`skimage.transform._geometric:EuclideanTransform`

source: /skimage/transform/_geometric.py

Signature

def EuclideanTransform(matrix = None, *, rotation = None, translation = None, dimensionality = None)

Summary

Euclidean transformation, also known as a rigid transform.

Extended Summary

Has the following form

X = a0 * x - b0 * y + a1 =
  = x * cos(rotation) - y * sin(rotation) + a1

Y = b0 * x + a0 * y + b1 =
  = x * sin(rotation) + y * cos(rotation) + b1

where the homogeneous transformation matrix is

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

The Euclidean transformation is a rigid transformation with rotation and translation parameters. The similarity transformation extends the Euclidean transformation with a single scaling factor.

In 2D and 3D, the transformation parameters may be provided either via matrix, the homogeneous transformation matrix, above, or via the implicit parameters rotation and/or translation (where a1 is the translation along x, b1 along y, etc.). Beyond 3D, if the transformation is only a translation, you may use the implicit parameter translation; otherwise, you must use matrix.

The implicit parameters are applied in the following order:

Rotation;
Translation.

Parameters

matrix : array_like of shape (K, K), with K=D+1 (D being the dimensionality), optional: Homogeneous transformation matrix.
rotation : float or sequence of float, optional: Rotation angle, clockwise, in radians. If given as a vector, it is interpreted as Euler rotation angles ^[1]. Only 2D (single rotation) and 3D (Euler rotations) values are supported. For higher dimensions, you must provide or estimate the transformation matrix instead, and pass that as matrix above.
translation : (x, y[, z, ...]) sequence of float, length D, optional: Translation parameters for each axis.
dimensionality : int, optional: Fallback number of dimensions for transform when no other parameter is specified. Otherwise ignored, and we infer dimensionality from the input parameters.

Attributes

params : ndarray of shape (K, K), with K=D+1 (D being the dimensionality): Homogeneous transformation matrix.

Examples

import numpy as np
import skimage as ski

✓

Define a transform with an homogeneous transformation matrix:

tform = ski.transform.EuclideanTransform(np.diag([2., 3., 1.]))
tform.params

✓

array([[2., 0., 0.],
       [0., 3., 0.],
       [0., 0., 1.]])

Define a transform with parameters:

tform = ski.transform.EuclideanTransform(
            rotation=0.2, translation=[1, 2])
np.round(tform.params, 2)

✓

array([[ 0.98, -0.2 ,  1.  ],
       [ 0.2 ,  0.98,  2.  ],
       [ 0.  ,  0.  ,  1.  ]])

You can estimate a transformation to map between source and destination points:

src = np.array([[150, 150],
                [250, 100],
                [150, 200]])
dst = np.array([[200, 200],
                [300, 150],
                [150, 400]])
tform = ski.transform.EuclideanTransform.from_estimate(src, dst)
np.allclose(tform.params, [[ 0.99, 0.12,  16.77],
                           [-0.12, 0.99, 122.91],
                           [ 0.  , 0.  ,   1.  ]], atol=0.01)

✓

True

Apply the transformation to some image data.

img = ski.data.astronaut()
warped = ski.transform.warp(img, inverse_map=tform.inverse)

✓

The estimation can fail - for example, if all the input or output points are the same. If this happens, you will get a transform that is not "truthy" - meaning that ``bool(tform)`` is ``False``:

if tform:
    print("Estimation succeeded.")
bad_src = np.ones((3, 2))
bad_tform = ski.transform.EuclideanTransform.from_estimate(
     bad_src, dst)
if not bad_tform:
    print("Estimation failed.")

✓

Estimation failed.

Trying to use this failed estimation transform result will give a suitable error:

bad_tform.params  # doctest: +IGNORE_EXCEPTION_DETAIL

✓

Traceback (most recent call last):
  File "<doctest skimage.transform._geometric:EuclideanTransform[0]>", line 1, in <module>
    bad_tform.params  # doctest: +IGNORE_EXCEPTION_DETAIL
    ^^^^^^^^^^^^^^^^
  File "/opt/hostedtoolcache/Python/3.14.7/x64/lib/python3.14/site-packages/_skimage2/_shared/utils.py", line 546, in __getattr__
    raise self.error_cls(msg)
_skimage2._shared.utils.FailedEstimationAccessError: FailedEstimation has no attribute 'params'. EuclideanTransform: Poor conditioning for estimation

Hint: You can check for a failed estimation by truth testing the returned object. For failed estimations, `bool(estimation_result)` will be `False`. E.g.

    if not estimation_result:
        raise RuntimeError(f'Failed estimation: {estimation_result}')