Approximate a rigid affine transformation from point correspondences.

vector_to_rigid approximates a rigid affine transformation, i.e., a transformation consisting of a rotation and a translation, from at least two point correspondences and returns it in form of the homogeneous transformation matrix HomMat2D. The matrix consists of 2 components: a rotation matrix R and a translation vector t (also see hom_mat2d_rotate and hom_mat2d_translate):

                              / 1 0 tx \   / R00 R01 0 \
  HomMat2D  =  |  R   t |  =  | 0 1 ty | * | R10 R11 0 |  =  H(t) * H(R)
               | 0 0  1 |     \ 0 0 1  /   \  0   0  1 /
                         

The point correspondences are passed in the tuples (Rows1, Columns1) and (Rows2,Columns2), where corresponding points must be at the same index positions in the tuples. The transformation is always overdetermined. Therefore, the returned transformation is the transformation that minimizes the distances between the original points (Rows1,Columns1) and the transformed points (Rows2,Columns2), as described in the following equation (points in form of homogeneous vectors):

             || /   Rows2[i]  \                /   Rows1[i]  \ ||^2
 sum of all  || | Columns2[i] |  -  HomMat2D * | Columns1[i] | ||  =  minimum
             || \      1      /                \      1      / ||

HomMat2D can be used directly with operators that transform data using affine transformations, e.g., affine_trans_image.

vector_to_rigid is reentrant and processed without parallelization.

affine_trans_image, affine_trans_region, affine_trans_contour_xld, affine_trans_polygon_xld, affine_trans_point_2d

vector_to_hom_mat2d, vector_to_similarity

dvf_to_hom_mat2d

Basic operators