Computes an optimal limited affine transformation with 4 degrees of freedom between two 2D point sets

H = cv.estimateAffinePartial2D(from, to)
[H, inliers] = cv.estimateAffinePartial2D(...)
[...] = cv.estimateAffinePartial2D(..., 'OptionName', optionValue, ...)

Input

• from First input 2D point set. Cell array of 2-element vectors {[x,y],...} or Nx2/Nx1x2/1xNx2 numeric array.
• to Second input 2D point set. Same size and type as from.

Output

• H Output 2D affine transformation (4 degrees of freedom) matrix 2x3 or empty matrix if transformation could not be estimated.
• inliers Output vector of same length as number of points, indicating which points are inliers.

Options

• Method Robust method used to compute transformation. RANSAC is the default method. The following methods are possible:
  • Ransac RANSAC-based robust method.
  • LMedS Least-Median of squares robust method
• RansacThreshold Maximum reprojection error in the RANSAC algorithm to consider a point as an inlier. Applies only to RANSAC. default 3.0.
• MaxIters The maximum number of robust method iterations. default 2000
• Confidence Confidence level, between 0 and 1, for the estimated transformation. Anything between 0.95 and 0.99 is usually good enough. Values too close to 1 can slow down the estimation significantly. Values lower than 0.8-0.9 can result in an incorrectly estimated transformation. default 0.99.
• RefineIters Maximum number of iterations of refining algorithm (Levenberg-Marquardt). Passing 0 will disable refining, so the output matrix will be output of robust method. default 10

The function estimates an optimal 2D affine transformation with 4 degrees of freedom limited to combinations of translation, rotation, and uniform scaling. Uses the selected algorithm for robust estimation.

The computed transformation is then refined further (using only inliers) with the Levenberg-Marquardt method to reduce the re-projection error even more.

Estimated transformation matrix is:

[cos(theta)*s, -sin(theta)*s, tx;
 sin(theta)*s,  cos(theta)*s, ty]

Where theta is the rotation angle, s the scaling factor and tx, ty are translations in x, y axes respectively.

Note: The RANSAC method can 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.