# estimateExtrinsics

Calculate location of calibrated camera

Since R2022b

## Description

example

camExtrinsics = estimateExtrinsics(imagePoints,worldPoints,intrinsics) returns the camera extrinsics, which are 3-D rigid transformation that enables you to transform points from the world coordinate to the camera coordinate system.

## Examples

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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.

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

Load an image at a new location.

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,newIntrinsics);

Calculate the camera pose.

camPose = extr2pose(camExtrinsics);
figure
plotCamera(AbsolutePose=camPose,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

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

## Output Arguments

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Camera extrinsics, returned as a rigidtform3d or object. The "R" and the "Translation" properties of the object represent the orientation and location of the camera.

## Tips

• This function does not account for lens distortion when intrinsics is a cameraIntrinsics object. In this case, you can either undistort the image using the undistortImage function before detecting the points, or you can undistort the detected points using the undistortPoints function.

## Algorithms

The estimateExtrinsics 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 estimateExtrinsics 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 estimateExtrinsics function on one of the calibration images returns rotation matrix and translation vector slightly different from the ones obtained during calibration.

## Version History

Introduced in R2022b

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