similaritytransform

SimilarityTransform

class skimage.transform.SimilarityTransform(matrix=None, scale=None, rotation=None, translation=None) [source]

Bases: skimage.transform._geometric.ProjectiveTransform

2D similarity transformation of the form:

..:math:

X = a0 * x - b0 * y + a1 =

= m * x * cos(rotation) - m * y * sin(rotation) + a1

Y = b0 * x + a0 * y + b1 =

= m * x * sin(rotation) + m * y * cos(rotation) + b1

where m is a zoom factor and the homogeneous transformation matrix is:

[[a0  b0  a1]
 [b0  a0  b1]
 [0   0    1]]

Parameters:	matrix : (3, 3) array, optional Homogeneous transformation matrix. scale : float, optional Scale factor. rotation : float, optional Rotation angle in counter-clockwise direction as radians. translation : (tx, ty) as array, list or tuple, optional x, y translation parameters.

Attributes

params

((3, 3) array) Homogeneous transformation matrix.

__init__(matrix=None, scale=None, rotation=None, translation=None) [source]

estimate(src, dst) [source]

Set the transformation matrix with the explicit parameters.

You can determine the over-, well- and under-determined parameters with the total least-squares method.

Number of source and destination coordinates must match.

The transformation is defined as:

X = a0 * x - b0 * y + a1
Y = b0 * x + a0 * y + b1

These equations can be transformed to the following form:

0 = a0 * x - b0 * y + a1 - X
0 = b0 * x + a0 * y + b1 - Y

which exist for each set of corresponding points, so we have a set of N * 2 equations. The coefficients appear linearly so we can write A x = 0, where:

A   = [[x 1 -y 0 -X]
       [y 0  x 1 -Y]
        ...
        ...
      ]
x.T = [a0 a1 b0 b1 c3]

In case of total least-squares the solution of this homogeneous system of equations is the right singular vector of A which corresponds to the smallest singular value normed by the coefficient c3.

Parameters:	src : (N, 2) array Source coordinates. dst : (N, 2) array Destination coordinates.
Returns:	success : bool True, if model estimation succeeds.

rotation

scale

translation