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摘抄自matlab帮助文件

Evaluating the Accuracy of Single Camera Calibration- MATLAB & Simulink

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 several 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

Estimate camera parameters using a set of images of a checkerboard calibration pattern.

% Create a set 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. Use 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 close 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. TheshowReprojectionErrors function provides a useful 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);

Estimation Errors

Estimation errors represent 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 used 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  ]
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  ][   -0.7283 +/- 0.0050       -0.0996 +/- 0.0072        0.1964 +/- 0.0027  ][   -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

The principal point is the optical center of the camera, the point where the optical axis intersects the image plane. You can easily visualize and interpret the standard error of the estimated principal point. Plot an ellipse around the estimated principal point , whose radii are equal to 1.96 times the corresponding estimation errors. The ellipse represents 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 ellipse representing 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 represents the translation from the pattern's coordinate system into the camera's coordinate system. Equivalently, each translation vector represents 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 representing 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.
labelOffset = 10;
for i = 1:params.NumPatternsellipsoid(vectors(i,1), vectors(i,2), vectors(i,3), ...errors(i,1), errors(i,2), errors(i,3), 5)text(vectors(i,1) + labelOffset, vectors(i,2) + labelOffset, ...vectors(i,3) + labelOffset, num2str(i), ...'fontsize', 12, 'Color', 'r');
end
colormap('hot');
hold off% Set view properties.
xlim([-400, 200]);
zlim([-100, 1100]);xlabel('X (mm)');
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 several ways to improve it:

Modify calibration settings. 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 close to the edges and the corners of the image in order to get a better estimate of the distortion coefficients.