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