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摘抄⾃matlab帮助⽂件
Overview
Camera calibration is the process of estimating parameters of the camera using images of a special calibration pattern. The parameters include camera intrinsics, distortion coefficients, and camera extrinsics. Once you calibrate a camera, there are veral ways to evaluate the accuracy of the estimated parameters:
Plot the relative locations of the camera and the calibration pattern
Calculate the reprojection errors
Calculate the parameter estimation errors
Calibrate the Camera
校园春色合集Estimate camera parameters using a t of images of a checkerboard calibration pattern.
% Create a t of calibration images.
images = imageDatastore(fullfile(toolboxdir('vision'), 'visiondata', ...
'calibration', 'fishEye'));
imageFileNames = images.Files;
% Detect calibration pattern.
[imagePoints, boardSize] = detectCheckerboardPoints(imageFileNames);
% Generate world coordinates of the corners of the squares.
squareSize = 29; % millimeters
worldPoints = generateCheckerboardPoints(boardSize, squareSize);
% Calibrate the camera.
[params, ~, estimationErrors] = estimateCameraParameters(imagePoints, worldPoints);
Extrinsics
You can quickly discover obvious errors in your calibration by plotting relative locations of the camera and the calibration pattern. U the showExtrinsics function to either plot the locations of the calibration pattern in the camera's coordinate system, or the locations of the camera in the pattern's coordinate system. Look for obvious problems, such as the pattern being behind the camera, or the camera being behind the pattern. Also check if a pattern is too far or too clo to the camera.
figure;
showExtrinsics(params, 'CameraCentric');
figure;
showExtrinsics(params, 'PatternCentric');
Reprojection Errors
Reprojection errors provide a qualitative measure of accuracy. A reprojection error is the distance between a pattern keypoint detected in a calibration image, and a corresponding world point projected into the same image.
The showReprojectionErrors function provides a uful visualization of the average reprojection error in each calibration image. If the overall mean reprojection error is too high, consider excluding the images with the highest error and recalibrating.
figure;
showReprojectionErrors(params);
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Estimation Errors
Estimation errors reprent the uncertainty of each estimated parameter. The estimateCameraParameters function optionally returns estimationErrors output, containing the standard error corresponding to each estimated camera parameter. The returned standard error (in the same units as the corresponding parameter) can be ud to calculate confidence intervals. For example +/- corresponds to the 95% confidence interval. In other words, the probability that the actual value of a given parameter is within of its estimate is 95%.
displayErrors(estimationErrors, params);
Standard Errors of Estimated Camera Parameters
----------------------------------------------
Intrinsics
----------
Focal length (pixels): [ 714.1881 +/- 3.3220 710.3793 +/- 4.0580 ]
Principal point (pixels):[ 563.6511 +/- 5.3966 355.7271 +/- 3.3039 ]
苏州特色美食Radial distortion: [ -0.3535 +/- 0.0091 0.1728 +/- 0.0488 ]
Extrinsics
----------
Rotation vectors:
[ -0.6096 +/- 0.0054 -0.1789 +/- 0.0073 -0.3835 +/- 0.0024 ]
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[ -0.7283 +/- 0.0050 -0.0996 +/- 0.0072 0.1964 +/- 0.0027 ]
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[ -0.6722 +/- 0.0051 -0.1444 +/- 0.0074 -0.1329 +/- 0.0026 ]
[ -0.5836 +/- 0.0056 -0.2901 +/- 0.0074 -0.5622 +/- 0.0025 ]
[ -0.3157 +/- 0.0065 -0.1441 +/- 0.0075 -0.1067 +/- 0.0011 ]
[ -0.7581 +/- 0.0052 0.1947 +/- 0.0072 0.4324 +/- 0.0030 ]
[ -0.7515 +/- 0.0051 0.0767 +/- 0.0072 0.2070 +/- 0.0029 ]
[ -0.6223 +/- 0.0053 0.0231 +/- 0.0073 0.3663 +/- 0.0024 ]
[ 0.3443 +/- 0.0063 -0.2226 +/- 0.0073 -0.0437 +/- 0.0014 ]
Translation vectors (mm):
[ -146.0550 +/- 6.0391 -26.8706 +/- 3.7321 797.9021 +/- 3.9002 ]
[ -209.4397 +/- 6.9636 -59.4589 +/- 4.3581 921.8201 +/- 4.6295 ]
[ -129.3864 +/- 7.0906 -44.1054 +/- 4.3754 937.6825 +/- 4.4914 ]
[ -151.0086 +/- 6.6904 -27.3276 +/- 4.1343 884.2782 +/- 4.3926 ]
[ -174.9537 +/- 6.7056 -24.3522 +/- 4.1609 886.4963 +/- 4.6686 ]
[ -134.3140 +/- 7.8887 -103.5007 +/- 4.8928 1042.4549 +/- 4.8185 ]
[ -173.9888 +/- 7.6890 -73.1717 +/- 4.7816 1017.2382 +/- 4.8126 ]
[ -202.9489 +/- 7.4327 -87.9116 +/- 4.6485 983.6961 +/- 4.9072 ]
[ -319.8898 +/- 6.3213 -119.8920 +/- 4.0925 829.4588 +/- 4.9590 ]
Interpreting Principal Point Estimation Error
停止间转法The principal point is the optical center of the camera, the point where the optical axis intercts the image plane. You can easily visualize and interpret the standard error of the estimated principal point. Plot an ellip around the estimated principal point , who radii are equal to 1.96 times the corresponding estimation errors. The ellip reprents the uncertainty region, which contains the actual principal point with 95% probability.
principalPoint = params.PrincipalPoint;
principalPointError = estimationErrors.IntrinsicsErrors.PrincipalPointError;
fig = figure;
ax = axes('Parent', fig);
imshow(imageFileNames{1}, 'InitialMagnification', 60, 'Parent', ax);
hold(ax, 'on');
% Plot the principal point.
plot(principalPoint(1), principalPoint(2), 'g+', 'Parent', ax);
% Plot the ellip reprenting the 95% confidence region.
halfRectSize = 1.96 * principalPointError;
rectangle('Position', [principalPoint-halfRectSize, 2 * halfRectSize], ...
'Curvature', [1,1], 'EdgeColor', 'green', 'Parent', ax);
legend('Estimated principal point');
title('Principal Point Uncertainty');
hold(ax, 'off');
Interpreting Translation Vectors Estimation Errors
You can also visualize the standard errors of the translation vectors. Each translation vector reprents the translation from the pattern's coordinate system into the camera's coordinate system. Equivalently, each translation vector reprents the location of the pattern's origin in the camera's coordinate system. You can plot the estimation errors of the translation vectors as ellipsoids reprenting uncertainty volumes for each pattern's location at 95% confidence level.
% Get translation vectors and corresponding errors.
vectors = params.TranslationVectors;
errors = 1.96 * estimationErrors.ExtrinsicsErrors.TranslationVectorsError;
% Set up the figure.
fig = figure;
ax = axes('Parent', fig, 'CameraViewAngle', 5, 'CameraUpVector', [0, -1, 0], ...
'CameraPosition', [-1500, -1000, -6000]);
hold on
% Plot camera location.
plotCamera('Size', 40, 'AxesVisible', true);
% Plot an ellipsoid showing 95% confidence volume of uncertainty of
% location of each checkerboard origin.
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labelOfft = 10;
for i = 1:params.NumPatterns
ellipsoid(vectors(i,1), vectors(i,2), vectors(i,3), ...
errors(i,1), errors(i,2), errors(i,3), 5)
text(vectors(i,1) + labelOfft, vectors(i,2) + labelOfft, ...
vectors(i,3) + labelOfft, num2str(i), ...
'fontsize', 12, 'Color', 'r');
end
colormap('hot');
hold off
% Set view properties.
xlim([-400, 200]);
zlim([-100, 1100]);
xlabel('X (mm)');
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ylabel('Y (mm)');
zlabel('Z (mm)');
grid on
axis 'equal'
cameratoolbar('Show');
cameratoolbar('SetMode', 'orbit');
cameratoolbar('SetCoordSys', 'Y');
title('Translation Vectors Uncertainty');
How to Improve Calibration Accuracy
Whether or not a particular reprojection or estimation error is acceptable depends on the precision requirements of your particular application. However, if you have determined that your calibration accuracy is unacceptable, there are veral ways to improve it:
Modify calibration ttings. Try using 3 radial distortion coefficients, estimating tangential distortion, or the skew.
Take more calibration images. The pattern in the images must be in different 3D orientations, and it should be positioned such that you have keypoints in all parts of the field of view. In particular, it is very important to have keypoints clo to the edges and the corners of the image in order to get a better estimate of the distortion
coefficients.
Exclude images that have high reprojection errors and re-calibrate.
Summary
This example showed how to interpret camera calibration errors.
