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fixed some gfx

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added some comments to the tex
This commit is contained in:
FrankE
2016-07-12 17:20:09 +02:00
parent f8d5449dbc
commit 83dab61ca1
10 changed files with 7680 additions and 29 deletions
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competition/tex/chapters/graph.tex
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@@ -1,12 +1,17 @@
\subsection{Transition}
To enhance the quality of the proposal distribution, the transition step is
based on a \SI{20}{\centimeter}-gridded graph $G = (V,E)$
based on random walks along a \SI{20}{\centimeter}-gridded graph $G = (V,E)$
with vertices $v_i \in V$ and undirected edges $e_{i,j} \in E$
derived from the buildings floorplan. This ensures that only valid
movements can be sampled from the previous state.%
derived from the buildings floorplan (figure \ref{fig:graphOverview}).
This ensures that only valid movements can be sampled from the previous state.%
\noindent\hspace{1mm}\input{gfx/graphOverview}
\begin{figure}
%\noindent\hspace{1mm}
\input{gfx/graphOverview}
\caption{The floorplan-based graph that is used for the transition step.}
\label{fig:graphOverview}
\end{figure}
The graph is built once and offline using the floorplan created by our editor.
Besides realistic stairwells, additional semantic information (e.g. doors)
@@ -14,18 +19,27 @@
and is used during the online phase.
If the pedestrian's destination is know beforehand, this information can
be included as prior knowledge into the transition step. A shortest-path
calculation imposes additional constraints to the transition by favouring
movements that approach the desired destination (pedestrian sticking to the shortest path)
be included as prior knowledge for the random walk: A shortest-path
calculation imposes constraints by favouring
moves (edges) that approach the desired destination (pedestrian sticking to the shortest path)
over movements that depart from the destination.
To ensure that the calculated shortest path is realistic (resembled human walking paths)
each node within the graph contains a weight, denoting the likelyhood for being visited
by the pedestrian. Using this approach, nodes near to walls receive a lower likelyhood.
During the path-calculation this importance is used to artificially increase/decrease the
To ensure that the calculated shortest path is realistic (resembles human walking paths)
each node within the graph contains a weight, denoting the likelihood for being visited
by the pedestrian. Using this approach, nodes near walls receive a lower likelihood.
During the path-calculation this importance is hereafter used to artificially increase the
weight $\delta(\mEdgeAB)$ between two nodes. This ensures that the resulting path is
farther away from obstacles and looks much more realistic
farther away from obstacles and looks much more realistic, as can be seen in figure \ref{fig:graphPaths}.
\noindent\hspace{1mm}\input{gfx/graphPaths}
\begin{figure}
%\noindent\hspace{1mm}
\input{gfx/graphPaths}
\caption{%
Shortest path calculation based on the underlying graph.
Just using the distance between two nodes as weight $\delta(\mEdgeAB)$ results in very unrealistic walking paths (blue).
Artificially increasing this weight for edges near walls, creates much better path estimations (green).%
}
\label{fig:graphPaths}
\end{figure}