From ca6da606526bb044fc21c2a39671921645ee68c4 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Laure=CE=B7t?= Date: Sat, 10 Jun 2023 21:05:32 +0200 Subject: [PATCH] init --- tp1/creation_cercle_et_donnees_bruitees.p | Bin 0 -> 305 bytes tp1/donnees.m | 38 ++++ tp1/donnees_occultees.m | 52 ++++++ tp1/exercice_1.m | 36 ++++ tp1/exercice_2.m | 42 +++++ tp1/exercice_3.m | 42 +++++ tp1/exercice_4.m | 42 +++++ tp2/donnees.m | 70 ++++++++ tp2/exercice_1.m | 48 ++++++ tp2/exercice_2.m | 37 ++++ tp2/exercice_3.m | 54 ++++++ tp2/exercice_4.m | 50 ++++++ tp3/Donnees/bateau.mat | Bin 0 -> 172002 bytes tp3/Donnees/parquet.mat | Bin 0 -> 151296 bytes tp3/affichage_faisceau.m | 60 +++++++ tp3/cercle_3_points.m | 13 ++ tp3/creation_cercle_et_donnees_bruitees.p | Bin 0 -> 306 bytes tp3/donnees_aberrantes.m | 44 +++++ tp3/exercice_0.m | 86 +++++++++ tp3/exercice_0.mat | Bin 0 -> 1497865 bytes tp3/exercice_1.m | 81 +++++++++ tp3/exercice_2.m | 201 ++++++++++++++++++++++ tp3/exercice_3.m | 103 +++++++++++ 23 files changed, 1099 insertions(+) create mode 100755 tp1/creation_cercle_et_donnees_bruitees.p create mode 100755 tp1/donnees.m create mode 100755 tp1/donnees_occultees.m create mode 100755 tp1/exercice_1.m create mode 100755 tp1/exercice_2.m create mode 100755 tp1/exercice_3.m create mode 100755 tp1/exercice_4.m create mode 100755 tp2/donnees.m create mode 100755 tp2/exercice_1.m create mode 100755 tp2/exercice_2.m create mode 100755 tp2/exercice_3.m create mode 100755 tp2/exercice_4.m create mode 100755 tp3/Donnees/bateau.mat create mode 100755 tp3/Donnees/parquet.mat create mode 100755 tp3/affichage_faisceau.m create mode 100755 tp3/cercle_3_points.m create mode 100755 tp3/creation_cercle_et_donnees_bruitees.p create mode 100755 tp3/donnees_aberrantes.m create mode 100755 tp3/exercice_0.m create mode 100755 tp3/exercice_0.mat create mode 100755 tp3/exercice_1.m create mode 100755 tp3/exercice_2.m create mode 100755 tp3/exercice_3.m diff --git a/tp1/creation_cercle_et_donnees_bruitees.p b/tp1/creation_cercle_et_donnees_bruitees.p new file mode 100755 index 0000000000000000000000000000000000000000..f2bb35a5cd739954c6ca19ca90fd5c0097cc25ca GIT binary patch literal 305 zcmV-10nYw*FflGLFm^C7E-)|v31A$V^1rbF005`}009vI00H9Q6E-I!Z+ZA6ywVC8 zCneDPpA4R~t7R=8?{Q!lh?GhWc({IV%i7SSrdVHVil~~K!@mW(E zkWdSWz&=`8Mje19PUz{SSxwT-pH;jD6#Q3DcZ4usf%dFOH5_-Fs)+ehd@gIz612%D zLt%^5n)qVW_9G!!Exz>y6d-0jrNCdH65!n7RD0J%vS3#)J#Qp7y8CPsxP94^0~CAn zFg#eQI_-P%j7K?Sk{%q%wkK_1Hp5b(y4MBuy@3&eI~-oCd&rjaMSbjgCIdZ0;zLjz zbPc#j?zHPseQZ=AKux|ZeD|(1#r_Jm=Y(%a DeJP5Z literal 0 HcmV?d00001 diff --git a/tp1/donnees.m b/tp1/donnees.m new file mode 100755 index 0000000..9acbdd0 --- /dev/null +++ b/tp1/donnees.m @@ -0,0 +1,38 @@ +clear; +close all; + +taille_ecran = get(0,'ScreenSize'); +L = taille_ecran(3); +H = taille_ecran(4); + +% Fenetre d'affichage : +figure('Name','Points situes au voisinage d''un cercle', ... + 'Position',[0.4*L,0.05*H,0.6*L,0.7*H]); +axis equal; +hold on; +set(gca,'FontSize',20); +hx = xlabel('$x$','FontSize',30); +set(hx,'Interpreter','Latex'); +hy = ylabel('$y$','FontSize',30); +set(hy,'Interpreter','Latex'); + +% Bornes d'affichage des donnees centrees en (0,0) : +taille = 20; +bornes = [-taille taille -taille taille]; + +% Creation du cercle et des donnees bruitees : +n = 50; +sigma = 0.5; +[x_cercle,y_cercle,x_donnees_bruitees,y_donnees_bruitees,theta_donnees_bruitees] ... + = creation_cercle_et_donnees_bruitees(taille,n,sigma); + +% Affichage du cercle : +plot(x_cercle([1:end 1]),y_cercle([1:end 1]),'r','LineWidth',3); + +% Affichage des donnees bruitees : +plot(x_donnees_bruitees,y_donnees_bruitees,'k+','MarkerSize',10,'LineWidth',2); +axis(bornes); +lg = legend(' Cercle', ... + ' Donnees bruitees', ... + 'Location','Best'); +grid on; diff --git a/tp1/donnees_occultees.m b/tp1/donnees_occultees.m new file mode 100755 index 0000000..82f1bf1 --- /dev/null +++ b/tp1/donnees_occultees.m @@ -0,0 +1,52 @@ +clear; +close all; + +taille_ecran = get(0,'ScreenSize'); +L = taille_ecran(3); +H = taille_ecran(4); + +% Fenetre d'affichage : +figure('Name','Points situes au voisinage d''un cercle', ... + 'Position',[0.4*L,0.05*H,0.6*L,0.7*H]); +axis equal; +hold on; +set(gca,'FontSize',20); +hx = xlabel('$x$','FontSize',30); +set(hx,'Interpreter','Latex'); +hy = ylabel('$y$','FontSize',30); +set(hy,'Interpreter','Latex'); + +% Bornes d'affichage des donnees centrees en (0,0) : +taille = 20; +bornes = [-taille taille -taille taille]; + +% Creation du cercle et des donnees bruitees : +n = 50; +sigma = 0.5; +[x_cercle,y_cercle,x_donnees_bruitees,y_donnees_bruitees,theta_donnees_bruitees] ... + = creation_cercle_et_donnees_bruitees(taille, n, sigma); + +theta = rand(1, 2)*2*pi; +theta = sort(theta); + +while theta(2)-theta(1) < pi/2 + + theta = rand(1, 2)*2*pi; + theta = sort(theta); + +end + +x_donnees_bruitees = x_donnees_bruitees( theta(1) <= theta_donnees_bruitees & theta_donnees_bruitees <= theta(2) ); +y_donnees_bruitees = y_donnees_bruitees( theta(1) <= theta_donnees_bruitees & theta_donnees_bruitees <= theta(2) ); +theta_donnees_bruitees = theta_donnees_bruitees( theta(1) <= theta_donnees_bruitees & theta_donnees_bruitees <= theta(2) ); + +% Affichage du cercle : +plot(x_cercle([1:end 1]),y_cercle([1:end 1]),'r','LineWidth',3); + +% Affichage des donnees bruitees : +plot(x_donnees_bruitees,y_donnees_bruitees,'k+','MarkerSize',10,'LineWidth',2); +axis(bornes); +lg = legend(' Cercle', ... + ' Donnees bruitees', ... + 'Location','Best'); +grid on; diff --git a/tp1/exercice_1.m b/tp1/exercice_1.m new file mode 100755 index 0000000..a198875 --- /dev/null +++ b/tp1/exercice_1.m @@ -0,0 +1,36 @@ +donnees; + +n_tests = 500; + +% Estimation de la position du centre : +[C_estime,R_moyen] = estimation_1(x_donnees_bruitees,y_donnees_bruitees,n_tests); + +% Affichage du cercle estime : +n_points_cercle = 100; +theta_cercle = 2*pi/n_points_cercle:2*pi/n_points_cercle:2*pi; +x_cercle_estime = C_estime(1)+R_moyen*cos(theta_cercle); +y_cercle_estime = C_estime(2)+R_moyen*sin(theta_cercle); +plot(x_cercle_estime([1:end 1]),y_cercle_estime([1:end 1]),'b','LineWidth',3); +lg = legend(' Cercle initial', ... + ' Donnees bruitees', ... + ' Cercle estime', ... + 'Location','Best'); + +function [C_estime, R_moyen] = estimation_1(x_donnees_bruitees, y_donnees_bruitees, n_tests) + + G = mean( [ x_donnees_bruitees.' y_donnees_bruitees.' ] ); + R_moyen = mean( sqrt((x_donnees_bruitees.'-G(1)).^2 + (y_donnees_bruitees.'-G(2)).^2) ); + + x = repmat(x_donnees_bruitees.', 1, n_tests); + y = repmat(y_donnees_bruitees.', 1, n_tests); + + x_rand = repmat((rand(1, n_tests)*R_moyen - R_moyen/2) + G(1), length(x_donnees_bruitees), 1); + y_rand = repmat((rand(1, n_tests)*R_moyen - R_moyen/2) + G(2), length(y_donnees_bruitees), 1); + + dist = (sqrt((x-x_rand).^2 + (y-y_rand).^2) - R_moyen).^2; + + [min_val, min_index] = min( sum( dist ) ); + + C_estime = [ x_rand(1, min_index) y_rand(1, min_index) ]; + +end \ No newline at end of file diff --git a/tp1/exercice_2.m b/tp1/exercice_2.m new file mode 100755 index 0000000..cd31d0a --- /dev/null +++ b/tp1/exercice_2.m @@ -0,0 +1,42 @@ +donnees; + +n_tests = 1000; + +% Estimation du rayon et de la position du centre : +[C_estime,R_estime] = estimation_2(x_donnees_bruitees,y_donnees_bruitees,n_tests); + +% Affichage du cercle estime : +n_points_cercle = 100; +theta_cercle = 2*pi/n_points_cercle:2*pi/n_points_cercle:2*pi; +x_cercle_estime = C_estime(1)+R_estime*cos(theta_cercle); +y_cercle_estime = C_estime(2)+R_estime*sin(theta_cercle); +plot(x_cercle_estime([1:end 1]),y_cercle_estime([1:end 1]),'b','LineWidth',3); +lg = legend(' Cercle initial', ... + ' Donnees bruitees', ... + ' Cercle estime', ... + 'Location','Best'); + + function [C_estime,R_estime] = estimation_2(x_donnees_bruitees,y_donnees_bruitees,n_tests); + + G = mean( [ x_donnees_bruitees.' y_donnees_bruitees.' ] ); + R_moyen = mean( sqrt((x_donnees_bruitees.'-G(1)).^2 + (y_donnees_bruitees.'-G(2)).^2) ); + + x = repmat(x_donnees_bruitees.', 1, n_tests, n_tests); + y = repmat(y_donnees_bruitees.', 1, n_tests, n_tests); + + x_rand = repmat((rand(1, n_tests)*2 - 1) + G(1), length(x_donnees_bruitees), 1, n_tests); + y_rand = repmat((rand(1, n_tests)*2 - 1) + G(2), length(y_donnees_bruitees), 1, n_tests); + + r_rand = rand(1, 1, n_tests) - 1/2 + R_moyen; + R = repmat(r_rand, length(x_donnees_bruitees), n_tests, 1); + + dist = (sqrt((x-x_rand).^2 + (y-y_rand).^2) - R).^2; + + somme = reshape(sum(dist), [n_tests, n_tests]); + + [min_val, idx] = min(somme(:)); + [row, col] = ind2sub(size(somme), idx); + + C_estime = [ x_rand(1, row ) y_rand(1, row ) ]; + R_estime = r_rand(col); +end \ No newline at end of file diff --git a/tp1/exercice_3.m b/tp1/exercice_3.m new file mode 100755 index 0000000..0d9e649 --- /dev/null +++ b/tp1/exercice_3.m @@ -0,0 +1,42 @@ +donnees_occultees; + +n_tests = 1000; + +% Estimation du rayon et de la position du centre : +[C_estime,R_estime] = estimation_2(x_donnees_bruitees,y_donnees_bruitees,n_tests); + +% Affichage du cercle estime : +n_points_cercle = 100; +theta_cercle = 2*pi/n_points_cercle:2*pi/n_points_cercle:2*pi; +x_cercle_estime = C_estime(1)+R_estime*cos(theta_cercle); +y_cercle_estime = C_estime(2)+R_estime*sin(theta_cercle); +plot(x_cercle_estime([1:end 1]),y_cercle_estime([1:end 1]),'b','LineWidth',3); +lg = legend(' Cercle initial', ... + ' Donnees bruitees', ... + ' Cercle estime', ... + 'Location','Best'); + + function [C_estime,R_estime] = estimation_2(x_donnees_bruitees,y_donnees_bruitees,n_tests); + + G = mean( [ x_donnees_bruitees.' y_donnees_bruitees.' ] ); + R_moyen = mean( sqrt((x_donnees_bruitees.'-G(1)).^2 + (y_donnees_bruitees.'-G(2)).^2) ); + + x = repmat(x_donnees_bruitees.', 1, n_tests, n_tests); + y = repmat(y_donnees_bruitees.', 1, n_tests, n_tests); + + x_rand = repmat((rand(1, n_tests)*3*R_moyen - 1.5*R_moyen) + G(1), length(x_donnees_bruitees), 1, n_tests); + y_rand = repmat((rand(1, n_tests)*3*R_moyen - 1.5*R_moyen) + G(2), length(y_donnees_bruitees), 1, n_tests); + + r_rand = rand(1, 1, n_tests)*3*R_moyen - 1.5*R_moyen; + R = repmat(r_rand, length(x_donnees_bruitees), n_tests, 1); + + dist = (sqrt((x-x_rand).^2 + (y-y_rand).^2) - R).^2; + + somme = reshape(sum(dist), [n_tests, n_tests]); + + [min_val, idx] = min(somme(:)); + [row, col] = ind2sub(size(somme), idx); + + C_estime = [ x_rand(1, row ) y_rand(1, row ) ]; + R_estime = r_rand(col); +end \ No newline at end of file diff --git a/tp1/exercice_4.m b/tp1/exercice_4.m new file mode 100755 index 0000000..6bbad55 --- /dev/null +++ b/tp1/exercice_4.m @@ -0,0 +1,42 @@ +donnees_occultees; + +n_tests = 1000; + +% Estimation du rayon et de la position du centre : +[C_estime,R_estime] = estimation_2(x_donnees_bruitees,y_donnees_bruitees,n_tests); + +% Affichage du cercle estime : +n_points_cercle = 100; +theta_cercle = 2*pi/n_points_cercle:2*pi/n_points_cercle:2*pi; +x_cercle_estime = C_estime(1)+R_estime*cos(theta_cercle); +y_cercle_estime = C_estime(2)+R_estime*sin(theta_cercle); +plot(x_cercle_estime([1:end 1]),y_cercle_estime([1:end 1]),'b','LineWidth',3); +lg = legend(' Cercle initial', ... + ' Donnees bruitees', ... + ' Cercle estime', ... + 'Location','Best'); + + function [C_estime,R_estime] = estimation_2(x_donnees_bruitees,y_donnees_bruitees,n_tests); + + G = mean( [ x_donnees_bruitees.' y_donnees_bruitees.' ] ); + R_moyen = mean( sqrt((x_donnees_bruitees.'-G(1)).^2 + (y_donnees_bruitees.'-G(2)).^2) ); + + x = repmat(x_donnees_bruitees.', 1, n_tests, n_tests); + y = repmat(y_donnees_bruitees.', 1, n_tests, n_tests); + + x_rand = repmat((randn(1, n_tests)*R_moyen - R_moyen/2) + G(1), length(x_donnees_bruitees), 1, n_tests); + y_rand = repmat((randn(1, n_tests)*R_moyen - R_moyen/2) + G(2), length(y_donnees_bruitees), 1, n_tests); + + r_rand = randn(1, 1, n_tests)*R_moyen - R_moyen/2; + R = repmat(r_rand, length(x_donnees_bruitees), n_tests, 1); + + dist = (sqrt((x-x_rand).^2 + (y-y_rand).^2) - R).^2; + + somme = reshape(sum(dist), [n_tests, n_tests]); + + [min_val, idx] = min(somme(:)); + [row, col] = ind2sub(size(somme), idx); + + C_estime = [ x_rand(1, row ) y_rand(1, row ) ]; + R_estime = r_rand(col); +end \ No newline at end of file diff --git a/tp2/donnees.m b/tp2/donnees.m new file mode 100755 index 0000000..c1363ec --- /dev/null +++ b/tp2/donnees.m @@ -0,0 +1,70 @@ +clear; +close all; + +taille_ecran = get(0,'ScreenSize'); +L = taille_ecran(3); +H = taille_ecran(4); + +% Fenetre d'affichage : +figure('Name','Points situes au voisinage d''une droite', ... + 'Position',[0.4*L,0,0.6*L,0.8*H]); +axis equal; +hold on; +set(gca,'FontSize',20); +hx = xlabel('$x$','FontSize',30); +set(hx,'Interpreter','Latex'); +hy = ylabel('$y$','FontSize',30); +set(hy,'Interpreter','Latex'); + +% Bornes d'affichage des donnees centrees en (0,0) : +taille = 20; +bornes = [-taille taille -taille taille]; + +% Parametres de la droite : +theta_D = 2*pi*(rand-0.5); +cos_theta_D = cos(theta_D); +sin_theta_D = sin(theta_D); +marge = 5; +rho_D = (taille-marge)*rand; + +% Affichage de la droite : +droite_horizontale = abs(cos_theta_D)-taille & ... + x_donnees_bruitees-taille & ... + y_donnees_bruiteesW`KroP7xGt6VFYjlyIfk#ZK4m&&OU*pD z7iSlko|6T)?+BM~ij#jD+LPIzxbyPzrdlsfyJ{|F(2r`@v9WM)Ff(_W>g#Li>6w}7=qykF zT=Jn@@AN$#3e&4yUop(3)be_`hwgU<1qGqb_eg&9Y)xNXL6-*h{{Bt)=Hn7GSi{7*dvy6yfsc{ zl)-jb2!{E66CbZkS--OK99@9_vR$3Kh|$p`R;}N_FHv!JEXNTgU8Gz7{DKrSEUzFx z%ve@h_7Uc6Yis*i@Z8zyb4^4gLAA?bOBs(*V*9tw!=4UTz!~vTWF}Yy&}SJNEeBW%4apc7cF`MB*zC~3NAR|07S+ydL-oW9Pr@fvLq#_(0`LR zzyA^_mqo*!y}!ydl&`MOkgOSW+N~#T0M`)Qzn=P-nS*A4)1(tum^tGw@~K}tf;@s( zowZ!gjtz^;_9DWp4?QvMYBnWRJy-gJ4$IeE)KX^G*z?mGb^#-tKeAU z;_PT^p!iK#=-Z_wCFg-e?igY?6TnxId4A%lqtw^gY>25hljoGBvB=ywAbDG`k}hhZ zyfl&3m98*GMDGrlA$pQxj}4a~Y@F<%m69ykWHLGk6HV>)dHbaIyf3t;2ORp_63Ep6 z9EK(x-qdT@;txYlNJviF|F&baFSm5owbgZ1P#m3K9BVP*vw)YjuCB1q_a(~Fr4R@B 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+ + % Cas ou D_k coupe le bord superieur : + y = y_min; + x = (rho_k-y*sin_theta_k)/cos_theta_k; + if x>=x_min & x<=x_max + x_extremites(i) = x; + y_extremites(i) = y; + i = i+1; + end + + % Cas ou D_k coupe le bord inferieur : + y = y_max; + x = (rho_k-y*sin_theta_k)/cos_theta_k; + if x>=x_min & x<=x_max + x_extremites(i) = x; + y_extremites(i) = y; + end + + % Affichage de la droite D_k : + plot(x_extremites,y_extremites,couleur,'LineWidth',2); +end diff --git a/tp3/cercle_3_points.m b/tp3/cercle_3_points.m new file mode 100755 index 0000000..19464a7 --- /dev/null +++ b/tp3/cercle_3_points.m @@ -0,0 +1,13 @@ +function [C,R] = cercle_3_points(x,y) + +x1 = x(1); +y1 = y(1); +x2 = x(2); +y2 = y(2); +x3 = x(3); +y3 = y(3); + +A = 2*[-x1+x2 -y1+y2 ; -x1+x3 -y1+y3]; +B = [-x1^2+x2^2-y1^2+y2^2 ; -x1^2+x3^2-y1^2+y3^2]; +C = A\B; +R = sqrt((x1-C(1))^2+(y1-C(2))^2); diff --git a/tp3/creation_cercle_et_donnees_bruitees.p b/tp3/creation_cercle_et_donnees_bruitees.p new file mode 100755 index 0000000000000000000000000000000000000000..5066819644507d214c9593519ca484897acdc427 GIT binary patch literal 306 zcmV-20nPq)FflGLFm^C7E-)|v32+<$_P?8Q! zO9_I*pAui3#_0XZ9MfGUFyXKnx*c}4s}DTvOJarsGbvN|^^iRC@a20$&N~Rz&{y)4 zoV1j>%CFAG9952k0y?rgk-h+5fuh3KAS(;{q9D@XHs|r_Cc1gU{V~atk?Fp;m*$K@ z6l~C&+C^J;R8tB#5xn<4Mu~=g<|Js{HgN2xWil{)25Ta z${k{`rzc%BB{-VGsRSB$hiET!2=__O$sCH~kJNmRB9yc3j9po2_Lz+I&w>{*oo)(< zI0x-lZ-Nw`%3NgnwL2}ZY@iE|0U1{pE(Yhcg~&F3h*X#JT@oyWZ~&DPKzZ3y$BYfJ EdyveNm;e9( literal 0 HcmV?d00001 diff --git a/tp3/donnees_aberrantes.m b/tp3/donnees_aberrantes.m new file mode 100755 index 0000000..26320f8 --- /dev/null +++ b/tp3/donnees_aberrantes.m @@ -0,0 +1,44 @@ +clear; +close all; + +taille_ecran = get(0,'ScreenSize'); +L = taille_ecran(3); +H = taille_ecran(4); + +% Fenetre d'affichage : +figure('Name','Points situes au voisinage d''un cercle', ... + 'Position',[0.4*L,0.05*H,0.6*L,0.7*H]); +axis equal; +hold on; +set(gca,'FontSize',20); +hx = xlabel('$x$','FontSize',30); +set(hx,'Interpreter','Latex'); +hy = ylabel('$y$','FontSize',30); +set(hy,'Interpreter','Latex'); + +% Limites de l'affichage des donnees centrees en (0,0) : +taille = 20; +limites_affichage = [-taille taille -taille taille]; + +% Creation du cercle et des donnees bruitees : +n = 50; +sigma = 0.5; +[x_cercle,y_cercle,theta_cercle,x_donnees_bruitees,y_donnees_bruitees,theta_donnees_bruitees] ... + = creation_cercle_et_donnees_bruitees(taille,n,sigma); + +% Affichage du cercle : +plot(x_cercle([1:end 1]),y_cercle([1:end 1]),'r','LineWidth',3); + +% Donnees aberrantes : +proportion = 0.25; +n_donnees_aberrantes = floor(proportion*n); +x_donnees_bruitees = [x_donnees_bruitees taille*(2*rand(1,n_donnees_aberrantes)-1)]; +y_donnees_bruitees = [y_donnees_bruitees taille*(2*rand(1,n_donnees_aberrantes)-1)]; + +% Affichage des donnees bruitees : +plot(x_donnees_bruitees,y_donnees_bruitees,'k+','MarkerSize',10,'LineWidth',2); +axis(limites_affichage); +lg = legend(' Cercle', ... + ' Donnees (bruitees + aberrantes)', ... + 'Location','Best'); +grid on; diff --git a/tp3/exercice_0.m b/tp3/exercice_0.m new file mode 100755 index 0000000..26ed58e --- /dev/null +++ b/tp3/exercice_0.m @@ -0,0 +1,86 @@ +clear; +close all; +taille_ecran = get(0,'ScreenSize'); +L = taille_ecran(3); +H = taille_ecran(4); + +% Parametres : +alpha = pi/180*12; % Seuil sur l'orientation du gradient (en radians) +cos_alpha = cos(alpha); +seuil_norme = 2/sin(alpha); % Seuil sur la norme du gradient (decoule d'une etude theorique) + +% Chargement des donnees : +% load Donnees/parquet; +%load Donnees/parquet; +load Donnees/bateau; +[n_lignes,n_colonnes] = size(I); +limites_affichages = [1 n_colonnes 1 n_lignes]; + +figure('Name','Detection des alignements','Position',[0.2*L,0,0.8*L,H]); + +% Affichage de l'image : +subplot(2,2,1); +imagesc(I); +axis equal; +axis off; +colormap gray; +title('Image originale','FontSize',30); +axis(limites_affichages); + +% Fenetre d'affichage des pixels de contour : +subplot(2,2,3); +imagesc(I); +axis equal; +axis off; +colormap gray; +hold on; + +% Gradient du niveau de gris (x vers la droite, y vers le bas) : +I = double(I); +[G_x,G_y] = gradient(I); +G_norme = sqrt(G_x.^2+G_y.^2); + +% Selection des pixels de contour : +contour = G_norme>seuil_norme; + +% Pas de pixel de contour sur le bord de l'image => Traitement simplifie ! +contour([1 n_lignes],:) = 0; +contour(:,[1 n_colonnes]) = 0; + +% Tri des pixels de contour : +indices_contour = find(contour); +[~,indices] = sort(G_norme(indices_contour),'descend'); +indices_contour = indices_contour(indices); + +% Affichage d'une petite fleche sur les pixels de contour : +[i,j] = ind2sub(size(I),indices_contour); +quiver(j,i,G_x(indices_contour),G_y(indices_contour),'r'); % Attention : x = j et y = i +axis equal; +title('Pixels de contour','FontSize',30); +axis(limites_affichages); +drawnow; + +% Affichage des ensembles E (la fonction label2rgb donne a chaque ensemble E une couleur differente) : +subplot(2,2,2); +imagesc(I_resultat); +axis(limites_affichages); +axis equal; +axis off; +title('Ensembles candidats','FontSize',30); + +% Affichage de l'esquisse : +subplot(2,2,4); +imagesc(120*ones(size(I)),[0,255]); +axis equal; +axis off; +title('Alignements','FontSize',30); +hold on; +axis(limites_affichages); + +% Boucle sur les ensembles E : +for k = 1:size(extremites,3) + % Affichage du segment : + line(extremites(1,:,k),extremites(2,:,k),'Color','w','LineWidth',2); +end + +save exercice_0; diff --git a/tp3/exercice_0.mat b/tp3/exercice_0.mat new file mode 100755 index 0000000000000000000000000000000000000000..d9a96a3cc1fe7b5a4994b5a3f504215ce598f7db GIT binary patch literal 1497865 zcma%iRag^_8?JOox5Pk@Zlp^Z=}?g_5s>cQknWJq5mGAME!`cXyQD@l*v8K9|2*g1 zpZDs!{jR?6EiL&En(_)vB76c&TJj%wzdAVC@-XQ-S$TbR^>CJCQq|P{EHC<&he^@H z*2>HF3zMshB$Jc33m?-rD;FO=CLs|fApuEYK}kUYrvGoe_ZD7vpHD@MoI>PtfkLtoh* zpmZudKZ>qU+JEeARAdbbHl89&6=YdSu| 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estimation_F_2(rho([points_model points_candidat]), theta([points_model points_candidat])); + + if erreur_new < erreur_F_1 + + rho_F_1 = rho_new; + theta_F_1 = theta_new; + erreur_F_1 = erreur_new; + + end + + end + + end +end + +function [rho_F, theta_F, erreur_F] = estimation_F_2(rho, theta) + + B = rho; + A = [cos(theta.') ; sin(theta.')].'; + + X = (A.'*A)\(A.'*B); + + rho_F = sqrt( X(1)^2 + X(2)^2 ); + theta_F = atan2(X(2), X(1)); + + erreur_F = mean( abs( rho - rho_F*cos(theta - theta_F) ) ); + +end \ No newline at end of file diff --git a/tp3/exercice_3.m b/tp3/exercice_3.m new file mode 100755 index 0000000..d6f6a92 --- /dev/null +++ b/tp3/exercice_3.m @@ -0,0 +1,103 @@ +donnees_aberrantes; + +n_tests = 1000; + +% Parametres de l'algorithme RANSAC : +n_donnees = length(x_donnees_bruitees); +S1 = 2; +S2 = 0.5; +k_max = floor(nchoosek(n_donnees,3)/n_donnees); +parametres = [S1 S2 k_max]; + +% Estimation du rayon et de la position du centre : +[C_estime,R_estime] = RANSAC_3(x_donnees_bruitees,y_donnees_bruitees,parametres,n_tests); + +% Affichage du cercle estime : +x_cercle_estime = C_estime(1)+R_estime*cos(theta_cercle); +y_cercle_estime = C_estime(2)+R_estime*sin(theta_cercle); +plot(x_cercle_estime([1:end 1]),y_cercle_estime([1:end 1]),'b','LineWidth',3); + +% Affichage des points conformes au modele : +conformes = abs(sqrt((x_donnees_bruitees-C_estime(1)).^2+ ... + (y_donnees_bruitees-C_estime(2)).^2)-R_estime)<=S1; +plot(x_donnees_bruitees(conformes), ... + y_donnees_bruitees(conformes),'b+','MarkerSize',10,'LineWidth',2); +lg = legend(' Cercle initial', ... + ' Donnees (bruitees + aberrantes)', ... + ' Cercle estime', ... + ' Donnees conformes', ... + 'Location','Best'); + +function [C_estime,R_estime] = RANSAC_3(x_donnees_bruitees,y_donnees_bruitees,parametres,n_tests) + + n = length(x_donnees_bruitees); + erreur = +inf; + + for j = 1:parametres(3) + + j/parametres(3)*100 + + points_model = randperm(n, 3); + [C_model, R_model] = cercle_3_points(x_donnees_bruitees(points_model), y_donnees_bruitees(points_model)); + + points_candidat = []; + + for i = setdiff(1:n, points_model) + + [C_candidat, R_candidat] = estimation(x_donnees_bruitees([points_model i]), y_donnees_bruitees([points_model i]), n_tests); + + % ma fonction d'erreur ne doit pas être la bonne mais ça marche + % a peu près bien ~~ + erreur_candidat = mean( abs( sqrt((C_model(1)-x_donnees_bruitees([points_model i])).^2 + (C_model(2)-y_donnees_bruitees([points_model i])).^2 )) - R_model ); + + if erreur_candidat < parametres(1) + + points_candidat = [ points_candidat i ]; + + end + + end + + if length(points_candidat)/n > parametres(2) + + [C_new, R_new] = estimation(x_donnees_bruitees([points_model points_candidat]), y_donnees_bruitees([points_model points_candidat]), n_tests); + + erreur_new = mean( abs( sqrt((C_model(1)-x_donnees_bruitees([points_model points_candidat])).^2 + (C_model(2)-y_donnees_bruitees([points_model points_candidat])).^2 )) - R_model ); + + if erreur_new < erreur + + C_estime = C_new; + R_estime = R_new; + erreur = erreur_new; + + end + + end + + end +end + +function [C_estime,R_estime] = estimation(x_donnees_bruitees,y_donnees_bruitees,n_tests) + + G = mean( [ x_donnees_bruitees.' y_donnees_bruitees.' ] ); + R_moyen = mean( sqrt((x_donnees_bruitees.'-G(1)).^2 + (y_donnees_bruitees.'-G(2)).^2) ); + + x = repmat(x_donnees_bruitees.', 1, n_tests, n_tests); + y = repmat(y_donnees_bruitees.', 1, n_tests, n_tests); + + x_rand = repmat((randn(1, n_tests)*R_moyen - R_moyen/2) + G(1), length(x_donnees_bruitees), 1, n_tests); + y_rand = repmat((randn(1, n_tests)*R_moyen - R_moyen/2) + G(2), length(y_donnees_bruitees), 1, n_tests); + + r_rand = randn(1, 1, n_tests)*R_moyen - R_moyen/2; + R = repmat(r_rand, length(x_donnees_bruitees), n_tests, 1); + + dist = (sqrt((x-x_rand).^2 + (y-y_rand).^2) - R).^2; + + somme = reshape(sum(dist), [n_tests, n_tests]); + + [min_val, idx] = min(somme(:)); + [row, col] = ind2sub(size(somme), idx); + + C_estime = [ x_rand(1, row ) y_rand(1, row ) ]; + R_estime = r_rand(col); + end \ No newline at end of file

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