vector_to_hom_mat2d — Approximate an affine transformation from point correspondences.
vector_to_hom_mat2d approximates an affine transformation from at
least three point correspondences and returns it as the homogeneous
transformation matrix HomMat2D (see
hom_mat2d_to_affine_par for the content of the homogeneous
transformation matrix).
The point correspondences are passed in the tuples
(Px,Py) and (Qx,Qy),
where corresponding points must be at the same index positions in the tuples.
If more than three point correspondences are passed, the transformation is
overdetermined. In this case, the returned transformation is the
transformation that minimizes the distances between the input points
(Px,Py) and the transformed points
(Qx,Qy), as described in the following equation
(points as homogeneous vectors):
HomMat2D can be used directly with operators that transform data
using affine transformations, e.g., affine_trans_image.
It should be noted that homogeneous transformation matrices refer to
a general right-handed mathematical coordinate system. If a
homogeneous transformation matrix is used to transform images,
regions, XLD contours, or any other data that has been extracted
from images, the row coordinates of the transformation must be
passed in the x coordinates, while the column coordinates must be
passed in the y coordinates. Consequently, the order of passing row
and column coordinates follows the usual order
(Row,Column). This convention is essential to
obtain a right-handed coordinate system for the transformation of
iconic data, and consequently to ensure in particular that rotations
are performed in the correct mathematical direction.
Furthermore, it should be noted that if a homogeneous transformation matrix is used to transform images, regions, XLD contours, or any other data that has been extracted from images, it is assumed that the origin of the coordinate system of the homogeneous transformation matrix lies in the upper left corner of a pixel. The image processing operators that return point coordinates, however, assume a coordinate system in which the origin lies in the center of a pixel. Therefore, to obtain a consistent homogeneous transformation matrix, 0.5 must be added to the point coordinates before computing the transformation.
Px (input_control) point.x-array → (real)
X coordinates of the original points.
Py (input_control) point.y-array → (real)
Y coordinates of the original points.
Qx (input_control) point.x-array → (real)
X coordinates of the transformed points.
Qy (input_control) point.y-array → (real)
Y coordinates of the transformed points.
HomMat2D (output_control) hom_mat2d → (real)
Output transformation matrix.
affine_trans_image,
affine_trans_image_size,
affine_trans_region,
affine_trans_contour_xld,
affine_trans_polygon_xld,
affine_trans_point_2d
vector_to_aniso,
vector_to_similarity,
vector_to_rigid
vector_field_to_hom_mat2d,
point_line_to_hom_mat2d
Foundation