\relax \ifx\hyper@anchor\@undefined \global \let \oldcontentsline\contentsline \gdef \contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} \global \let \oldnewlabel\newlabel \gdef \newlabel#1#2{\newlabelxx{#1}#2} \gdef \newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} \AtEndDocument{\let \contentsline\oldcontentsline \let \newlabel\oldnewlabel} \else \global \let \hyper@last\relax \fi \providecommand*\HyPL@Entry[1]{} \HyPL@Entry{0<>} \citation{Aylward2002a} \citation{Wink2000a} \citation{Wink2004a} \citation{WikipediaAStar2007} \citation{Sethian1999a} \citation{Andrews2007a} \citation{Deschamps2001a} \@writefile{toc}{\contentsline {section}{\numberline {1}Background}{2}{section.1}} \@writefile{brf}{\backcite{Aylward2002a,Wink2000a}{{2}{1}{section.1}}} \@writefile{brf}{\backcite{Wink2004a}{{2}{1}{section.1}}} \@writefile{brf}{\backcite{WikipediaAStar2007}{{2}{1}{section.1}}} \@writefile{brf}{\backcite{Sethian1999a}{{2}{1}{section.1}}} \@writefile{brf}{\backcite{Andrews2007a}{{2}{1}{section.1}}} \@writefile{brf}{\backcite{Deschamps2001a}{{2}{1}{section.1}}} \newlabel{fig:Background:Synthetic:01:Speed}{{1(a)}{2}{Subfigure 1(a)\relax }{subfigure.1.1}{}} \newlabel{sub@fig:Background:Synthetic:01:Speed}{{(a)}{2}{Subfigure 1(a)\relax }{subfigure.1.1}{}} \newlabel{fig:Background:Synthetic:01:Arrival}{{1(b)}{2}{Subfigure 1(b)\relax }{subfigure.1.2}{}} \newlabel{sub@fig:Background:Synthetic:01:Arrival}{{(b)}{2}{Subfigure 1(b)\relax }{subfigure.1.2}{}} \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces The minimal path is extracted by back-propagating from an end point to a start point embedded in the arrival function. 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The resultant paths have been laid over the original image: the minimal path (green) and centered path (yellow). Original image courtesy of \href {http://upload.wikimedia.org/wikipedia/en/6/63/Cerebral_Angiogram_Lateral.jpg}{Wikipedia}.}}{5}{figure.3}} \newlabel{fig:Speed:RealDSA01}{{3}{5}{\label {fig:Speed:RealDSA01}A digital subtraction angiography (DSA) image of the cerebral vessels. The resultant paths have been laid over the original image: the minimal path (green) and centered path (yellow). Original image courtesy of \href {http://upload.wikimedia.org/wikipedia/en/6/63/Cerebral_Angiogram_Lateral.jpg}{Wikipedia}}{figure.3}{}} \@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {Uncentered Speed}}}{5}{figure.3}} \@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {Centered Speed}}}{5}{figure.3}} \@writefile{lof}{\contentsline {subfigure}{\numberline{(c)}{\ignorespaces {Overlay}}}{5}{figure.3}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.4}Optimizer}{6}{subsection.2.4}} \newlabel{sec:Implementation:Optimizer}{{2.4}{6}{Optimizer\relax }{subsection.2.4}{}} \@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces The top images (a and b) depict a continuous arrival function and extracted paths using the gradient descent (blue) and iterate neighborhood (red) optimizers for a synthetic dataset (\texttt {Data/Synthetic-02}\normalfont ). The bottom image (c) depicts a discontinuous arrival function (note that visited pixels are directly adjacent to non-visited pixels). The maze image (\texttt {Data/Synthetic-03}\normalfont ) is courtesy of \href {http://en.wikipedia.org/wiki/Image:Cg_pp_maze.png}{Wikipedia}.}}{6}{figure.4}} \newlabel{fig:Optimizers:Continuous}{{4}{6}{\label {fig:Optimizers:Continuous}The top images (a and b) depict a continuous arrival function and extracted paths using the gradient descent (blue) and iterate neighborhood (red) optimizers for a synthetic dataset (\code {Data/Synthetic-02}). The bottom image (c) depicts a discontinuous arrival function (note that visited pixels are directly adjacent to non-visited pixels). 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