\relax 
\@writefile{toc}{\author{Gilles Perrot}{}}
\@writefile{loa}{\addvspace {10\p@ }}
\@writefile{toc}{\contentsline {chapter}{\numberline {3}Setting up the environnement.}{25}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{algo:memcopy:H2D}{{7}{25}}
\newlabel{algo:memcopy:kernel}{{8}{25}}
\newlabel{algo:memcopy:D2H}{{9}{25}}
\@writefile{loa}{\contentsline {algocf}{\numberline {1}{\ignorespaces Global memory management on CPU and GPU sides.\relax }}{25}}
\newlabel{algo:memcopy}{{1}{25}}
\@writefile{toc}{\contentsline {section}{\numberline {3.1}Data transfers, memory management.}{26}}
\newlabel{lst:main1}{{3.1}{27}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {3.1}Generic main.cu file used to launch CUDA kernels}{27}}
\newlabel{lst:fkern1}{{3.2}{27}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {3.2}fast\_kernels.cu file featuring one kernel skeleton}{27}}
\newlabel{lst:mkfile}{{3.3}{28}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {3.3}Generic Makefile based on those provided by NV SDK}{28}}
\@writefile{toc}{\contentsline {section}{\numberline {3.2}Performance measurements}{28}}
\newlabel{lst:chronos}{{3.4}{28}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {3.4}Time measurement technique using cutil functions}{28}}
\@writefile{toc}{\author{Gilles Perrot}{}}
\@writefile{loa}{\addvspace {10\p@ }}
\@writefile{toc}{\contentsline {chapter}{\numberline {4}Implementing a fast median filter}{31}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{toc}{\contentsline {section}{\numberline {4.1}Introduction}{31}}
\@writefile{toc}{\contentsline {section}{\numberline {4.2}Median filtering}{32}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.1}Basic principles}{32}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.2}A naive implementation}{32}}
\newlabel{img:sap_example_ref}{{4.1(a)}{33}}
\newlabel{sub@img:sap_example_ref}{{(a)}{33}}
\newlabel{img:sap_example_med3}{{4.1(b)}{33}}
\newlabel{sub@img:sap_example_med3}{{(b)}{33}}
\newlabel{img:sap_example_med5}{{4.1(c)}{33}}
\newlabel{sub@img:sap_example_med5}{{(c)}{33}}
\newlabel{img:sap_example_med3_it2}{{4.1(d)}{33}}
\newlabel{sub@img:sap_example_med3_it2}{{(d)}{33}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.1}{\ignorespaces Example of median filtering, applied to salt \& pepper noise reduction.\relax }}{33}}
\@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {Airplane image, corrupted by salt and pepper noise of density 0.25}}}{33}}
\@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {Image denoised by a $3\times 3$ median filter}}}{33}}
\@writefile{lof}{\contentsline {subfigure}{\numberline{(c)}{\ignorespaces {Image denoised by a $5\times 5$ median filter}}}{33}}
\@writefile{lof}{\contentsline {subfigure}{\numberline{(d)}{\ignorespaces {Image denoised by 2 iterations of a $3\times 3$ median filter}}}{33}}
\newlabel{fig:sap_examples}{{4.1}{33}}
\newlabel{lst:medianGeneric}{{4.1}{34}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {4.1}Generic CUDA kernel achieving median filtering}{34}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.2}{\ignorespaces Example of 5x5 median filtering\relax }}{35}}
\newlabel{fig:median_1}{{4.2}{35}}
\newlabel{algoMedianGeneric}{{2}{35}}
\newlabel{algoMedianGeneric:memcpyH2D}{{1}{35}}
\newlabel{algoMedianGeneric:cptstart}{{3}{35}}
\newlabel{algoMedianGeneric:cptend}{{5}{35}}
\newlabel{algoMedianGeneric:memcpyD2H}{{7}{35}}
\@writefile{loa}{\contentsline {algocf}{\numberline {2}{\ignorespaces generic n$\times $n median filter\relax }}{35}}
\@writefile{toc}{\contentsline {section}{\numberline {4.3}NVidia GPU tuning recipes}{35}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.3}{\ignorespaces Illustration of window overlapping in 5x5 median filtering\relax }}{36}}
\newlabel{fig:median_overlap}{{4.3}{36}}
\@writefile{lot}{\contentsline {table}{\numberline {4.1}{\ignorespaces Performance results of \texttt  {kernel medianR}. \relax }}{36}}
\newlabel{tab:medianHisto1}{{4.1}{36}}
\@writefile{toc}{\contentsline {section}{\numberline {4.4}A 3$\times $3 median filter: using registers }{37}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.4.1}The simplest way}{37}}
\newlabel{lst:kernelMedian3RegTri9}{{4.2}{38}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {4.2}3$\times $3 median filter kernel using one register per neighborhood pixel and bubble sort}{38}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.4.2}Further optimization}{38}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.4}{\ignorespaces Comparison of pixel throughputs on GPU C2070 and CPU for generic median, 3$\times $3 median register-only and \textit  {libJacket}.\relax }}{39}}
\newlabel{fig:compMedians1}{{4.4}{39}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.5}{\ignorespaces Forgetful selection with the minimal element register count. Illustration for 3$\times $3 pixel window represented in a row and supposed sorted.\relax }}{39}}
\newlabel{fig:forgetful_selection}{{4.5}{39}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.4.2.1}Reducing register count }{39}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.6}{\ignorespaces Determination of the Median value by the forgetful selection process, applied to a $3\times 3$ neighborhood window.\relax }}{41}}
\newlabel{fig:forgetful3}{{4.6}{41}}
\newlabel{lst:medianForget1pix3}{{4.3}{41}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {4.3}3$\times $3 median filter kernel using the minimum register count of 6 to find the median value by forgetful selection method. The optimal thread block size is 128 on GTX280 and 256 on C2070.}{41}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.4.2.2}More data output per thread}{42}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.7}{\ignorespaces Illustration of how window overlapping is used to combine 2 pixel selections in a 3$\times $3 median kernel.\relax }}{42}}
\newlabel{fig:median3_overlap}{{4.7}{42}}
\newlabel{lst:medianForget2pix3}{{4.4}{43}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {4.4}3$\times $3 median filter kernel processing 2 output pixel values per thread using combined forgetful selection.}{43}}
\@writefile{toc}{\contentsline {section}{\numberline {4.5}A 5$\times $5 and more median filter }{43}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.8}{\ignorespaces Comparison of pixel throughput on GPU C2070 for the different 3$\times $3 median kernels.\relax }}{44}}
\newlabel{fig:compMedians2}{{4.8}{44}}
\newlabel{sec:median5}{{4.5.1}{44}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.5.1}A register-only 5$\times $5 median filter }{44}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.9}{\ignorespaces Reducing register count in a 5$\times $5 register-only median kernel outputting 2 pixels simultaneously.}}{45}}
\newlabel{fig:median5overlap}{{4.9}{45}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.10}{\ignorespaces First iteration of the $5\times 5$ selection process, with $k_{25}=14$, which shows how Instruction Level Parallelism is maximized by the use of an incomplete sorting network.}}{45}}
\newlabel{fig:bitonic}{{4.10}{45}}
\newlabel{lst:medianForget2pix5}{{4.5}{46}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {4.5}kernel 5$\times $5 median filter processing 2 output pixel values per thread by a combined forgetfull selection.}{46}}
\@writefile{lot}{\contentsline {table}{\numberline {4.2}{\ignorespaces Performance of various 5$\times $5 median kernel implementations, applied on 4096$\times $4096 pixel image with C2070 GPU card.\relax }}{47}}
\newlabel{tab:median5comp}{{4.2}{47}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.5.2}Fast approximated n$\times $n median filter }{47}}
\@writefile{lot}{\contentsline {table}{\numberline {4.3}{\ignorespaces Measured performance of one generic pseudo-separable median kernel applied to 4096$\times $4096 pixel image with various window sizes.\relax }}{48}}
\newlabel{tab:medianSeparable}{{4.3}{48}}
\newlabel{img:sap_example_ref}{{4.11(a)}{49}}
\newlabel{sub@img:sap_example_ref}{{(a)}{49}}
\newlabel{img:sap_example_sep_med3}{{4.11(b)}{49}}
\newlabel{sub@img:sap_example_sep_med3}{{(b)}{49}}
\newlabel{img:sap_example_sep_med5}{{4.11(c)}{49}}
\newlabel{sub@img:sap_example_sep_med5}{{(c)}{49}}
\newlabel{img:sap_example_sep_med3_it2}{{4.11(d)}{49}}
\newlabel{sub@img:sap_example_sep_med3_it2}{{(d)}{49}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.11}{\ignorespaces Example of separable median filtering (smoother), applied to salt \& pepper noise reduction.\relax }}{49}}
\@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {Airplane image, corrupted with by salt and pepper noise of density 0.25}}}{49}}
\@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {Image denoised by a $3\times 3$ separable smoother}}}{49}}
\@writefile{lof}{\contentsline {subfigure}{\numberline{(c)}{\ignorespaces {Image denoised by a $5\times 5$ separable smoother}}}{49}}
\@writefile{lof}{\contentsline {subfigure}{\numberline{(d)}{\ignorespaces {Image background estimation by a $55\times 55$ separable smoother}}}{49}}
\newlabel{fig:sap_examples2}{{4.11}{49}}
\newlabel{lst:medianSeparable}{{4.6}{50}}
\@writefile{lol}{\contentsline {lstlisting}{\numberline {4.6}generic pseudo median kernel.}{50}}
\@writefile{toc}{\contentsline {section}{Bibliography}{51}}
\@setckpt{Chapters/chapter3/ch3}{
\setcounter{page}{53}
\setcounter{equation}{0}
\setcounter{enumi}{3}
\setcounter{enumii}{0}
\setcounter{enumiii}{0}
\setcounter{enumiv}{11}
\setcounter{footnote}{0}
\setcounter{mpfootnote}{0}
\setcounter{part}{2}
\setcounter{chapter}{4}
\setcounter{section}{5}
\setcounter{subsection}{2}
\setcounter{subsubsection}{0}
\setcounter{paragraph}{0}
\setcounter{subparagraph}{0}
\setcounter{figure}{11}
\setcounter{table}{3}
\setcounter{numauthors}{0}
\setcounter{parentequation}{0}
\setcounter{subfigure}{0}
\setcounter{lofdepth}{1}
\setcounter{subtable}{0}
\setcounter{lotdepth}{1}
\setcounter{lstnumber}{70}
\setcounter{ContinuedFloat}{0}
\setcounter{AlgoLine}{7}
\setcounter{algocfline}{2}
\setcounter{algocfproc}{2}
\setcounter{algocf}{2}
\setcounter{nprt@mantissa@digitsbefore}{0}
\setcounter{nprt@mantissa@digitsafter}{0}
\setcounter{nprt@exponent@digitsbefore}{0}
\setcounter{nprt@exponent@digitsafter}{0}
\setcounter{nprt@digitsfirstblock}{0}
\setcounter{nprt@blockcnt}{0}
\setcounter{nprt@cntprint}{0}
\setcounter{proposition}{0}
\setcounter{theorem}{0}
\setcounter{exercise}{0}
\setcounter{example}{0}
\setcounter{definition}{0}
\setcounter{proof}{0}
\setcounter{lstlisting}{6}
}