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Camera projection matrix


camMatrix = cameraMatrix(cameraParams,rotationMatrix,translationVector)



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.


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Create a set of calibration images.

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

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, ...

Load image at new location.

imOrig = imread(fullfile(matlabroot,'toolbox','vision','visiondata', ...
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(...

Calculate camera matrix

P = cameraMatrix(cameraParams,rotationMatrix,translationVector)
P =

   1.0e+05 *

    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.

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

Introduced in R2014b