Calculates an essential matrix from the corresponding points in two images

E = cv.findEssentialMat(points1, points2)
[E, mask] = cv.findEssentialMat(...)
[...] = cv.findEssentialMat(..., 'OptionName', optionValue, ...)

Input

• points1 Cell array of N (N>=5) 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

• E Essential matrix, 3x3.
• mask Output vector of N elements, every element of which is set to 0 for outliers and to 1 for the other points (inliers). The array is computed only in the RANSAC and LMedS robust methods.

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).
• Method Method for computing a essential matrix. One of:
  • Ransac for the RANSAC algorithm. (default)
  • LMedS for the LMedS algorithm.
• Confidence Parameter used for the RANSAC or LMedS methods only. It specifies a desirable level of confidence (probability) that the estimated matrix is correct. In the range 0..1 exclusive. default 0.999
• Threshold Parameter used for RANSAC. It is the maximum distance from a point to an epipolar line in pixels, beyond which the point is considered an outlier and is not used for computing the final essential matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution, and the image noise. default 1.0

This function estimates essential matrix based on the five-point algorithm solver in [Nister03]. [SteweniusCFS] is also a related. The epipolar geometry is described by the following equation:

[p2;1]' * inv(K)' * E * inv(K) * [p1;1] = 0

where E is an essential matrix, p1 and p2 are corresponding points in the first and the second images, respectively. The result of this function may be passed further to cv.decomposeEssentialMat or cv.recoverPose to recover the relative pose between cameras.

K is the camera matrix with focal length fx and fy and principal point [cx,cy]:

K = [fx  0 cx;
     0  fy cy;
     0   0  1]

Example

Estimation of essential matrix using the RANSAC algorithm:

% initialize the points here
points1 = {[1,1],[3,1],[5,1],...}
points2 = {[2,3],[4,3],[6,3],...}
% estimate essential matrix
[E, mask] = cv.findEssentialMat(points1, points2, 'Method','Ransac');

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.

[SteweniusCFS]:

Henrik Stewenius. "Calibrated fivepoint solver".