extrinsics

Compute location of calibrated camera

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Syntax

[rotationMatrix,translationVector] = extrinsics(imagePoints,worldPoints,cameraParams)

Description

example

[rotationMatrix,translationVector] = extrinsics(imagePoints,worldPoints,cameraParams) returns the 3-D rotation matrix and the 3-D translation vector to allow you to transform points from the world coordinate to the camera coordinate system.

Examples

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Open Live Script

Create a set of calibration images.

  images = imageDatastore(fullfile(toolboxdir('vision'),'visiondata', ...
      'calibration', 'slr'));

Detect the checkerboard corners in the images.

[imagePoints,boardSize] = detectCheckerboardPoints(images.Files);

Generate the world coordinates of the checkerboard corners in the pattern-centric coordinate system, with the upper-left corner at (0,0). The square size is in millimeters.

squareSize = 29;
worldPoints = generateCheckerboardPoints(boardSize, squareSize);

Calibrate the camera.

I = readimage(images,1); 
imageSize = [size(I,1), size(I,2)];
cameraParams = estimateCameraParameters(imagePoints,worldPoints, ...
                              'ImageSize',imageSize);

Load image at new location.

imOrig = imread(fullfile(matlabroot,'toolbox','vision','visiondata', ...
    'calibration','slr','image9.jpg'));
figure 
imshow(imOrig);
title('Input Image');

Undistort image.

[im,newOrigin] = undistortImage(imOrig,cameraParams,'OutputView','full');

Find reference object in new image.

[imagePoints,boardSize] = detectCheckerboardPoints(im);

Compensate for image coordinate system shift.

imagePoints = [imagePoints(:,1) + newOrigin(1), ...
             imagePoints(:,2) + newOrigin(2)];

Compute new extrinsics.

[rotationMatrix, translationVector] = extrinsics(...
imagePoints,worldPoints,cameraParams);

Compute camera pose.

[orientation, location] = extrinsicsToCameraPose(rotationMatrix, ...
  translationVector);
figure
plotCamera('Location',location,'Orientation',orientation,'Size',20);
hold on
pcshow([worldPoints,zeros(size(worldPoints,1),1)], ...
  'VerticalAxisDir','down','MarkerSize',40);

Input Arguments

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Image coordinates of points, specified as an M-by-2 array. The array contains M number of [x, y] coordinates. The imagePoints and worldPoints inputs must both be double or both be single.

Data Types: single | double

World coordinates corresponding to image coordinates, specified as an M-by-2 matrix. The imagePoints and worldPoints inputs must both be double or both be single. The function assumes that the points are coplanar with z= 0 and the number of points, M, must be at least 4.

Data Types: single | double

Object for storing camera parameters, specified as a cameraParameters, cameraIntrinsics, or fisheyeIntrinsics object. These objects are returned by the estimateCameraParameters function, the estimateFisheyeParameters function, or the Camera Calibrator app. The object contains the intrinsic, extrinsic, and lens distortion parameters of a camera.

Output Arguments

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3-D rotation, returned as a 3-by-3 matrix. The rotation matrix together with the translation vector allows you to transform points from the world coordinate to the camera coordinate system.

If you set the imagePoints and worldPoints inputs to class double, then the function returns the rotationMatrix and translationVector as double. Otherwise, they are single.

3-D translation, returned as a 1-by-3 vector.

If you set the imagePoints and worldPoints inputs to class double, then the function returns the rotationMatrix and translationVector as double. Otherwise, they are single.

Algorithms

The extrinsics function uses two different algorithms to compute the extrinsics depending on whether worldPoints are specified as an M-by-2 matrix. Use an M-by-2 matrix for coplanar points where z= 0.

The extrinsics function computes the rotation matrix and translation vector for a single image in closed form. During calibration, the extrinsics are estimated numerically to minimize the reprojection errors for all calibration images. Therefore, using the extrinsics function on one of the calibration images returns rotation matrix and translation vector slightly different from the ones obtained during calibration.

Extended Capabilities

See Also

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Topics

Introduced in R2014a

Computer Vision Toolbox Documentation

Support