\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 \bibstyle{amsrn} \citation{Bergo:Falcao04a} \citation{Bergo:Beucher93} \citation{Bergo:Vincent91} \citation{Bergo:Falcao01} \citation{Bergo:Falcao02} \citation{Bergo:Danielsson80} \citation{Bergo:Felkel01} \citation{Bergo:Falcao04b} \citation{Bergo:Moga1998a} \citation{Bergo:Moga1998b} \citation{Bergo:Moga1998a} \citation{Bergo:Bruno04} \select@language{english} \@writefile{toc}{\select@language{english}} \@writefile{lof}{\select@language{english}} \@writefile{lot}{\select@language{english}} \@writefile{toc}{\contentsline {chapter}{\numberline {1}A partitioned algorithm for the image foresting transform}{425}{chapter.1}} \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{425}{section.1.1}} \citation{Bergo:Ahuja93} \citation{Bergo:Falcao04a} \@writefile{toc}{\contentsline {section}{\numberline {2}Related works}{426}{section.1.2}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Related algorithms}{426}{subsection.1.2.1}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.2}The image foresting transform}{426}{subsection.1.2.2}} \newlabel{xxx:a.ift}{{1}{426}{The image foresting transform\relax }{nicealgorithm.1}{}} \citation{Bergo:Falcao04a} \citation{Bergo:Ahuja93} \citation{Bergo:Falcao04a} \citation{Bergo:Falcao04a} \citation{Bergo:Falcao04b} \citation{Bergo:Falcao04a} \citation{Bergo:Lotufo00} \citation{Bergo:Danielsson80} \citation{Bergo:Bergo06} \citation{Bergo:Falcao02} \citation{Bergo:Falcao04a} \citation{Bergo:Torres04} \citation{Bergo:Falcao04b} \newlabel{xxx:eq.fmax}{{1}{427}{The image foresting transform\relax }{equation.1}{}} \newlabel{xxx:eq.feuc}{{2}{427}{The image foresting transform\relax }{equation.2}{}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.3}The differential image foresting transform}{428}{subsection.1.2.3}} \newlabel{xxx:a.dift}{{2}{428}{The differential image foresting transform\relax }{nicealgorithm.2}{}} \@writefile{toc}{\contentsline {section}{\numberline {3}The partitioned image foresting transform}{429}{section.1.3}} \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Labels of an EDT with the Partitioned IFT: (a) Partial result after the first iteration and (b) final result after the second iteration. (c) PIFT notation: $\delimiter "426830A s,t \delimiter "526930B $ is an inter-partition edge, $P^\ast (s)$ is the optimum path assigned to $s$, and $R(s)$ the root of $P^\ast (s)$.}}{429}{figure.1.1}} \newlabel{xxx:f.pift1}{{1}{429}{The partitioned image foresting transform\relax }{figure.1.1}{}} \newlabel{xxx:a.pift}{{3}{430}{The partitioned image foresting transform\relax }{nicealgorithm.3}{}} \newlabel{xxx:a.pift2}{{4}{431}{The partitioned image foresting transform\relax }{nicealgorithm.4}{}} \@writefile{toc}{\contentsline {paragraph}{Performance Considerations.}{431}{paragraph*.1}} \citation{Bergo:Falcao04b} \@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Partition crossings and PIFT iterations: In the PIFT-EDT, paths cross at most $N_P - 1$ partition boundaries. In (a), $P^\ast (p)$ crosses 2 boundaries to reach $p$ from $a$. The numbers are the iteration in which the path segment is propagated. (b) For general path-cost functions, a path may cross partition boundaries several times.}}{432}{figure.1.2}} \newlabel{xxx:f.bound}{{2}{432}{Performance Considerations}{figure.1.2}{}} \@writefile{toc}{\contentsline {section}{\numberline {4}Experimental results}{432}{section.1.4}} \@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Images from the evaluation applications: (a) Slice from the WS-BRAIN input image. (b) gradient intensity of (a). (c) 3D renderization of the WS-BRAIN result. (d) Visualization of the discrete Voronoi diagram, result of the EDT-RND. (e) Slice from the distance map computed in EDT-BRAIN.}}{433}{figure.1.3}} \newlabel{xxx:f.app1}{{3}{433}{Experimental results\relax }{figure.1.3}{}} \citation{Bergo:Falcao04b} \citation{Bergo:Falcao04a} \citation{Bergo:Falcao01} \citation{Bergo:Bergo06} \citation{Bergo:Beucher93} \citation{Bergo:Falcao04b} \citation{Bergo:Vincent91} \citation{Bergo:Danielsson80} \citation{Bergo:Falcao04a} \citation{Bergo:Falcao02} \citation{Bergo:Torres04} \@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Number of processed nodes and upper bound for the speedup factor in each application, using up to 10 partitions.}}{434}{table.1.1}} \newlabel{xxx:t.exp1}{{1}{434}{Experimental results\relax }{table.1.1}{}} \@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Number of processed nodes vs. number of partitions for (a) EDT-RND, EDT-BRAIN and (b) WS-BRAIN.}}{434}{figure.1.4}} \newlabel{xxx:f.plot1}{{4}{434}{Experimental results\relax }{figure.1.4}{}} \bibcite{Bergo:Ahuja93}{{1}{}} \@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces PIFT performance on two parallel computer systems. Times are given in seconds.}}{435}{table.1.2}} \newlabel{xxx:t.exp2}{{2}{435}{Experimental results\relax }{table.1.2}{}} \@writefile{toc}{\contentsline {section}{\numberline {5}Conclusion and future works}{435}{section.1.5}} \bibcite{Bergo:Bergo06}{{2}{}} \bibcite{Bergo:Beucher93}{{3}{}} \bibcite{Bergo:Bruno04}{{4}{}} \bibcite{Bergo:Danielsson80}{{5}{}} \bibcite{Bergo:Falcao04b}{{6}{}} \bibcite{Bergo:Falcao02}{{7}{}} \bibcite{Bergo:Falcao01}{{8}{}} \bibcite{Bergo:Falcao04a}{{9}{}} \bibcite{Bergo:Felkel01}{{10}{}} \bibcite{Bergo:Lotufo00}{{11}{}} \bibcite{Bergo:Moga1998a}{{12}{}} \bibcite{Bergo:Moga1998b}{{13}{}} \bibcite{Bergo:Torres04}{{14}{}} \bibcite{Bergo:Vincent91}{{15}{}} \newlabel{[bibenv:1]}{13.21579pt}