Finds a perspective transformation between two planes

H = cv.findHomography(srcPoints, dstPoints)
[H, mask] = cv.findHomography(...)
[...] = cv.findHomography(..., 'OptionName', optionValue, ...)

Input

• srcPoints Coordinates of the points in the original plane, a numeric array of size Nx2/1xNx2/Nx1x2 or cell array of 2-elements vectors {[x,y], ...} (single floating-point precision).
• dstPoints Coordinates of the points in the target plane, of same size and type as srcPoints.

Output

• H 3x3 Homography matrix.
• mask Nx1 mask array of same length as input points, indicates inliers (which points were actually used in the best computation of H).

Options

• Method Method used to compute a homography matrix. The following methods are possible:
  • 0 a regular method using all the points, i.e. the least squares method (default)
  • Ransac RANSAC-based robust method.
  • LMedS Least-Median of squares robust method.
  • Rho PROSAC-based robust method, introduced in [Bazargani15]. (weighted RANSAC modification, faster in the case of many outliers).
• RansacReprojThreshold Maximum allowed reprojection error to treat a point pair as an inlier (used in the RANSAC and RHO methods only). That is, if || dstPoints_i - convertPointsToHomogeneous(H*srcPoints_i) ||_2 > RansacReprojThreshold then the point i is considered as an outlier. If srcPoints and dstPoints are measured in pixels, it usually makes sense to set this parameter somewhere in the range of 1 to 10. default 3.0.
• MaxIters The maximum number of RANSAC iterations. default 2000
• Confidence Confidence level, between 0 and 1. default 0.995

The function finds and returns the perspective transformation H between the source and the destination planes:

s_i * [x_i'; y_i'; 1] ~ H * [x_i; y_i; 1]

so that the back-projection error:

sum_{i} (x_i' - (h11*x_i + h12*y_i + h13)/(h31*x_i + h32*y_i + h33))^2 +
        (y_i' - (h21*x_i + h22*y_i + h23)/(h31*x_i + h32*y_i + h33))^2

is minimized. If the parameter method is set to the default value 0, the function uses all the point pairs to compute an initial homography estimate with a simple least-squares scheme.

However, if not all of the point pairs (srcPoints_i, dstPoints_i) fit the rigid perspective transformation (that is, there are some outliers), this initial estimate will be poor. In this case, you can use one of the three robust methods. The methods RANSAC, LMedS and RHO try many different random subsets of the corresponding point pairs (of four pairs each, collinear pairs are discarded), estimate the homography matrix using this subset and a simple least-squares algorithm, and then compute the quality/goodness of the computed homography (which is the number of inliers for RANSAC or the least median re-projection error for LMedS). The best subset is then used to produce the initial estimate of the homography matrix and the mask of inliers/outliers.

Regardless of the method, robust or not, the computed homography matrix is refined further (using inliers only in case of a robust method) with the Levenberg-Marquardt method to reduce the re-projection error even more.

The methods RANSAC and RHO handle practically any ratio of outliers but need a threshold to distinguish inliers from outliers. The method LMedS does not need any threshold but it works correctly only when there are more than 50% of inliers. Finally, if there are no outliers and the noise is rather small, use the default method (Method=0).

The function is used to find initial intrinsic and extrinsic matrices. Homography matrix is determined up to a scale. Thus, it is normalized so that h33 = 1. Note that whenever an H matrix cannot be estimated, an empty one will be returned.

References

[Fischler81]:

Fischler, M. A., and R. C. Bolles. "Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography", Communications of the Association for Computing Machinery 24 (1981): 381-395.

[Rousseeuw84]:

Rousseeuw, P. J. "Least median of squares regression", Journal of the American Statistical Association, 79 (1984): 871-880.

[Inui03]:

Inui, K., S. Kaneko, and S. Igarashi. "Robust Line Fitting using LMedS Clustering", Systems and Computers in Japan 34 (2003): 92-100.

[Bazargani15]:

Hamid Bazargani, Olexa Bilaniuk, and Robert Laganiere. "A fast and robust homography scheme for real-time planar target detection". Journal of Real-Time Image Processing (2015): 1-20.