (MOTA) as described in \cite{Bernardin_2008}. It is the most common metric for tracking accuracy, i.e.\ to evaluate the whole trajectory and not just detections in each frame, used in computer vision. MOTA is basically the ratio of the number of correct detections of each object over the number of frames in which the object appears (in the ground truth):
\begin{displaymath}
MOTA = 1 - \frac{\sum_{t} (m_t + fp_t + mme_t)}{\sum_t g_t}
\begin{displaymath}
The MOTA performance results where $m_t$, $fp_t$ and $mme_t$ are
dependent on respectively the
maximum distance allowed between a tracked trajectory number of misses, overdetections (false positives), and
mismatches. These depends on matching the trajectories produced by the tracker to the ground truth. In this
study, work, a road user is considered to be tracked in a frame if its centroid is within a given distance in world space from the ground truth bounding box center. Since there may be multiple matches, the hungarian algorithm is used to associate uniquely the ground truth and tracker output so that overdetections (more than one trajectory for the same road user) can be counted. The tracking results depend on these choices and a 5~m distance
threshold is used as it is approximately the length of a passenger vehicle.
The complementary performance measure of Multiple Object Tracking Precision (MOTP) is
another performance metric used to find reported in the results. It is the average distance between the ground truth and
tracked road
users user trajectories \cite{Bernardin_2008}. This is particularly important
when measuring for traffic
data variables such as
time-to-collision (TTC), gap time and
vehicle interactions as they require a certain level distance headway, and safety analysis based on the proximity in time and space of
precision interacting road users as measured for example by the time to
acquire reliable results. collision indicator~\cite{St_Aubin_2015}.
The relationship between %MOTP is the
parameters average distance between expected and
MOTA is evaluated using Spearman's Rank Correlation Coefficient, calculated as: actual detections, determined by:
\begin{displaymath}\rho %\begin{equation}
%MOTP = \frac{\sum_{i,t} d_{t}^{i}}{\sum_{t} c_t}
%\end{equation}
Once the genetic algorithm finds a local maximum, the optimized or calibrated tracking parameters can be applied to the other video sequences to determine the performance of the tracking parameters under different conditions. The relationship between the tracking parameters and MOTA is evaluated using Spearman's Rank Correlation Coefficient $\rho$, calculated as:
\begin{displaymath}
\rho = 1-\frac{6\sum d_{i}^{2}}{n(n^{2}-1)}
\end{displaymath}
\subsection{Effect of where $d_i$ is the difference between the ranks $x_i$ and $y_i$ for each corresponding MOTA
on Traffic Data} and tracking parameter values in a sample of size $n$.
%\subsection{Effect of MOTA on Traffic Data}
The road user trajectories obtained
by using with the calibrated tracking parameters are analyzed to generate
the traffic variables. The objective is to identify the relationship of different tracking
performance with accuracy of traffic variables. It is validated performance, measured by
comparing the impact of MOTA, with the
calibrated tracking parameters on relevant traffic
data variables including traffic flow and
average speed extracted from speed profiles. spot speeds.
\subsection{Over-fitting}
...
