cameraProjection

Camera projection matrix

Since R2022b

Syntax

camProjection = cameraProjection(intrinsics,tform)

Description

camProjection = cameraProjection(intrinsics,tform) returns a 3-by-4 camera projection matrix camProjection. You can use camProjection to project a 3-D world point in homogeneous coordinates into an image according to the transformation tform.

Examples

Calculate Camera Projection Matrix

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 = patternWorldPoints("checkerboard",boardSize,squareSize);

Calibrate the camera.

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

Load an image at a new location.

imOrig = readimage(images,9); 
figure 
imshow(imOrig)
title("Input Image")

Undistort the image.

[im,newIntrinsics] = undistortImage(imOrig,intrinsics,OutputView="full");

Find the reference object in the new image.

[imagePoints,boardSize] = detectCheckerboardPoints(im);

Compensate for the image coordinate system shift.

newOrigin = intrinsics.PrincipalPoint-newIntrinsics.PrincipalPoint;
imagePoints = imagePoints+newOrigin;

Calculate new extrinsics.

camExtrinsics = estimateExtrinsics(imagePoints,worldPoints,intrinsics);

Calculate the camera projection matrix.

P = cameraProjection(intrinsics,camExtrinsics)

P = 3×4
105 ×

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

Input Arguments

intrinsics — Camera intrinsics

cameraIntrinsics object

Camera intrinsics, specified as cameraIntrinsics object. The object stores information about a camera’s intrinsic calibration parameters, including the lens distortion parameters.

tform — Transformation

rigidtform3d object

Transformation from world coordinates to camera coordinates, specified as a rigidtform3d object. You can use the estimateExtrinsics function to create the tform object. The R and Translation properties of the object represent the rotation matrix and translation needed to project 3-D world points in homogeneous coordinates into an image.

Output Arguments

camProjection — Camera projection matrix

3-by-4 matrix

Camera projection matrix, returned as a 3-by-4 matrix. The matrix contains the 3-D world points in homogenous coordinates that are projected into the image.

The function calculates camProjection using the intrinsic matrix K and the R and Translation properties of the tform object as follows:

camProjection = K × [tform.R tform.Translation']

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

w × [x,y,1]' = camProjection× [X,Y,Z,1]'

(X,Y,Z) are the world coordinates of a point

(x,y) are the coordinates of the corresponding image point

w is an arbitrary scale factor

When the R and Translation properties of the transformation tform are of data type double, the function returns camProjection as double. Otherwise the function returns camProjection as single.

Data Types: single | double

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• Use in a MATLAB Function block is not supported.

Version History

Introduced in R2022b

R2022b: Recommended over cameraMatrix

Starting in R2022b, many 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.