Recover relative camera rotation and translation from an estimated essential matrix and the corresponding points in two images, using cheirality check

[R, t, good] = cv.recoverPose(E, points1, points2)
[R, t, good, mask, triangulatedPoints] = cv.recoverPose(...)
[...] = cv.recoverPose(..., 'OptionName', optionValue, ...)

Input

• E The input essential matrix, 3x3.
• points1 Cell array of N 2D points from the first image, or numeric array Nx2/Nx1x2/1xNx2. The point coordinates should be floating-point (single or double precision).
• points2 Cell array or numeric array of the second image points of the same size and format as points1.

Output

• R Recovered relative rotation, 3x3 matrix.
• t Recovered relative translation, 3x1 vector.
• good the number of inliers which pass the cheirality check.
• mask Output mask for inliers in points1 and points2. In the output mask only inliers which pass the cheirality check. Vector of length N, see the Mask input option.
• triangulatedPoints 3D points which were reconstructed by triangulation, see cv.triangulatePoints

Options

• CameraMatrix Camera matrix K = [fx 0 cx; 0 fy cy; 0 0 1]. Note that this function assumes that points1 and points2 are feature points from cameras with the same camera matrix. default eye(3).
• DistanceThreshold threshold distance which is used to filter out far away points (i.e. infinite points). default 50.0
• Mask Input mask of length N for inliers in points1 and points2 (0 for outliers and to 1 for the other points (inliers). If it is not empty, then it marks inliers in points1 and points2 for then given essential matrix E. Only these inliers will be used to recover pose. Not set by default.

This function decomposes an essential matrix using cv.decomposeEssentialMat and then verifies possible pose hypotheses by doing cheirality check. The cheirality check basically means that the triangulated 3D points should have positive depth. Some details can be found in [Nister03].

This function can be used to process output E and mask from cv.findEssentialMat. In this scenario, points1 and points2 are the same input for cv.findEssentialMat.

Example

% Estimation of fundamental matrix using the RANSAC algorithm
point_count = 100;
points1 = cell(1, point_count);
points2 = cell(1, point_count);
% initialize the points here ...
for i=1:point_count
    points1{i} = ...;  % [x,y]
    points2{i} = ...;  % [x,y]
end

% cametra matrix with both focal lengths = 1, and principal point = [0 0]
cameraMatrix = eye(3,3);

[E, mask] = cv.findEssentialMat(points1, points2, ...
    'CameraMatrix',cameraMatrix, 'Method','Ransac');
[R, t, ~, mask] = cv.recoverPose(E, points1, points2, ...
    'CameraMatrix',cameraMatrix, 'Mask',mask);

References

[Nister03]:

David Nister. "An efficient solution to the five-point relative pose problem". Pattern Analysis and Machine Intelligence, IEEE Transactions on, 26(6):756-770, 2004.