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Spatial Intersection.m
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Spatial Intersection.m
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% IMBDC Exercise 4 Spatial intersection
% Worked by Karam Mawas 2946939
close all
clear all
clc
% points are already measured by the ginput function
% x = [135.437062937063,3565.83706293706,3955.65524475524,3907.67762237762,3283.96853146853,2270.44125874126,2612.28181818182,1850.63706293706,2426.36853146853]';
% y = [177.081818181819,2348.06923076923,2072.19790209790,1556.43846153846,650.860839160840,1676.38251748252,1220.59510489511,428.964335664336,380.986713286714]';
% Note
% R0020774=im1\R0020813=im2\R0020814=im3\R0020815=im4\R0020816=im5\R0020849=im6\R0020850=im7\R0020851=im8\R0020852=im9
% reading the images
% im71 = imread('C:\Users\ehteshamhasnain\Downloads\Karam\Exercise 2\Ricoh-UAV_Subblock\R0020771.jpg');
% im72 = imread('C:\Users\ehteshamhasnain\Downloads\Karam\Exercise 2\Ricoh-UAV_Subblock\R0020772.jpg');
% im73 = imread('C:\Users\ehteshamhasnain\Downloads\Karam\Exercise 2\Ricoh-UAV_Subblock\R0020773.jpg');
% im74 = imread('C:\Users\ehteshamhasnain\Downloads\Karam\Exercise 2\Ricoh-UAV_Subblock\R0020774.jpg');
% im75 = imread('C:\Users\ehteshamhasnain\Downloads\Karam\Exercise 2\Ricoh-UAV_Subblock\R0020775.jpg');
% im12 = imread('C:\Users\ehteshamhasnain\Downloads\Karam\Exercise 2\Ricoh-UAV_Subblock\R0020812.jpg');
% im13 = imread('C:\Users\ehteshamhasnain\Downloads\Karam\Exercise 2\Ricoh-UAV_Subblock\R0020813.jpg');
% im14 = imread('C:\Users\ehteshamhasnain\Downloads\Karam\Exercise 2\Ricoh-UAV_Subblock\R0020814.jpg');
% im15 = imread('C:\Users\ehteshamhasnain\Downloads\Karam\Exercise 2\Ricoh-UAV_Subblock\R0020815.jpg');
% im16 = imread('C:\Users\ehteshamhasnain\Downloads\Karam\Exercise 2\Ricoh-UAV_Subblock\R0020816.jpg');
% im49 = imread('C:\Users\ehteshamhasnain\Downloads\Karam\Exercise 2\Ricoh-UAV_Subblock\R0020849.jpg');
% im50 = imread('C:\Users\ehteshamhasnain\Downloads\Karam\Exercise 2\Ricoh-UAV_Subblock\R0020850.jpg');
% im51 = imread('C:\Users\ehteshamhasnain\Downloads\Karam\Exercise 2\Ricoh-UAV_Subblock\R0020851.jpg');
% im52 = imread('C:\Users\ehteshamhasnain\Downloads\Karam\Exercise 2\Ricoh-UAV_Subblock\R0020852.jpg');
% im53 = imread('C:\Users\ehteshamhasnain\Downloads\Karam\Exercise 2\Ricoh-UAV_Subblock\R0020853.jpg');
% im71 = rgb2gray(im71); im72 = rgb2gray(im72);
% initializing the interior orientatin of the camera and rotation matricies
% for all the images
% Interior Orientation for the images (the K matrix)
K = [-3933.36363636,-0.00000000,2143.50000000;
-0.00000000,3933.36363636,1423.50000000;
0.00000000,0.00000000,1.00000000];
% rotation matricies
% R_71 = [-0.888776619260 -0.457304048725 -0.030807922295;
% 0.458330362120 -0.886297121687 -0.066413035232;
% 0.003065977044 -0.073146559110 0.997316489724];
% X0_71 = [512906.565340; 5427602.989520; 515.744690];
%
% R_72 = [-0.870960174003 -0.488580136412 -0.052132769008;
% 0.488253956273 -0.872479485577 0.019688103784;
% -0.055103987919 -0.008306476422 0.998446069132];
% X0_72 = [512891.972680; 5427626.881650; 515.419150];
%
% R_73 = [-0.853199280893 -0.519667012797 0.044689852260;
% 0.517892492096 -0.854220979117 -0.045758993294;
% 0.061954448707 -0.015897001214 0.997952369423];
% X0_73 = [512876.458510; 5427651.545480; 514.346390];
R_74 = [-0.898364354805 -0.424038535386 -0.114598457768;
0.431222964600 -0.901052927842 -0.046372147116;
-0.083595698552 -0.091076570722 0.992328986500];
X0_74= [512862.179910; 5427675.837710; 514.907080];
% R_75 = [ -0.865048359102 -0.501663541135 0.005002790291;
% 0.500877525330 -0.864173861893 -0.048220753218;
% 0.028513874422 -0.039207498226 0.998824174241];
% X0_75 = [512846.973530; 5427700.537190; 515.308980];
%
% R_12 = [ 0.886120155244 0.448624945312 -0.116304466445;
% -0.443803228369 0.893694064736 0.065951596980;
% 0.133528142953 -0.006824741672 0.991021522441];
% X0_12= [512892.209370; 5427714.738940; 515.158090];
R_13 = [0.872990632012, 0.487238787937, 0.022039055070;
-0.486140187346, 0.872897199467, -0.041451144856;
-0.039434435028, 0.025472390784, 0.998897433494];
X0_13 = [512906.392000; 5427691.184110; 516.570080];
R_14 = [0.867281138830 0.493392418024 -0.066237059618;
-0.493411639320 0.869625609377 0.017212021948;
0.066093724462 0.017754474173 0.997655450661];
X0_14 = [512920.853830; 5427668.335460; 516.113920];
R_15 = [0.858414149205 0.508703759544 -0.065921418897;
-0.507788494956 0.860915774482 0.031222966529;
0.072636029862 0.006671901839 0.997336198527];
X0_15 = [512936.566090; 5427645.080020; 515.434980];
R_16 = [0.854735681670 0.514751542165 0.066766490992;
-0.512025217779 0.857252179862 -0.054303558625;
-0.085188560491 0.012229062108 0.996289796797];
X0_16 = [512952.422120; 5427622.063810; 515.982850];
R_49 = [-0.867233884963 -0.496431897214 -0.038219892721;
0.497756374147 -0.862573995849 -0.090579764190;
0.011999198600 -0.097578036019 0.995155538657];
X0_49 = [513010.498970; 5427654.064230; 514.392000];
R_50 = [-0.839539757811 -0.528716554759 -0.125027196158;
0.538291662815 -0.840647830782 -0.059609649767;
-0.073587232584 -0.117345768246 0.990360989678];
X0_50 = [512996.502990; 5427678.079250; 513.677870];
R_51 = [-0.827570749773 -0.557530411593 0.065471324026;
0.549857636160 -0.828569770064 -0.105492730048;
0.113062965097 -0.051302790236 0.992262460056];
X0_51 = [512980.99511; 5427701.52671; 514.79429];
R_52 = [-0.866544118547 -0.490057510421 -0.094577624687;
0.490759244246 -0.871123481449 0.017298677877;
-0.090866136699 -0.031424776041 0.995367182829];
X0_52 = [512966.499230; 5427725.063170; 517.490680];
% R_53 = [ -0.857743949672 -0.514007847249 -0.008440957694;
% 0.513687553089 -0.857617486843 0.024846409457;
% -0.020010362361 0.016975842479 0.999655643795];
% X0_13 = [512951.374930; 5427750.327570; 515.903230];
% to be consistent with my type of naming
R1 = R_74; R2 = R_13; R3 = R_14; R4 = R_15; R5 = R_16; R6 = R_49;
R7 = R_50; R8 = R_51; R9 = R_52;
X0_1 = X0_74; X0_2 = X0_13; X0_3 = X0_14; X0_4 = X0_15; X0_5 = X0_16;
X0_6 = X0_49; X0_7 = X0_50; X0_8 = X0_51; X0_9 = X0_52;
% Computing the Projection matricies
P1 = K*R1*[eye(3) -X0_1];
P2 = K*R2*[eye(3) -X0_2];
P3 = K*R3*[eye(3) -X0_3];
P4 = K*R4*[eye(3) -X0_4];
P5 = K*R5*[eye(3) -X0_5];
P6 = K*R6*[eye(3) -X0_6];
P7 = K*R7*[eye(3) -X0_7];
P8 = K*R8*[eye(3) -X0_8];
P9 = K*R9*[eye(3) -X0_9];
x_h = ones(2,9);
x = ones(1,9); y = ones(1,9); f = ones(1,9);
for i=1:9
m = imread(['E:\UNI\UNI\Third semester\Image-based Data Collection\Labs\Exercise 4\im' num2str(i) '.jpg']);
f(i) = figure(i);
% imshow(rgb2gray(m))
imshow(m)
[x(i),y(i)] = ginput(1);
% x = imtool(rgb2gray(m));
% [x,y] = getline('close')
hold on; plot(x(i),y(i),'r+');
% The homogeneous coordinates of the images points
x_h(1,i) = x(i); x_h(2,i) = y(i);
end
% computing the A matrix
A = [
x_h(1,1)*P1(3,:) - P1(1,:)
x_h(2,1)*P1(3,:) - P1(2,:)
x_h(1,2)*P2(3,:) - P2(1,:)
x_h(2,2)*P2(3,:) - P2(2,:)
x_h(1,3)*P3(3,:) - P3(1,:)
x_h(2,3)*P3(3,:) - P3(2,:)
x_h(1,4)*P4(3,:) - P4(1,:)
x_h(2,4)*P4(3,:) - P4(2,:)
x_h(1,5)*P5(3,:) - P5(1,:)
x_h(2,5)*P5(3,:) - P5(2,:)
x_h(1,6)*P6(3,:) - P6(1,:)
x_h(2,6)*P6(3,:) - P6(2,:)
x_h(1,7)*P7(3,:) - P7(1,:)
x_h(2,7)*P7(3,:) - P7(2,:)
x_h(1,8)*P8(3,:) - P8(1,:)
x_h(2,8)*P8(3,:) - P8(2,:)
x_h(1,9)*P9(3,:) - P9(1,:)
x_h(2,9)*P9(3,:) - P9(2,:)
];
% Extracting the Object coordinates of the points
[U, V, X] = svd(A,0);
X = X(:,end);
% Coordinates of 3d point after normalisation
Terrain_Point_3D = X(:)./X(4);
% computing the back transformation for the points
% the normalized images coordinates
x_trafo_1 = P1*Terrain_Point_3D; x_trafo_1 = x_trafo_1(:)./x_trafo_1(3);
x_trafo_2 = P2*Terrain_Point_3D; x_trafo_2 = x_trafo_2(:)./x_trafo_2(3);
x_trafo_3 = P3*Terrain_Point_3D; x_trafo_3 = x_trafo_3(:)./x_trafo_3(3);
x_trafo_4 = P4*Terrain_Point_3D; x_trafo_4 = x_trafo_4(:)./x_trafo_4(3);
x_trafo_5 = P5*Terrain_Point_3D; x_trafo_5 = x_trafo_5(:)./x_trafo_5(3);
x_trafo_6 = P6*Terrain_Point_3D; x_trafo_6 = x_trafo_6(:)./x_trafo_6(3);
x_trafo_7 = P7*Terrain_Point_3D; x_trafo_7 = x_trafo_7(:)./x_trafo_7(3);
x_trafo_8 = P8*Terrain_Point_3D; x_trafo_8 = x_trafo_8(:)./x_trafo_8(3);
x_trafo_9 = P9*Terrain_Point_3D; x_trafo_9 = x_trafo_9(:)./x_trafo_9(3);
x_trafo = [x_trafo_1,x_trafo_2,x_trafo_3,x_trafo_4,x_trafo_5,x_trafo_6,x_trafo_7,x_trafo_8,x_trafo_9];
% plotting the computed points
for i=1:9
m = imread(['E:\UNI\UNI\Third semester\Image-based Data Collection\Labs\Exercise 4\im' num2str(i) '.jpg']);
f(i) = figure(i);
imshow(m)
plot(x_h(1,i), x_h(2,i), 'r+'); hold on;
plot(x_trafo(1,i), x_trafo(2,i),'b+')
end
% difference between the computed image coordinates and the original ones
diff = ones(2,9); diff_x = ones(1,9); diff_y = ones(1,9);
for i=1:9
for j = 1:2
diff(j,i) = x_h(j,i) - x_trafo(j,i);
end
diff_x(1,i) = diff(1,i)^2;
diff_y(1,i) = diff(2,i)^2;
end
% Error Estimation
VV_x = sum(diff_x,2); VV_y = sum(diff_y,2);
sigma_0_x = sqrt(VV_x/(2*9-3))
sigma_0_y = sqrt(VV_y/(2*9-3))