Computes an optimal affine transformation between two 2D point sets

M = cv.estimateRigidTransform(src, dst)
M = cv.estimateRigidTransform(src, dst, 'OptionName', optionValue, ...)

Input

• src First input 2D point set stored in a cell array of 2-element vectors {[x,y], ...}, or first image (8-bit numeric array, 1- or 3-channels).
• dst Second input 2D point set of the same size and the same type as src, or second image (8-bit numeric array, 1- or 3-channels).

Output

• M output 2x3 affine transformation [A|b] matrix (see below).

Options

• FullAffine If true, the function finds an optimal affine transformation with no additional resrictions (6 degrees of freedom). Otherwise, the class of transformations to choose from is limited to combinations of translation, rotation, and uniform scaling (5 degrees of freedom).

The function finds an optimal affine transform [A|b] (a 2x3 floating-point matrix) that approximates best the affine transformation between:

• Two point sets
• Two raster images. In this case, the function first finds some features in the src image and finds the corresponding features in dst image. After that, the problem is reduced to the first case.

In case of point sets, the problem is formulated as follows: you need to find a 2x2 matrix A and 2x1 vector b so that:

[A*|b*] = argmin_{[A|b]} \sum_i || dst{i} - A*src{i}' - b ||^2

where src{i} and dst{i} are the i-th points in src and dst, respectively. [A|b] can be either arbitrary (when FullAffine=true) or have a form of:

[ a11, a12, b1;
 -a12, a11, b2 ]

when FullAffine=false.