# triangulate

3-D locations of undistorted matching points in stereo images

## Description

example

worldPoints = triangulate(matchedPoints1,matchedPoints2,stereoParams) returns the 3-D locations of matching pairs of undistorted image points from two stereo images.

worldPoints = triangulate(matchedPoints1,matchedPoints2,camProjection1,camProjection2) returns the 3-D locations of the matching pairs in a world coordinate system. These locations are defined by camera projection matrices.

[worldPoints,reprojectionErrors] = triangulate(___) additionally returns reprojection errors for the world points using any of the input arguments from previous syntaxes.

[worldPoints,reprojectionErrors,validIndex] = triangulate(___) additionally returns the indices of valid and invalid world points. Valid points are located in front of the cameras.

## Examples

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Read in the stereo pair of images.

Undistort the images.

I1 = undistortImage(I1,stereoParams.CameraParameters1);
I2 = undistortImage(I2,stereoParams.CameraParameters2);

Detect a face in both images.

face1 = faceDetector(I1);
face2 = faceDetector(I2);

Find the center of the face.

center1 = face1(1:2) + face1(3:4)/2;
center2 = face2(1:2) + face2(3:4)/2;

Compute the distance from camera 1 to the face.

point3d = triangulate(center1, center2, stereoParams);
distanceInMeters = norm(point3d)/1000;

Display the detected face and distance.

distanceAsString = sprintf('%0.2f meters', distanceInMeters);
I1 = insertObjectAnnotation(I1,'rectangle',face1,distanceAsString,'FontSize',18);
I2 = insertObjectAnnotation(I2,'rectangle',face2, distanceAsString,'FontSize',18);
I1 = insertShape(I1,'filled-rectangle',face1);
I2 = insertShape(I2,'filled-rectangle',face2);

imshowpair(I1, I2, 'montage');

## Input Arguments

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Coordinates of corresponding points in image one, specified as an M-by-2 matrix of M number of [x y] coordinates, or as one of the point feature objects described in Point Feature Types. The matchedPoints1 input must contain points which do not lie on a single planar surface, (e.g., a wall, table, or book) and are putatively matched by using a function such as matchFeatures.

Coordinates of corresponding points in image one, specified as an M-by-2 matrix of M number of [x y] coordinates, or as one of the point feature objects described in Point Feature Types. The matchedPoints1 input must contain points which do not lie on a single planar surface, (e.g., a wall, table, or book) and are putatively matched by using a function such as matchFeatures.

Camera parameters for stereo system, specified as a stereoParameters object. The object contains the intrinsic, extrinsic, and lens distortion parameters of the stereo camera system. You can use the estimateCameraParameters function to estimate camera parameters and return a stereoParameters object.

When you pass a stereoParameters object to the function, the origin of the world coordinate system is located at the optical center of camera 1. The x-axis points to the right, the y-axis points down, and the z-axis points away from the camera.

Projection matrix for camera 1, specified as a 3-by-4 matrix. The matrix maps a 3-D point in homogeneous coordinates onto the corresponding point in the image from the camera. This input describes the location and orientation of camera 1 in the world coordinate system. camProjection1 must be a real and nonsparse numeric matrix. You can obtain the camera matrix using the cameraProjection function.

Camera projection matrices, passed to the function, define the world coordinate system.

Projection matrix for camera 2, specified as a 3-by-4 matrix. The matrix maps a 3-D point in homogeneous coordinates onto the corresponding point in the image from the camera. This input describes the location and orientation of camera 2 in the world coordinate system. camProjection2 must be a real and nonsparse numeric matrix. You can obtain the camera matrix using the cameraProjection function.

Camera projection matrices, passed to the function, define the world coordinate system.

## Output Arguments

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3-D locations of matching pairs of undistorted image points, returned as an M-by-3 matrix. The matrix contains M number of [x y z] locations of matching pairs of undistorted image points from two stereo images.

When you specify the camera geometry using stereoParams, the world point coordinates are relative to the optical center of camera 1.

When you specify the camera geometry using camProjection1 and camProjection2, the world point coordinates are defined by the camera matrices.

The function returns worldPoints as data type double when matchedPoints1 and matchedPoints2 are of data type double. Otherwise, the function returns worldPoints as data type single.

Data Types: single | double

Reprojection errors, returned as an M-by-1 vector. The function projects each world point back into both images. Then, in each image, the function calculates the reprojection error as the distance between the detected and the reprojected point. The reprojectionErrors vector contains the average reprojection error for each world point.

Validity of world points, returned as an M-by-1 logical vector. Valid points, denoted as a logical 1 (true), are located in front of the cameras. Invalid points, denoted as a logical 0 (false), are located behind the cameras.

The validity of a world point with respect to the position of a camera is determined by projecting the world point onto the image using the camera matrix and homogeneous coordinates. The world point is valid if the resulting scale factor is positive.

## Tips

The triangulate function does not account for lens distortion. You can undistort the images using the undistortImage function before detecting the points. Alternatively, you can undistort the points themselves using the undistortPoints function.

## References

[1] Hartley, Richard, and Andrew Zisserman. Multiple View Geometry in Computer Vision. 2nd ed. Cambridge, UK ; New York: Cambridge University Press, 2003.

## Version History

Introduced in R2014b

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