103 lines
3.8 KiB
Matlab
Executable file
103 lines
3.8 KiB
Matlab
Executable file
donnees_aberrantes;
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n_tests = 1000;
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% Parametres de l'algorithme RANSAC :
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n_donnees = length(x_donnees_bruitees);
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S1 = 2;
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S2 = 0.5;
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k_max = floor(nchoosek(n_donnees,3)/n_donnees);
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parametres = [S1 S2 k_max];
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% Estimation du rayon et de la position du centre :
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[C_estime,R_estime] = RANSAC_3(x_donnees_bruitees,y_donnees_bruitees,parametres,n_tests);
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% Affichage du cercle estime :
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x_cercle_estime = C_estime(1)+R_estime*cos(theta_cercle);
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y_cercle_estime = C_estime(2)+R_estime*sin(theta_cercle);
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plot(x_cercle_estime([1:end 1]),y_cercle_estime([1:end 1]),'b','LineWidth',3);
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% Affichage des points conformes au modele :
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conformes = abs(sqrt((x_donnees_bruitees-C_estime(1)).^2+ ...
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(y_donnees_bruitees-C_estime(2)).^2)-R_estime)<=S1;
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plot(x_donnees_bruitees(conformes), ...
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y_donnees_bruitees(conformes),'b+','MarkerSize',10,'LineWidth',2);
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lg = legend(' Cercle initial', ...
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' Donnees (bruitees + aberrantes)', ...
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' Cercle estime', ...
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' Donnees conformes', ...
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'Location','Best');
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function [C_estime,R_estime] = RANSAC_3(x_donnees_bruitees,y_donnees_bruitees,parametres,n_tests)
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n = length(x_donnees_bruitees);
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erreur = +inf;
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for j = 1:parametres(3)
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j/parametres(3)*100
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points_model = randperm(n, 3);
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[C_model, R_model] = cercle_3_points(x_donnees_bruitees(points_model), y_donnees_bruitees(points_model));
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points_candidat = [];
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for i = setdiff(1:n, points_model)
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[C_candidat, R_candidat] = estimation(x_donnees_bruitees([points_model i]), y_donnees_bruitees([points_model i]), n_tests);
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% ma fonction d'erreur ne doit pas être la bonne mais ça marche
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% a peu près bien ~~
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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 );
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if erreur_candidat < parametres(1)
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points_candidat = [ points_candidat i ];
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end
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end
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if length(points_candidat)/n > parametres(2)
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[C_new, R_new] = estimation(x_donnees_bruitees([points_model points_candidat]), y_donnees_bruitees([points_model points_candidat]), n_tests);
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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 );
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if erreur_new < erreur
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C_estime = C_new;
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R_estime = R_new;
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erreur = erreur_new;
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end
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end
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end
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end
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function [C_estime,R_estime] = estimation(x_donnees_bruitees,y_donnees_bruitees,n_tests)
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G = mean( [ x_donnees_bruitees.' y_donnees_bruitees.' ] );
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R_moyen = mean( sqrt((x_donnees_bruitees.'-G(1)).^2 + (y_donnees_bruitees.'-G(2)).^2) );
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x = repmat(x_donnees_bruitees.', 1, n_tests, n_tests);
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y = repmat(y_donnees_bruitees.', 1, n_tests, n_tests);
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x_rand = repmat((randn(1, n_tests)*R_moyen - R_moyen/2) + G(1), length(x_donnees_bruitees), 1, n_tests);
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y_rand = repmat((randn(1, n_tests)*R_moyen - R_moyen/2) + G(2), length(y_donnees_bruitees), 1, n_tests);
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r_rand = randn(1, 1, n_tests)*R_moyen - R_moyen/2;
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R = repmat(r_rand, length(x_donnees_bruitees), n_tests, 1);
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dist = (sqrt((x-x_rand).^2 + (y-y_rand).^2) - R).^2;
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somme = reshape(sum(dist), [n_tests, n_tests]);
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[min_val, idx] = min(somme(:));
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[row, col] = ind2sub(size(somme), idx);
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C_estime = [ x_rand(1, row ) y_rand(1, row ) ];
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R_estime = r_rand(col);
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end |