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cameraMatrix

(Not recommended) Camera projection matrix

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cameraMatrix is not recommended. Use the cameraProjection function instead. For more information, see Compatibility Considerations.

Syntax

camMatrix = cameraMatrix(cameraParams,tform)
camMatrix = cameraMatrix(cameraParams,rotationMatrix,translationVector)

Description

camMatrix = cameraMatrix(cameraParams,tform) returns a 4-by-3 camera projection matrix camMatrix, which can be used to project a 3-D world point in homogeneous coordinates into an image. cameraParams can be a cameraParameters object or a cameraIntrinsics object.

example

camMatrix = cameraMatrix(cameraParams,rotationMatrix,translationVector) returns a 4-by-3 camera projection matrix. You can use this matrix to project 3-D world points in homogeneous coordinates into an image.

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 = undistortImage(imOrig,cameraParams);

Find reference object in new image.

[imagePoints,boardSize] = detectCheckerboardPoints(im);

Compute new extrinsics.

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

Calculate camera matrix

P = cameraMatrix(cameraParams,rotationMatrix,translationVector)
P = 4×3
105 ×

    0.0157   -0.0271    0.0000
    0.0404   -0.0046   -0.0000
    0.0199    0.0387    0.0000
    8.9399    9.4399    0.0072

Input Arguments

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Camera parameters, specified as a cameraParameters or cameraIntrinsics object. You can return the cameraParameters object using the estimateCameraParameters function. The cameraParameters object contains the intrinsic, extrinsic, and lens distortion parameters of a camera.

Transformation from world coordinates to camera coordinates, specified as a rigid3d object. You can use the extrinsics function to obtain the rotation and translation to create the tform object.

Rotation of camera, specified as a 3-by-3 matrix. You can obtain this matrix using the extrinsics function. You can also obtain the matrix using the relativeCameraPose function by transposing its orientation output. The rotationMatrix and translationVector inputs must be real, nonsparse, and of the same class.

Translation of camera, specified as a 1-by-3 vector. The translation vector describes the transformation from the world coordinates to the camera coordinates. You can obtain this vector using the extrinsics function. You can also obtain the vector using the location and orientation outputs of the relativeCameraPose function:

  • translationVector = -relativeLocation * relativeOrientation'

The translationVector inputs must be real, nonsparse, and of the same class.

Output Arguments

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Camera projection matrix, returned as a 4-by-3 matrix. The matrix contains the 3-D world points in homogenous coordinates that are projected into the image. When you set rotationMatrix and translationVector to double, the function returns camMatrix as double. Otherwise it returns camMatrix as single.

The function computes camMatrix as follows:

camMatrix = [rotationMatrix; translationVector] × K.
K: the intrinsic matrix

Then, using the camera matrix and homogeneous coordinates, you can project a world point onto the image.

w × [x,y,1] = [X,Y,Z,1] × camMatrix.

(X,Y,Z): world coordinates of a point
(x,y): coordinates of the corresponding image point
w: arbitrary scale factor

Data Types: single | double

Extended Capabilities

Version History

Introduced in R2014b

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R2022b: Not recommended

Starting in R2022b, most Computer Vision Toolbox™ functions create and perform geometric transformations using the premultiply convention. However, the cameraMatrix function uses the postmultiply convention. Although there are no plans to remove cameraMatrix at this time, you can streamline your geometric transformation workflows by switching to the cameraProjection function, which supports the premultiply convention. For more information, see Migrate Geometric Transformations to Premultiply Convention.

To update your code:

  • Change instances of the function name cameraMatrix to cameraProjection.

  • Specify the cameraParams argument as a cameraIntrinsics object. If you have a cameraParameters object, then you can get a cameraIntrinsics object by querying the Intrinsics property. If the Intrinsics property is empty according to the isempty function, then set the ImageSize property of the cameraParameters object to an arbitrary vector before querying the Intrinsics property. For example:

    load worldToImageCorrespondences.mat
if(isempty(cameraParams.Intrinsics))
    cameraParams.ImageSize = [128 128];
end
intrinsics = cameraParams.Intrinsics;

  • Specify the transformation as a rigidtform3d object using the tform argument. cameraProjection does not support the rotationMatrix and translationVector input arguments. Note that you create the rigidtform3d object using the transpose of rotationMatrix or the transpose of the transformation matrix in the T property of tform.

Discouraged UsageRecommended Replacement

This example specifies the transformation as a rotation matrix and a translation vector, then calculates the camera projection matrix using the cameraMatrix function.

camMatrix = cameraMatrix(cameraParams,rotationMatrix,translationVector)

This example specifies the transformation as a rigidtform3d object, then calculates the camera projection matrix using the cameraProjection function. Note that you create the rigidtform3d object using the transpose of the rotation matrix, rotationMatrix.

intrinsics = cameraParams.Intrinsics;
tform = rigidtform3d(rotationMatrix',translationVector);
camMatrix = cameraProjection(intrinsics,tform);

This example specifies the transformation as a rigid3d object.

camMatrix = cameraMatrix(cameraParams,tformOld);

This example starts with an existing rigid3d object tformOld, creates a rigidtform3d object using the transpose of the T property of tformOld, then calculates the camera projection matrix using the cameraProjection function.

intrinsics = cameraParams.Intrinsics;
tform = rigidtform3d(tformOld.T');
camMatrix = cameraProjection(intrinsics,tform);

See Also

Apps

Functions

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