From: Greg Burri Date: Fri, 29 Jan 2016 21:51:48 +0000 (+0100) Subject: Update report. X-Git-Tag: 1.0.11~26 X-Git-Url: http://git.euphorik.ch/index.cgi?a=commitdiff_plain;h=276f1c9741f196e022bdbd175b4f6ef0ebb6367d;p=master-thesis.git Update report. --- diff --git a/rapport/figures-sources/Example complet - 1412151257-5-29-100-0009.psd b/rapport/figures-sources/Example complet - 1412151257-5-29-100-0009.psd new file mode 100644 index 0000000..2612169 Binary files /dev/null and b/rapport/figures-sources/Example complet - 1412151257-5-29-100-0009.psd differ diff --git a/rapport/figures-sources/Fitting ellipse - circle -comparaison Ma.psd b/rapport/figures-sources/Fitting ellipse - circle -comparaison Ma.psd new file mode 100644 index 0000000..68e940e Binary files /dev/null and b/rapport/figures-sources/Fitting ellipse - circle -comparaison Ma.psd differ diff --git a/rapport/figures-sources/RBC_noyau_cytoplasme.svg b/rapport/figures-sources/RBC_noyau_cytoplasme.svg new file mode 100644 index 0000000..9d347e9 --- /dev/null +++ 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-[0.75 0 0 0.75 0 0] CT -N -80.459 374 M -80.459 374 L -82.946 374 L -82.946 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -82.946 374 M -82.946 373.762 L -85.432 373.762 L -85.432 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -85.432 374 M -85.432 373.787 L -87.919 373.787 L -87.919 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -87.919 374 M -87.919 374 L -90.405 374 L -90.405 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -90.405 374 M -90.405 373.716 L -92.892 373.716 L -92.892 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -92.892 374 M -92.892 373.674 L -95.378 373.674 L -95.378 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -95.378 374 M -95.378 374 L -97.865 374 L -97.865 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -97.865 374 M -97.865 373.593 L -100.351 373.593 L -100.351 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -100.351 374 M -100.351 373.606 L -102.838 373.606 L -102.838 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -102.838 374 M -102.838 374 L -105.324 374 L -105.324 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -105.324 374 M -105.324 373.566 L -107.81 373.566 L -107.81 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -107.81 374 M -107.81 373.062 L -110.297 373.062 L -110.297 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -110.297 374 M -110.297 374 L -112.783 374 L -112.783 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -112.783 374 M -112.783 373.206 L -115.27 373.206 L -115.27 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -115.27 374 M -115.27 373.267 L -117.756 373.267 L -117.756 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -117.756 374 M -117.756 367.561 L -120.243 367.561 L -120.243 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -120.243 374 M -120.243 374 L -122.729 374 L -122.729 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -122.729 374 M -122.729 373.414 L -125.216 373.414 L -125.216 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -125.216 374 M -125.216 373.289 L -127.702 373.289 L -127.702 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -127.702 374 M -127.702 374 L -130.189 374 L -130.189 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -130.189 374 M -130.189 373.084 L -132.675 373.084 L -132.675 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -132.675 374 M -132.675 372.853 L -135.161 372.853 L -135.161 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -135.161 374 M -135.161 374 L -137.648 374 L -137.648 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -137.648 374 M -137.648 372.459 L -140.134 372.459 L -140.134 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -140.134 374 M -140.134 371.898 L -142.621 371.898 L -142.621 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -142.621 374 M -142.621 374 L -145.107 374 L -145.107 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -145.107 374 M -145.107 371.261 L -147.594 371.261 L -147.594 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -147.594 374 M -147.594 370.398 L -150.08 370.398 L -150.08 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -150.08 374 M -150.08 374 L -152.567 374 L -152.567 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -152.567 374 M -152.567 369.058 L -155.053 369.058 L -155.053 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -155.053 374 M -155.053 367.579 L -157.54 367.579 L -157.54 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -157.54 374 M -157.54 366.493 L -160.026 366.493 L -160.026 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -160.026 374 M -160.026 374 L -162.512 374 L -162.512 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -162.512 374 M -162.512 365.021 L -164.999 365.021 L -164.999 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -164.999 374 M -164.999 361.706 L -167.485 361.706 L -167.485 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -167.485 374 M -167.485 374 L -169.972 374 L -169.972 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -169.972 374 M -169.972 355.478 L -172.458 355.478 L -172.458 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -172.458 374 M -172.458 343.897 L -174.945 343.897 L -174.945 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -174.945 374 M -174.945 374 L -177.431 374 L -177.431 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -177.431 374 M -177.431 328.619 L -179.918 328.619 L -179.918 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -179.918 374 M -179.918 308.779 L -182.404 308.779 L -182.404 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -182.404 374 M -182.404 374 L -184.891 374 L -184.891 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -184.891 374 M -184.891 285.477 L -187.377 285.477 L -187.377 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -187.377 374 M -187.377 258.97 L -189.864 258.97 L -189.864 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -189.864 374 M -189.864 374 L -192.35 374 L -192.35 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -192.35 374 M -192.35 241.796 L -194.836 241.796 L -194.836 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -194.836 374 M -194.836 229.808 L -197.323 229.808 L -197.323 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -197.323 374 M -197.323 225.613 L -199.809 225.613 L -199.809 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -199.809 374 M -199.809 374 L -202.296 374 L -202.296 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -202.296 374 M -202.296 230.192 L -204.782 230.192 L -204.782 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -204.782 374 M -204.782 243.295 L -207.269 243.295 L -207.269 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -207.269 374 M -207.269 374 L -209.755 374 L -209.755 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -209.755 374 M -209.755 247.786 L -212.242 247.786 L -212.242 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -212.242 374 M -212.242 261.54 L -214.728 261.54 L -214.728 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -214.728 374 M -214.728 374 L -217.215 374 L -217.215 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -217.215 374 M -217.215 293.356 L -219.701 293.356 L -219.701 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -219.701 374 M -219.701 299.968 L -222.188 299.968 L -222.188 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -222.188 374 M -222.188 374 L -224.674 374 L -224.674 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -224.674 374 M -224.674 313.328 L -227.16 313.328 L -227.16 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -227.16 374 M -227.16 319.115 L -229.647 319.115 L -229.647 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -229.647 374 M -229.647 374 L -232.133 374 L -232.133 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -232.133 374 M -232.133 329.579 L -234.62 329.579 L -234.62 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -234.62 374 M -234.62 334.998 L -237.106 334.998 L -237.106 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -237.106 374 M -237.106 340.033 L -239.593 340.033 L -239.593 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -239.593 374 M -239.593 374 L -242.079 374 L -242.079 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -242.079 374 M -242.079 340.969 L -244.566 340.969 L -244.566 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -244.566 374 M -244.566 344.529 L -247.052 344.529 L -247.052 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -247.052 374 M -247.052 374 L -249.539 374 L -249.539 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -249.539 374 M -249.539 349.593 L -252.025 349.593 L -252.025 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -252.025 374 M -252.025 351.801 L -254.511 351.801 L -254.511 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -254.511 374 M -254.511 374 L -256.998 374 L -256.998 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -256.998 374 M -256.998 354.028 L -259.484 354.028 L -259.484 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -259.484 374 M -259.484 355.363 L -261.971 355.363 L -261.971 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -261.971 374 M -261.971 374 L -264.457 374 L -264.457 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -264.457 374 M -264.457 356.97 L -266.944 356.97 L -266.944 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -266.944 374 M -266.944 356.015 L -269.43 356.015 L -269.43 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -269.43 374 M -269.43 374 L -271.917 374 L -271.917 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -271.917 374 M -271.917 359.097 L -274.403 359.097 L -274.403 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -274.403 374 M -274.403 359.797 L -276.89 359.797 L -276.89 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -276.89 374 M -276.89 360.412 L -279.376 360.412 L -279.376 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -279.376 374 M -279.376 374 L -281.862 374 L -281.862 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -281.862 374 M -281.862 360.863 L -284.349 360.863 L -284.349 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -284.349 374 M -284.349 361.395 L -286.835 361.395 L -286.835 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -286.835 374 M -286.835 374 L -289.322 374 L -289.322 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -289.322 374 M -289.322 361.752 L -291.808 361.752 L -291.808 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -291.808 374 M -291.808 362.056 L -294.295 362.056 L -294.295 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -294.295 374 M -294.295 374 L -296.781 374 L -296.781 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -296.781 374 M -296.781 362.25 L -299.268 362.25 L -299.268 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -299.268 374 M -299.268 362.186 L -301.754 362.186 L -301.754 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -301.754 374 M -301.754 374 L -304.241 374 L -304.241 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -304.241 374 M -304.241 362.027 L -306.727 362.027 L -306.727 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -306.727 374 M -306.727 362.162 L -309.214 362.162 L -309.214 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -309.214 374 M -309.214 374 L -311.7 374 L -311.7 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -311.7 374 M -311.7 362.081 L -314.186 362.081 L -314.186 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -314.186 374 M -314.186 362.201 L -316.673 362.201 L -316.673 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -316.673 374 M -316.673 361.752 L -319.159 361.752 L -319.159 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -319.159 374 M -319.159 374 L -321.646 374 L -321.646 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -321.646 374 M -321.646 362.056 L -324.132 362.056 L -324.132 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -324.132 374 M -324.132 360.949 L -326.619 360.949 L -326.619 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -326.619 374 M -326.619 374 L -329.105 374 L -329.105 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -329.105 374 M -329.105 361.005 L -331.592 361.005 L -331.592 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -331.592 374 M -331.592 360.77 L -334.078 360.77 L -334.078 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -334.078 374 M -334.078 374 L -336.565 374 L -336.565 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -336.565 374 M -336.565 360.108 L -339.051 360.108 L -339.051 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -339.051 374 M -339.051 358.249 L -341.538 358.249 L -341.538 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -341.538 374 M -341.538 374 L -344.024 374 L -344.024 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -344.024 374 M -344.024 357.387 L -346.51 357.387 L -346.51 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -346.51 374 M -346.51 354.944 L -348.997 354.944 L -348.997 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -348.997 374 M -348.997 374 L -351.483 374 L -351.483 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -351.483 374 M -351.483 350.01 L -353.97 350.01 L -353.97 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -353.97 374 M -353.97 340.344 L -356.456 340.344 L -356.456 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -356.456 374 M -356.456 323.861 L -358.943 323.861 L -358.943 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -358.943 374 M -358.943 374 L -361.429 374 L -361.429 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -361.429 374 M -361.429 298.699 L -363.916 298.699 L -363.916 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -363.916 374 M -363.916 262.439 L -366.402 262.439 L -366.402 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -366.402 374 M -366.402 374 L -368.889 374 L -368.889 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -368.889 374 M -368.889 189.718 L -371.375 189.718 L -371.375 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -371.375 374 M -371.375 148.852 L -373.861 148.852 L -373.861 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -373.861 374 M -373.861 374 L -376.348 374 L -376.348 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -376.348 374 M -376.348 59.844 L -378.834 59.844 L -378.834 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -378.834 374 M -378.834 103.716 L -381.321 103.716 L -381.321 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -381.321 374 M -381.321 374 L -383.807 374 L -383.807 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -383.807 374 M -383.807 156.491 L -386.294 156.491 L -386.294 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -386.294 374 M -386.294 160.26 L -388.78 160.26 L -388.78 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -388.78 374 M -388.78 374 L -391.267 374 L -391.267 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -391.267 374 M -391.267 270.475 L -393.753 270.475 L -393.753 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -393.753 374 M -393.753 251.039 L -396.24 251.039 L -396.24 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -396.24 374 M -396.24 289.382 L -398.726 289.382 L -398.726 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -398.726 374 M -398.726 374 L -401.212 374 L -401.212 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -401.212 374 M -401.212 281.713 L -403.699 281.713 L -403.699 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -403.699 374 M -403.699 344.122 L -406.185 344.122 L -406.185 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -406.185 374 M -406.185 374 L -408.672 374 L -408.672 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -408.672 374 M -408.672 341.917 L -411.158 341.917 L -411.158 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -411.158 374 M -411.158 360.106 L -413.645 360.106 L -413.645 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -413.645 374 M -413.645 374 L -416.131 374 L -416.131 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -416.131 374 M -416.131 355.858 L -418.618 355.858 L -418.618 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -418.618 374 M -418.618 374 L -421.104 374 L -421.104 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -421.104 374 M -421.104 374 L -423.591 374 L -423.591 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -423.591 374 M -423.591 374 L -426.077 374 L -426.077 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -426.077 374 M -426.077 374 L -428.564 374 L -428.564 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -428.564 374 M -428.564 374 L -431.05 374 L -431.05 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -431.05 374 M -431.05 374 L -433.536 374 L -433.536 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -433.536 374 M -433.536 374 L -436.023 374 L -436.023 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -436.023 374 M -436.023 374 L -438.509 374 L -438.509 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -438.509 374 M -438.509 374 L -440.996 374 L -440.996 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -440.996 374 M -440.996 374 L -443.482 374 L -443.482 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -443.482 374 M -443.482 374 L -445.969 374 L -445.969 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -445.969 374 M -445.969 374 L -448.455 374 L -448.455 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -448.455 374 M -448.455 374 L -450.942 374 L -450.942 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -450.942 374 M -450.942 374 L -453.428 374 L -453.428 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -453.428 374 M -453.428 374 L -455.915 374 L -455.915 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -455.915 374 M -455.915 374 L -458.401 374 L -458.401 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -458.401 374 M -458.401 374 L -460.888 374 L -460.888 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -460.888 374 M -460.888 374 L -463.374 374 L -463.374 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -463.374 374 M -463.374 374 L -465.86 374 L -465.86 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -465.86 374 M -465.86 374 L -468.347 374 L -468.347 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -N -468.347 374 M -468.347 374 L -470.833 374 L -470.833 374 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -73 374 M -73 373.794 L -75.486 373.794 L -75.486 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -75.486 374 M -75.486 373.784 L -77.973 373.784 L -77.973 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -77.973 374 M -77.973 373.765 L -80.459 373.765 L -80.459 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -80.459 374 M -80.459 374 L -82.946 374 L -82.946 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -82.946 374 M -82.946 373.762 L -85.432 373.762 L -85.432 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -85.432 374 M -85.432 373.787 L -87.919 373.787 L -87.919 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -87.919 374 M -87.919 374 L -90.405 374 L -90.405 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -90.405 374 M -90.405 373.716 L -92.892 373.716 L -92.892 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -92.892 374 M -92.892 373.674 L -95.378 373.674 L -95.378 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -95.378 374 M -95.378 374 L -97.865 374 L -97.865 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -97.865 374 M -97.865 373.593 L -100.351 373.593 L -100.351 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -100.351 374 M -100.351 373.606 L -102.838 373.606 L -102.838 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -102.838 374 M -102.838 374 L -105.324 374 L -105.324 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -105.324 374 M -105.324 373.566 L -107.81 373.566 L -107.81 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -107.81 374 M -107.81 373.062 L -110.297 373.062 L -110.297 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -110.297 374 M -110.297 374 L -112.783 374 L -112.783 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -112.783 374 M -112.783 373.206 L -115.27 373.206 L -115.27 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -115.27 374 M -115.27 373.267 L -117.756 373.267 L -117.756 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -117.756 374 M -117.756 367.561 L -120.243 367.561 L -120.243 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -120.243 374 M -120.243 374 L -122.729 374 L -122.729 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -122.729 374 M -122.729 373.414 L -125.216 373.414 L -125.216 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -125.216 374 M -125.216 373.289 L -127.702 373.289 L -127.702 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -127.702 374 M -127.702 374 L -130.189 374 L -130.189 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -130.189 374 M -130.189 373.084 L -132.675 373.084 L -132.675 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -132.675 374 M -132.675 372.853 L -135.161 372.853 L -135.161 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -135.161 374 M -135.161 374 L -137.648 374 L -137.648 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -137.648 374 M -137.648 372.459 L -140.134 372.459 L -140.134 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -140.134 374 M -140.134 371.898 L -142.621 371.898 L -142.621 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -142.621 374 M -142.621 374 L -145.107 374 L -145.107 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -145.107 374 M -145.107 371.261 L -147.594 371.261 L -147.594 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -147.594 374 M -147.594 370.398 L -150.08 370.398 L -150.08 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -150.08 374 M -150.08 374 L -152.567 374 L -152.567 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -152.567 374 M -152.567 369.058 L -155.053 369.058 L -155.053 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -155.053 374 M -155.053 367.579 L -157.54 367.579 L -157.54 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -157.54 374 M -157.54 366.493 L -160.026 366.493 L -160.026 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -160.026 374 M -160.026 374 L -162.512 374 L -162.512 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -162.512 374 M -162.512 365.021 L -164.999 365.021 L -164.999 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -164.999 374 M -164.999 361.706 L -167.485 361.706 L -167.485 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -167.485 374 M -167.485 374 L -169.972 374 L -169.972 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -169.972 374 M -169.972 355.478 L -172.458 355.478 L -172.458 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -172.458 374 M -172.458 343.897 L -174.945 343.897 L -174.945 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -174.945 374 M -174.945 374 L -177.431 374 L -177.431 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -177.431 374 M -177.431 328.619 L -179.918 328.619 L -179.918 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -179.918 374 M -179.918 308.779 L -182.404 308.779 L -182.404 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -182.404 374 M -182.404 374 L -184.891 374 L -184.891 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -184.891 374 M -184.891 285.477 L -187.377 285.477 L -187.377 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -187.377 374 M -187.377 258.97 L -189.864 258.97 L -189.864 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -189.864 374 M -189.864 374 L -192.35 374 L -192.35 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -192.35 374 M -192.35 241.796 L -194.836 241.796 L -194.836 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -194.836 374 M -194.836 229.808 L -197.323 229.808 L -197.323 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -197.323 374 M -197.323 225.613 L -199.809 225.613 L -199.809 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -199.809 374 M -199.809 374 L -202.296 374 L -202.296 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -202.296 374 M -202.296 230.192 L -204.782 230.192 L -204.782 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -204.782 374 M -204.782 243.295 L -207.269 243.295 L -207.269 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -207.269 374 M -207.269 374 L -209.755 374 L -209.755 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -209.755 374 M -209.755 247.786 L -212.242 247.786 L -212.242 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -212.242 374 M -212.242 261.54 L -214.728 261.54 L -214.728 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -214.728 374 M -214.728 374 L -217.215 374 L -217.215 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -217.215 374 M -217.215 293.356 L -219.701 293.356 L -219.701 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -219.701 374 M -219.701 299.968 L -222.188 299.968 L -222.188 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -222.188 374 M -222.188 374 L -224.674 374 L -224.674 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -224.674 374 M -224.674 313.328 L -227.16 313.328 L -227.16 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -227.16 374 M -227.16 319.115 L -229.647 319.115 L -229.647 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -229.647 374 M -229.647 374 L -232.133 374 L -232.133 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -232.133 374 M -232.133 329.579 L -234.62 329.579 L -234.62 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -234.62 374 M -234.62 334.998 L -237.106 334.998 L -237.106 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -237.106 374 M -237.106 340.033 L -239.593 340.033 L -239.593 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -239.593 374 M -239.593 374 L -242.079 374 L -242.079 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -242.079 374 M -242.079 340.969 L -244.566 340.969 L -244.566 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -244.566 374 M -244.566 344.529 L -247.052 344.529 L -247.052 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -247.052 374 M -247.052 374 L -249.539 374 L -249.539 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -249.539 374 M -249.539 349.593 L -252.025 349.593 L -252.025 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -252.025 374 M -252.025 351.801 L -254.511 351.801 L -254.511 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -254.511 374 M -254.511 374 L -256.998 374 L -256.998 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -256.998 374 M -256.998 354.028 L -259.484 354.028 L -259.484 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -259.484 374 M -259.484 355.363 L -261.971 355.363 L -261.971 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -261.971 374 M -261.971 374 L -264.457 374 L -264.457 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -264.457 374 M -264.457 356.97 L -266.944 356.97 L -266.944 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -266.944 374 M -266.944 356.015 L -269.43 356.015 L -269.43 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -269.43 374 M -269.43 374 L -271.917 374 L -271.917 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -271.917 374 M -271.917 359.097 L -274.403 359.097 L -274.403 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -274.403 374 M -274.403 359.797 L -276.89 359.797 L -276.89 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -276.89 374 M -276.89 360.412 L -279.376 360.412 L -279.376 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -279.376 374 M -279.376 374 L -281.862 374 L -281.862 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -281.862 374 M -281.862 360.863 L -284.349 360.863 L -284.349 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -284.349 374 M -284.349 361.395 L -286.835 361.395 L -286.835 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -286.835 374 M -286.835 374 L -289.322 374 L -289.322 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -289.322 374 M -289.322 361.752 L -291.808 361.752 L -291.808 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -291.808 374 M -291.808 362.056 L -294.295 362.056 L -294.295 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -294.295 374 M -294.295 374 L -296.781 374 L -296.781 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -296.781 374 M -296.781 362.25 L -299.268 362.25 L -299.268 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -299.268 374 M -299.268 362.186 L -301.754 362.186 L -301.754 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -301.754 374 M -301.754 374 L -304.241 374 L -304.241 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -304.241 374 M -304.241 362.027 L -306.727 362.027 L -306.727 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -306.727 374 M -306.727 362.162 L -309.214 362.162 L -309.214 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -309.214 374 M -309.214 374 L -311.7 374 L -311.7 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -311.7 374 M -311.7 362.081 L -314.186 362.081 L -314.186 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -314.186 374 M -314.186 362.201 L -316.673 362.201 L -316.673 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -316.673 374 M -316.673 361.752 L -319.159 361.752 L -319.159 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -319.159 374 M -319.159 374 L -321.646 374 L -321.646 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -321.646 374 M -321.646 362.056 L -324.132 362.056 L -324.132 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -324.132 374 M -324.132 360.949 L -326.619 360.949 L -326.619 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -326.619 374 M -326.619 374 L -329.105 374 L -329.105 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -329.105 374 M -329.105 361.005 L -331.592 361.005 L -331.592 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -331.592 374 M -331.592 360.77 L -334.078 360.77 L -334.078 374 L -S -GR -GS -[0.75 0 0 0.75 0 0] CT -2 setlinecap -10.0 ML -N -334.078 374 M -334.078 374 L -336.565 374 L -336.565 374 L -S -GR -GS -[0.75 0 0 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-1 -1 scale -(1.5) t -GR -GR -GS -[0.75 0 0 0.75 50.75 178.59999] CT -0.149 GC -/Helvetica 13 F -GS -[1 0 0 1 0 0] CT --8 5.5 moveto -1 -1 scale -(2) t -GR -GR -GS -[0.75 0 0 0.75 50.75 152.875] CT -0.149 GC -/Helvetica 13 F -GS -[1 0 0 1 0 0] CT --19 5.5 moveto -1 -1 scale -(2.5) t -GR -GR -GS -[0.75 0 0 0.75 50.75 127.15] CT -0.149 GC -/Helvetica 13 F -GS -[1 0 0 1 0 0] CT --8 5.5 moveto -1 -1 scale -(3) t -GR -GR -GS -[0.75 0 0 0.75 50.75 101.425] CT -0.149 GC -/Helvetica 13 F -GS -[1 0 0 1 0 0] CT --19 5.5 moveto -1 -1 scale -(3.5) t -GR -GR -GS -[0.75 0 0 0.75 50.75 75.69999] CT -0.149 GC -/Helvetica 13 F -GS -[1 0 0 1 0 0] CT --8 5.5 moveto -1 -1 scale -(4) t -GR -GR -GS -[0.75 0 0 0.75 50.75 49.97501] CT -0.149 GC -/Helvetica 13 F -GS -[1 0 0 1 0 0] CT --19 5.5 moveto -1 -1 scale -(4.5) t -GR -GR -GS -[0.75 0 0 0.75 50.75 24.25001] CT -0.149 GC -/Helvetica 13 F -GS -[1 0 0 1 0 0] CT --8 5.5 moveto -1 -1 scale -(5) t -GR -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -79.751 375 M -85.538 375 L -85.538 348.895 L -79.751 348.895 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -89.396 375 M -95.182 375 L -95.182 342.831 L -89.396 342.831 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -99.04 375 M -104.827 375 L -104.827 336.342 L -99.04 336.342 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -108.684 375 M -114.471 375 L -114.471 351.018 L -108.684 351.018 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -118.329 375 M -124.116 375 L -124.116 339.036 L -118.329 339.036 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -127.973 375 M -133.76 375 L -133.76 338.974 L -127.973 338.974 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -137.618 375 M -143.404 375 L -143.404 323.504 L -137.618 323.504 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -147.262 375 M -153.049 375 L -153.049 343.952 L -147.262 343.952 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -156.907 375 M -162.693 375 L -162.693 333.247 L -156.907 333.247 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -166.551 375 M -172.338 375 L -172.338 345.562 L -166.551 345.562 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -176.196 375 M -181.982 375 L -181.982 334.21 L -176.196 334.21 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -185.84 375 M -191.627 375 L -191.627 349.335 L -185.84 349.335 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -195.484 375 M -201.271 375 L -201.271 342.891 L -195.484 342.891 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -205.129 375 M -210.916 375 L -210.916 354.37 L -205.129 354.37 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -214.773 375 M -220.56 375 L -220.56 347.02 L -214.773 347.02 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -224.418 375 M -230.204 375 L -230.204 357.972 L -224.418 357.972 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -234.062 375 M -239.849 375 L -239.849 348.885 L -234.062 348.885 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -243.707 375 M -249.493 375 L -249.493 356.327 L -243.707 356.327 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -253.351 375 M -259.138 375 L -259.138 345.762 L -253.351 345.762 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -262.996 375 M -268.782 375 L -268.782 356.867 L -262.996 356.867 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -272.64 375 M -278.427 375 L -278.427 339.529 L -272.64 339.529 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -282.284 375 M -288.071 375 L -288.071 344.13 L -282.284 344.13 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -291.929 375 M -297.716 375 L -297.716 326.26 L -291.929 326.26 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -301.573 375 M -307.36 375 L -307.36 339.906 L -301.573 339.906 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -311.218 375 M -317.004 375 L -317.004 308.181 L -311.218 308.181 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -320.862 375 M -326.649 375 L -326.649 315.884 L -320.862 315.884 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -330.507 375 M -336.293 375 L -336.293 271.453 L -330.507 271.453 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -340.151 375 M -345.938 375 L -345.938 296.266 L -340.151 296.266 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -349.796 375 M -355.582 375 L -355.582 223.404 L -349.796 223.404 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -359.44 375 M -365.227 375 L -365.227 281.048 L -359.44 281.048 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -369.084 375 M -374.871 375 L -374.871 161.078 L -369.084 161.078 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -378.729 375 M -384.516 375 L -384.516 225.155 L -378.729 225.155 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -388.373 375 M -394.16 375 L -394.16 98.742 L -388.373 98.742 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -398.018 375 M -403.804 375 L -403.804 179.159 L -398.018 179.159 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -407.662 375 M -413.449 375 L -413.449 52.348 L -407.662 52.348 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -417.307 375 M -423.093 375 L -423.093 159.524 L -417.307 159.524 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -426.951 375 M -432.738 375 L -432.738 79.588 L -426.951 79.588 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -436.596 375 M -442.382 375 L -442.382 211.367 L -436.596 211.367 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -446.24 375 M -452.027 375 L -452.027 190.109 L -446.24 190.109 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -455.884 375 M -461.671 375 L -461.671 274.427 L -455.884 274.427 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -465.529 375 M -471.316 375 L -471.316 277.925 L -465.529 277.925 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -475.173 375 M -480.96 375 L -480.96 323.921 L -475.173 323.921 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -N -484.818 375 M -490.604 375 L -490.604 324.681 L -484.818 324.681 L -cp -f -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -79.751 375 M -79.751 348.895 L -85.538 348.895 L -85.538 375 L -79.751 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -89.396 375 M -89.396 342.831 L -95.182 342.831 L -95.182 375 L -89.396 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -99.04 375 M -99.04 336.342 L -104.827 336.342 L -104.827 375 L -99.04 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -108.684 375 M -108.684 351.018 L -114.471 351.018 L -114.471 375 L -108.684 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -118.329 375 M -118.329 339.036 L -124.116 339.036 L -124.116 375 L -118.329 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -127.973 375 M -127.973 338.974 L -133.76 338.974 L -133.76 375 L -127.973 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -137.618 375 M -137.618 323.504 L -143.404 323.504 L -143.404 375 L -137.618 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -147.262 375 M -147.262 343.952 L -153.049 343.952 L -153.049 375 L -147.262 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -156.907 375 M -156.907 333.247 L -162.693 333.247 L -162.693 375 L -156.907 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -166.551 375 M -166.551 345.562 L -172.338 345.562 L -172.338 375 L -166.551 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -176.196 375 M -176.196 334.21 L -181.982 334.21 L -181.982 375 L -176.196 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -185.84 375 M -185.84 349.335 L -191.627 349.335 L -191.627 375 L -185.84 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -195.484 375 M -195.484 342.891 L -201.271 342.891 L -201.271 375 L -195.484 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -205.129 375 M -205.129 354.37 L -210.916 354.37 L -210.916 375 L -205.129 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -214.773 375 M -214.773 347.02 L -220.56 347.02 L -220.56 375 L -214.773 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -224.418 375 M -224.418 357.972 L -230.204 357.972 L -230.204 375 L -224.418 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -234.062 375 M -234.062 348.885 L -239.849 348.885 L -239.849 375 L -234.062 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -243.707 375 M -243.707 356.327 L -249.493 356.327 L -249.493 375 L -243.707 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -253.351 375 M -253.351 345.762 L -259.138 345.762 L -259.138 375 L -253.351 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -262.996 375 M -262.996 356.867 L -268.782 356.867 L -268.782 375 L -262.996 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -272.64 375 M -272.64 339.529 L -278.427 339.529 L -278.427 375 L -272.64 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -282.284 375 M -282.284 344.13 L -288.071 344.13 L -288.071 375 L -282.284 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -291.929 375 M -291.929 326.26 L -297.716 326.26 L -297.716 375 L -291.929 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -301.573 375 M -301.573 339.906 L -307.36 339.906 L -307.36 375 L -301.573 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -311.218 375 M -311.218 308.181 L -317.004 308.181 L -317.004 375 L -311.218 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -320.862 375 M -320.862 315.884 L -326.649 315.884 L -326.649 375 L -320.862 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -330.507 375 M -330.507 271.453 L -336.293 271.453 L -336.293 375 L -330.507 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -340.151 375 M -340.151 296.266 L -345.938 296.266 L -345.938 375 L -340.151 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -349.796 375 M -349.796 223.404 L -355.582 223.404 L -355.582 375 L -349.796 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -359.44 375 M -359.44 281.048 L -365.227 281.048 L -365.227 375 L -359.44 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -369.084 375 M -369.084 161.078 L -374.871 161.078 L -374.871 375 L -369.084 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -378.729 375 M -378.729 225.155 L -384.516 225.155 L -384.516 375 L -378.729 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -388.373 375 M -388.373 98.742 L -394.16 98.742 L -394.16 375 L -388.373 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -398.018 375 M -398.018 179.159 L -403.804 179.159 L -403.804 375 L -398.018 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -407.662 375 M -407.662 52.348 L -413.449 52.348 L -413.449 375 L -407.662 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -417.307 375 M -417.307 159.524 L -423.093 159.524 L -423.093 375 L -417.307 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -426.951 375 M -426.951 79.588 L -432.738 79.588 L -432.738 375 L -426.951 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -436.596 375 M -436.596 211.367 L -442.382 211.367 L -442.382 375 L -436.596 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -446.24 375 M -446.24 190.109 L -452.027 190.109 L -452.027 375 L -446.24 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -455.884 375 M -455.884 274.427 L -461.671 274.427 L -461.671 375 L -455.884 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -465.529 375 M -465.529 277.925 L -471.316 277.925 L -471.316 375 L -465.529 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -475.173 375 M -475.173 323.921 L -480.96 323.921 L -480.96 375 L -475.173 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -2 setlinecap -10.0 ML -N -484.818 375 M -484.818 324.681 L -490.604 324.681 L -490.604 375 L -484.818 375 L -S -GR -GS -[0.75 0 0 0.75 0 0.25] CT -0.149 GC -2 setlinecap -10.0 ML -N -73 375 M -507 375 L -S -GR -%%Trailer -%%Pages: 1 -%%EOF diff --git a/rapport/logos/hes-so_logo.jpg b/rapport/logos/hes-so_logo.jpg new file mode 100644 index 0000000..c381702 Binary files /dev/null and b/rapport/logos/hes-so_logo.jpg differ diff --git a/rapport/logos/mse_logo.jpg b/rapport/logos/mse_logo.jpg new file mode 100644 index 0000000..8e249df Binary files /dev/null and b/rapport/logos/mse_logo.jpg differ diff --git a/rapport/main.tex b/rapport/main.tex index f0dc797..ce6a0b6 100644 --- a/rapport/main.tex +++ b/rapport/main.tex @@ -247,7 +247,7 @@ La parasitémie est établit en pourcentage comme étant le rapport entre nombre \label{fig:noyau-cytoplasme} \end{figure} -Certains artefacts comme des débris ou des plaquettes peuvent venir se supperposer aux érythrocyte et être confondus avec des parasites. Ces cas peuvent être relativement fréquents et altérer significativement la parasitémie si comptés comme étant des cas positifs d'infection. La figure~\ref{fig:RBC-artefact} montre quelques exemple de faux positifs potentiels. +Certains artefacts comme des débris ou des plaquettes peuvent venir se superposer aux érythrocyte et être confondus avec des parasites. Ces cas peuvent être relativement fréquents et altérer significativement la parasitémie si comptés comme étant des cas positifs d'infection. La figure~\ref{fig:RBC-artefact} montre quelques exemple de faux positifs potentiels. \begin{figure}[htbp] \centering @@ -286,25 +286,30 @@ La figure~\ref{fig:processusComplet} montre le processus complet du traitement d \begin{figure}[htbp] \centering - \includegraphics[width=0.8\linewidth]{img/schema_processus_2.pdf} + \includegraphics[width=0.9\linewidth]{img/schema_processus_2.pdf} \caption{Le processus complet.} \label{fig:processusComplet} \end{figure} -Dans le premier groupe, l'on va chercher à construire des ellipses qui correspondent le mieux aux bords des érythrocytes. Pour ce faire une estimation du rayon moyen est réalisée par granulométrie à l'aide d'une succession de fermeture par aire. La construction des ellipses utilise les pixels des bords des erytrocytes ainsi que son gradient, la méthode \emph{RANSAC} permet de créer un grand nombre d'ellipses candidates auquel un score est attribué. Finalement les ellipses sont élaguée en supprimant celles chevauchées par d'autres ellipses sont le score est supérieur. +Dans le premier groupe, l'on va chercher à construire des ellipses qui correspondent le mieux aux bords des érythrocytes. Pour ce faire une estimation du rayon moyen est réalisée par granulométrie à l'aide d'une succession de fermeture par aire. La construction des ellipses utilise les pixels des bords des érythrocytes ainsi que son gradient, la méthode \emph{RANSAC} permet de créer un grand nombre d'ellipses candidates auquel un score est attribué. Finalement les ellipses sont élaguée en supprimant celles chevauchées par d'autres ellipses sont le score est supérieur. -Dans le deuxième groupe, les zones colorées et sombre vont être extraites en comparant les valeurs d'intensité de l'image avec la moyenne d'intensité des éléments de l'avant-plan. Ces zones sombres correspondent aux leucocytes, aux plaquettes et à certains débris. Une fermeture morphoplogique, dont la taille de l'élément structurant est calculé en fonction du rayon moyen, va permettre de mettre en évidence le cytoplasme des parasites. Les noyaux sont, quant à eux, mis en évidence à l'aide d'une fermeture par aire. +Dans le deuxième groupe, les zones colorées et sombre vont être extraites en comparant les valeurs d'intensité de l'image avec la moyenne d'intensité des éléments de l'avant-plan. Ces zones sombres correspondent aux leucocytes, aux plaquettes et à certains débris. Une fermeture morphologique, dont la taille de l'élément structurant est calculé en fonction du rayon moyen, va permettre de mettre en évidence le cytoplasme des parasites. Les noyaux sont, quant à eux, mis en évidence à l'aide d'une fermeture par aire. -Le troisième groupe correspond à la mise en commun des informations du premier et du deuxième groupe afin de définir les erytrocytes et de les classer. La parasitémie est alors établit en calculant le rapport entre la population d'érythrocytes infecté et celle saine. +Le troisième groupe correspond à la mise en commun des informations du premier et du deuxième groupe afin de définir les érythrocytes et de les classer. La parasitémie est alors établit en calculant le rapport entre la population d'érythrocytes infecté et celle saine. \section{Détail de la méthode} % filtrage préliminaire (taille d'un érythrocyte: 7.5 \micro~m) -Les filtres gaussiens appliquées initialement vont permettre de supprimer une partie du bruit haute-fréquence. L'écart type de chaque filtre est choisi en fonction de la taille des objets. La taille d'un érytrocyte est d'environ 7.5~\textmu{m} et la taille d'un parasite d'environ 2.5~\textmu{m}. Des écarts types de 0.2~\textmu{m} et 0.15~\textmu{m} sont choisis pour pour la ségmentation des érytrocytes respectivement la ségmentation des parasites. +Les filtres gaussiens appliquées initialement vont permettre de supprimer une partie du bruit haute-fréquence. L'écart type de chaque filtre est choisi en fonction de la taille des objets. La taille d'un érythrocyte est d'environ 7.5~\textmu{m} et la taille d'un parasite d'environ 2.5~\textmu{m}. Des écarts types de 0.22~\textmu{m} et 0.15~\textmu{m} sont choisis pour pour la segmentation des érythrocytes respectivement la segmentation des parasites. -\subsection{Identification des érytrocytes} +Il est également important de supprimer avant le traitement la partie d'intensité plus élevée se trouvant au centre des érythrocytes (visible sur la figure~\ref{fig:medical-globules-rouges}) sans quoi les fermetures (par aire ou morphologiques) faites pendant la granulométrie s'appliqueraient qu'à une partie de la cellule. De plus, cette particularité gêne également lors de la recherche des bords. + +Cela est fait en réalisant une ouverture par aire en estimant sa surface à partir du rayon calculé à partir de la résolution de l'image. Si, après la granulométrie, cette ouverture n'est pas suffisante (le rayon trouvé est supérieur à celui estimé via la résolution) alors une deuxième ouverture par aire est réalisée. + +\subsection{Identification des érythrocytes} +\label{identification-erythrocytes} Le but de cette étape est d'identifier les érythrocytes. Le profil de ceux-ci est un disque biconcave et apparait de manière plus ou moins déformée sur les photographies. Ces déformations les font prendre une forme plus ou moins elliptique dont le rapport entre le grand axe et le petit axe n'excède pas 1.6 ($\pm 23~\%$ d'un rayon moyen). @@ -319,10 +324,11 @@ Le résultat de cette recherche sera une liste d'ellipses pouvant se recouvrir p \subsubsection{Granulométrie} +\label{granulometrie} -L'objectif est de déterminer le rayon moyen des érytrocytes. Pour ce faire nous allons appliquer une série de fermetures par aire et calculer les différences des sommes des intensités de chaque pixel. Chaque aire est calculée comme étant celui d'un cercle de rayon donné. Les rayons des aires vont être compris autour d'un rayon estimé à partir de la résolution donnée initialement. Les bornes inférieure et supérieure correspondent au rayon estimé minoré de 50~\% respectivement au rayon estimé majoré de 50~\%. +L'objectif est de déterminer le rayon moyen des érythrocytes. Pour ce faire nous allons appliquer une série de fermetures par aire et calculer les différences des sommes des intensités de chaque pixel. Chaque aire est calculée comme étant celui d'un cercle de rayon donné. Les rayons des aires vont être compris autour d'un rayon estimé à partir de la résolution donnée initialement. Les bornes inférieure et supérieure correspondent au rayon estimé minoré de 50~\% respectivement au rayon estimé majoré de 50~\%. -La fermeture suppose ici que les erythrocytes on un niveau d'intensité plus bas que le fond, ce qui est le cas pour la composante verte dans toutes les images étudiées. +La fermeture suppose ici que les érythrocytes on un niveau d'intensité plus bas que le fond, ce qui est le cas pour la composante verte dans toutes les images étudiées. Deux autres approches on également été essayées, à savoir la fermeture morphologique par un élément structurant en forme de disque et par un élément structurant de forme octogonale. Un des problèmes de ces deux approches est qu'elles ont tendance à sous-estimer légèrement le rayon moyen dans le cas d'éléments elliptiques. La figure~\ref{fig:granulometrie-ellipse-cercle-closing-comparaison} montre à gauche le résultat d'une granulometrie par aire (le cercle et l'ellipse ont la même aire) et à droite le résultat d'une granulometrie morphologique. Le rayon $r$ est plus proche de la moyenne entre les deux rayons de l'ellipse $a$ et $b$ que le rayon $r'$. Il est à noter que dans cet exemple $a = 2b$ et que donc $r = \sqrt{2}b = 1.41b$ ce qui n'est pas très éloigné de la moyenne $(a+b)/2 = (2+1)/2 = 1.5$. @@ -345,6 +351,8 @@ Deux autres approches on également été essayées, à savoir la fermeture morp Un autre problème de la granulométrie à l'aide de fermetures morphologique utilisant un disque comme élément structurant est sa complexité algorithmique quadratique en fonction du rayon du disque comme le montre la figure~\ref{fig:spectre-granulométrique-morpho-cercle}. La figure~\ref{fig:spectre-granulométrique-morpho-cercle} montre un exemple de progression du temps de calcul en fonction du rayon. Une solution à ce problème est l'utilisation d'une approximation du cercle, l'octogone, dont la dilaté ou l'érodé par un autre octogone crée un nouvel octogone. L'associativité de l'erosion ou de la dilatation, montré par l'équation~\ref{eq:dilatation-associatif}, permet la décomposition d'une dilatation ($e_{1} \oplus e_{2}$) en plusieurs dilatations successives ($\oplus~e_{1}$ puis $\oplus~e_{2}$). Cela permet de réduire la complexité algorithmique et ainsi de gagner du temps. +% TODO: Définition de la somme de Minkowski? + {\setlength{\abovedisplayskip}{0pt} \begin{flalign} \label{eq:dilatation-associatif} f' = f \oplus (e_{1} \oplus e_{2}) = (f \oplus e_{1}) \oplus e_{2} & @@ -407,14 +415,126 @@ Il faut remarquer que le spectre granulométrique par aire comporte un deuxième \label{fig:Granulometry-morpho-octagon} \end{figure} -\subsubsection{Calcul du gradient} +À partir du rayon moyen trouvé par granulométrie et des caractéristique des érythrocytes énoncées à la section~\ref{identification-erythrocytes}, les rayons minimum et maximum sont définis comme étant $rayon_{moyen} (1 + 0.23)$ et $rayon_{moyen} (1 - 0.23)$. + + +\subsubsection{Recherche des bords des érythrocytes et calcul du gradient associé} + +La construction d'ellipses nécessite la connaissance au préalable des bords des érythrocytes ainsi que du gradient associé. Cela est réalisé à l'aide d'une procédure s'apparentant au filtre de Canny. + +Le gradient est définit comme étant deux composantes $g_x$ et $g_y$ en chaque point correspondant aux dérivés partielles en $x$ et en $y$ d'une image $f$ comme montré par l'équation~\ref{eq:composantes-gradient}. + +{\setlength{\abovedisplayskip}{0pt} +\begin{flalign} \label{eq:composantes-gradient} + \nabla f = \begin{pmatrix}g_x \\ g_y \end{pmatrix} = \begin{pmatrix}\partial f / \partial x \\ \partial f / \partial y \end{pmatrix} +\end{flalign} + +Le filtre de Sobel permet d'obtenir une bonne approximation de ces deux composantes en appliquant deux convolutions avec les deux noyaux montrés à l'équation~\ref{eq:sobel-noyaux}. Une application sur une image réelle est montrée par la figure~\ref{fig:gradient}. + +{\setlength{\abovedisplayskip}{0pt} +\begin{flalign} \label{eq:sobel-noyaux} + K_x = \begin{pmatrix}-1 & 0 & 1 \\ -2 & 0 & 2 \\ -1 & 0 & 1 \end{pmatrix}, \quad K_y = K_x^\top = \begin{pmatrix}-1 & -2 & -1 \\ 0 & 0 & 0 \\ 1 & 2 & 1 \end{pmatrix} +\end{flalign} + +La norme euclidienne en chaque point est obtenu par l'équation~\ref{eq:gradient-norme}. La méthode de Otsu est ensuite appliquée afin de calculer un seuil qui sera utilisé pour la définition des bords par hystérèse. + +{\setlength{\abovedisplayskip}{0pt} +\begin{flalign} \label{eq:gradient-norme} + M(x, y) = \| \nabla f \| = \sqrt{g_x^2 + g_y^2} +\end{flalign} + +\begin{figure}[htbp] + \centering + \begin{subfigure}[t]{0.4\textwidth} + \includegraphics[width=1\linewidth]{img/gradient-exemple.jpg} + \end{subfigure} + ~ + \begin{subfigure}[t]{0.4\textwidth} + \includegraphics[width=1\linewidth,interpolate=false]{img/gradient-exemple.pdf} + \end{subfigure} + \caption{Une cellule dont le gradient de la partie jaune est montré à droite sous la forme d'un champ de vecteurs. Les bords sont également représentés} + \label{fig:gradient} +\end{figure} + +Afin de ne garder que les crêtes, un algorithme de suppression des non-maxima est appliqué. Celui ci est illustré par le figure~\ref{fig:non-maximum-suppression-schema} et va, pour chaque élément de la norme, le comparer à ses voisins en définissant l'orientation de l'arête du bord comme étant la tangente perpendiculaire au gradient. Pour chaque coté de l'arête, une interpolation est calculée entre les deux éléments les plus proche de la droite ayant la même direction que le gradient et passant par l'élément traité. Par exemple, par rapport à la figure~\ref{fig:non-maximum-suppression-schema}, la valeur des voisins du haut est calculée comme étant $\tau = n_1 \cdot (1 - v_x/v_y) + n_2 \cdot v_x/v_y$ et celle des voisins du bas comme étant $\upsilon = n_4 \cdot (1 - v_x/v_y) + n_3 \cdot v_x/v_y$ où $v_x$ et $v_y$ sont les composantes du gradient au point traité $e$. Si la norme de $e$ est strictement plus grande que les valeurs $\tau$ et $\upsilon$ alors celui-ci sera définit comme étant un maxima. La figure~\ref{fig:nms} montre la valeur de la norme ainsi que les maximas mis en évidence. + +\begin{figure}[htbp] + \centering + \begin{subfigure}[t]{0.35\textwidth} + \includegraphics[width=1\linewidth,interpolate=false]{img/non-maximum-suppression-schema.pdf} + \caption{Les voisins ($n_1$, $n_2$, $n_3$, $n_4$) de $e$ qui vont être utilisés pour déterminé si $e$ est un maxima} + \label{fig:non-maximum-suppression-schema} + \end{subfigure} + ~ + \begin{subfigure}[t]{0.35\textwidth} + \includegraphics[width=1\linewidth,interpolate=false]{img/nms.png} + \caption{Le résultat de l'application de la suppression des non-maxima. Les maximas sont mis en évidence en blanc et la norme du gradient est montré avec des niveaux d'intensité de gris} + \label{fig:nms} + \end{subfigure} + \caption{Suppression des non-maxima} + \label{fig:non-maximum-suppression} +\end{figure} + +Le résultat obtenu par l'étape précédente, la suppression des non-maxima, va prendre en compte tous les bords et ceci indépendamment de la norme du gradient (inclinaison de la pente). Il est nécessaire maintenant de ne garder que les bords les plus pertinent, pour ce faire une recherche par hystérèse est appliquée en ne gardant, dans un premier temps, que les éléments dont la norme est supérieure au seuil obtenu précédemment par la méthode de Otsu majoré d'un pourcentage (par exemple 10~\%). Puis, dans un second temps, nous y ajoutons récursivement tous les éléments 8-connexes dont la norme est supérieure au seuil. + +Finalement, les zones 8-connexes dont la surface est supérieure à un facteur du rayon moyen sont supprimées afin d'éliminer les bords de faible longueur qui ne correspondent, en général, pas aux bords des érythrocytes. + +%\subsubsection{Recherche des bords des érythrocytes} + +\subsubsection{Construction d'ellipses} + +L'étape précédente nous fournit une matrice de vecteurs définissant le gradient. Les éléments dont le vecteur est non-nul constituent les bords des érythrocytes. + +Une méthode proche de la méthode RANSAC~\ref{} (\emph{RANdom SAmple Consensus}) est appliquée qui consiste à faire glisser une fenêtre à travers la matrice et à tirer aléatoirement, un certain nombre de fois, trois points éloignés les uns des autres. À l'aide du gradient de deux des trois point il est éventuellement possible de construire une ellipse unique. Les ellipses ainsi construites sont alors ajoutées à l'ensemble des ellipses. Une fois la matrice entièrement traversée par la fenêtre, un score est attribué à chacune des ellipses en fonction de sa proximité aux autres ellipses. Finalement, les ellipses dont le score est trop faible, ou qui se trouve trop proche d'une ellipse ayant un score plus élevé sont supprimées. + +La taille de la fenêtre glissante est un carré dont la longueur des cotés correspond au rayon maximum (voir section~\ref{granulometrie}). La fenêtre va balayer toute la matrice de gauche à droite et de haut en bas. Un incrément d'un quart de sa dimension a été choisi. Pour chaque position un certain nombre de tirage de triplet de points non-égaux parmi les vecteurs non-nuls est effectué, ce nombre est égal à un coefficient multipliant le nombre courant d'élément du bord. Celui ci à été ajusté comme valant 1. + +\begin{figure}[htbp] + \centering + \includegraphics[width=0.6\linewidth]{img/construction-ellipse.pdf} + \caption{Le triplet de point $p_1$, $p_2$ et $p_3$ ainsi que les deux vecteurs du gradient $v_1$ et $v_2$ permettent possiblement la construction d'une ellipse.} + \label{fig:construction-ellipse} +\end{figure} + +À partir de chaque triplet de point et des deux vecteurs du gradient au deux premiers points une ellipse va tenter d'être construite comme montrer par la figure~\ref{fig:construction-ellipse}. Tout d'abord il faut s'assurer que les deux vecteurs $v_1$ et $v_2$ pointent bien dans + +\begin{figure}[htbp] + \centering + \begin{subfigure}[t]{0.4\textwidth} + \includegraphics[width=1\linewidth]{figures/ellipses/example-1-green-filtered.jpg} + \caption{} + \label{} + \end{subfigure} + ~ + \begin{subfigure}[t]{0.4\textwidth} + \includegraphics[width=1\linewidth]{figures/ellipses/example-2-edges.png} + \caption{} + \label{} + \end{subfigure} + ~ + \begin{subfigure}[t]{0.4\textwidth} + \includegraphics[width=1\linewidth]{figures/ellipses/example-3-all-ellipses.jpg} + \caption{} + \label{} + \end{subfigure} + ~ + \begin{subfigure}[t]{0.4\textwidth} + \includegraphics[width=1\linewidth]{figures/ellipses/example-4-ellipses.jpg} + \caption{} + \label{} + \end{subfigure} + \caption{} + \label{} +\end{figure} -\subsubsection{Recherche des bords des érythrocytes} -\subsubsection{Recherche d'ellipses} % RANSAC + scoring + pruning +\subsubsection{Élagage des ellipses} + +% suppression uniquement + \subsection{Segmentation des parasites} @@ -433,6 +553,7 @@ Il faut remarquer que le spectre granulométrique par aire comporte un deuxième \section{Implémentation} +% Float32