Portofolio 6
Pada portofolio 6 ini membahas tentang Kalibrasi kamera.
Berikut listing program calibrate.m:
% CALIBRATE
%
% Function to perform camera calibration
%
% Usage: C = calibrate(im, XYZ, uv)
%
% Where: im – is the image of the calibration target.
% XYZ – is a n x 3 array of XYZ coordinates
% of the calibration target points.
% uv – is a 2 x n array of the image coordinates
% of the calibration target points.
% C – is the 3 x 4 camera calibration matrix.
%
% This function plots the uv coordinates onto the image of
% the calibration target. It also projects the XYZ coordinates
% back into image coordinates using the calibration matrix
% and plots these points too as a visual check on the accuracy of
% the calibration process.
% Lines from the origin to the vanishing points in the X, Y and
% Z directions are overlaid on the image.
% The mean squared error between the positions of the uv coodinates
% and the projected XYZ coordinates is also reported.
%
% The function should also report the error in satisfying the
% camera calibration matrix constraint – the magnitude of
% (q1 x q3).(q2 x q3)
%
function C = calibrate(im, XYZ, uv)
% obtain rows so arbitrary number of points can be used
[rows, cols] = size(XYZ);
XYZ1 = [XYZ, ones(rows, 1)]; % makes it easier to work with
% build B matrix
for n = 1:rows
B(2*n-1, : ) = [XYZ1(n, : ) 0 0 0 0 -uv(1, n)*XYZ(n, : )];
B(2*n, : ) = [0 0 0 0 XYZ1(n, : ) -uv(2, n)*XYZ(n, : )];
end
c = B \ uv(: );
c(12) = 1;
C = reshape(c,4,3)’
XYZ1 = XYZ1′;
for i = 1:rows
suv(:,i) = C*XYZ1(:,i);
suv(:,i) = suv(:,i)/suv(3,i);
end
% calculate the mean squared error between the positions of the uv coordinates and suv.
mse = mean(mean((uv – suv(1:2,:)).^2));
fprintf(1, ‘mean squared error is %d\n’, mse);
% calculate the error in satisfying the camera calibration matrix constraint
q1 = C(1,1:3)’;
q2 = C(2,1:3)’;
q3 = C(3,1:3)’;
error = abs(dot(cross(q1, q3), cross(q2, q3)));
fprintf(1, ‘error in satisfying the camera calibration matrix is %d\n’, error);
% annotate image
imshow(im);
hold;
% plot uv coordinates
plot(uv(1, : ), uv(2, : ),’r+’)
% plot XYZ coordinates
plot(suv(1,: ), suv(2,: ),’bx’)
% draw vanishing lines
for i = 1:3
%a = [C(1,4), C(1,i)/C(3,i)];
%b = [C(2,4), C(2,i)/C(3,i)];
%fprintf(1, ‘%d %d %d enter\n’, i, a ,b);
%plot([C(1,4), C(1,i)/C(3,i)],[C(2,4), C(2,i)/C(3,i)],’bx’)
line([C(1,4), C(1,i)/C(3,i)],[C(2,4), C(2,i)/C(3,i)])
end
hold;
Urutan penomoran pada citra stereo:
Urutan penomoran pada stereo1 |
Urutan penomoran pada stereo2 |
Gambar posisi titik pusat target dan sumbu X, Y dan Z pada stereo1.jpg:
Gambar posisi titik pusat target dan sumbu X, Y dan Z pada stereo2.jpg:
Matriks kalibrasi pada citra stereo1.jpg:
% camera calibration maxtrix for stereo1.jpg
c1 = [0.6596 -0.7391 -0.0615 363.4235;
-0.1851 -0.1387 -0.9437 342.7417;
0.0005 0.0003 -0.0003 1.0000];
Matriks kalibrasi pada citra stereo2.jpg:
% camera calibration maxtrix for stereo2.jpg
c2 = [0.9234 -0.2221 -0.0257 347.7796;
-0.0741 -0.2278 -0.9168 339.8960;
0.0002 0.0004 -0.0002 1.0000];
Nilai error proyeksi yang diperoleh menggunakan matriks kalibrasi diatas :
untuk stereo1.jpg:
mean squared error is 5.415134e-002
error in satisfying the camera calibration matrix is 1.078512e-008
untuk stereo2:
mean squared error is 4.629411e-002
error in satisfying the camera calibration matrix is 4.484307e-009
