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Geometrical transformations of images

doc/source/user_guide/geometrical_transform.rst

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============================================ Geometrical transformations of images

Cropping, resizing and rescaling images

.. currentmodule:: skimage.transform

Images being NumPy arrays (as described in the :ref:numpy_images section), cropping an image can be done with simple slicing operations. Below we crop a 100x100 square corresponding to the top-left corner of the astronaut image. Note that this operation is done for all color channels (the color dimension is the last, third dimension)::

import skimage as ski img = ski.data.astronaut() top_left = img[:100, :100]

In order to change the shape of the image, :mod:skimage.color provides several functions described in :ref:sphx_glr_auto_examples_transform_plot_rescale.py .

.. literalinclude:: ../../examples/transform/plot_rescale.py :language: python :start-after: import matplotlib.pyplot as plt :end-before: fig, axes

.. image:: ../auto_examples/transform/images/sphx_glr_plot_rescale_001.png :target: ../auto_examples/transform/plot_rescale.html :align: center :width: 80%

Projective transforms (homographies)

Homographies <https://en.wikipedia.org/wiki/Homography>_ are transformations of a Euclidean space that preserve the alignment of points. Specific cases of homographies correspond to the conservation of more properties, such as parallelism (affine transformation), shape (similar transformation) or distances (Euclidean transformation). The different types of homographies available in scikit-image are presented in :ref:sphx_glr_auto_examples_transform_plot_transform_types.py.

Projective transformations can either be created using the explicit parameters (e.g. scale, shear, rotation and translation)::

import numpy as np import skimage as ski

tform = ski.transform.EuclideanTransform( rotation=np.pi / 12., translation = (100, -20) )

or the full transformation matrix::

matrix = np.array([[np.cos(np.pi/12), -np.sin(np.pi/12), 100], [np.sin(np.pi/12), np.cos(np.pi/12), -20], [0, 0, 1]]) tform = ski.transform.EuclideanTransform(matrix)

The transformation matrix of a transform is available as its tform.params attribute. Transformations can be composed by multiplying matrices with the @ matrix multiplication operator.

Transformation matrices use Homogeneous coordinates <https://en.wikipedia.org/wiki/Homogeneous_coordinates>_, which are the extension of Cartesian coordinates used in Euclidean geometry to the more general projective geometry. In particular, points at infinity can be represented with finite coordinates.

Transformations can be applied to images using :func:skimage.transform.warp::

img = ski.util.img_as_float(ski.data.chelsea()) tf_img = ski.transform.warp(img, tform.inverse)

.. image:: ../auto_examples/transform/images/sphx_glr_plot_transform_types_001.png :target: ../auto_examples/transform/plot_transform_types.html :align: center :width: 80%

The different transformations in :mod:skimage.transform have a from_estimate class method in order to generate a matching tranform by estimating the transform parameters from two sets of points (the source and the destination), as explained in the :ref:sphx_glr_auto_examples_transform_plot_geometric.py tutorial::

text = ski.data.text()

src = np.array([[0, 0], [0, 50], [300, 50], [300, 0]]) dst = np.array([[155, 15], [65, 40], [260, 130], [360, 95]])

tform3 = ski.transform.ProjectiveTransform.from_estimate(src, dst) warped = ski.transform.warp(text, tform3, output_shape=(50, 300))

.. image:: ../auto_examples/transform/images/sphx_glr_plot_geometric_002.png :target: ../auto_examples/transform/plot_geometric.html :align: center :width: 80%

The from_estimate class method uses least squares optimization to minimize the distance between source and optimization. Source and destination points can be determined manually, or using the different methods for feature detection available in :mod:skimage.feature, such as

  • :ref:sphx_glr_auto_examples_features_detection_plot_corner.py,
  • :ref:sphx_glr_auto_examples_features_detection_plot_orb.py,
  • :ref:sphx_glr_auto_examples_features_detection_plot_brief.py,
  • etc.

and matching points using :func:skimage.feature.match_descriptors before estimating transformation parameters. However, spurious matches are often made, and it is advisable to use the RANSAC algorithm (instead of simple least-squares optimization) to improve the robustness to outliers, as explained in :ref:sphx_glr_auto_examples_transform_plot_matching.py.

.. image:: ../auto_examples/transform/images/sphx_glr_plot_matching_001.png :target: ../auto_examples/transform/plot_matching.html :align: center :width: 80%

Examples showing applications of transformation estimation are

  • stereo matching :ref:sphx_glr_auto_examples_transform_plot_fundamental_matrix.py and
  • image rectification :ref:sphx_glr_auto_examples_transform_plot_geometric.py

The from_estimate class method is point-based, that is, it uses only a set of points from the source and destination images. For estimating translations (shifts), it is also possible to use a full-field method using all pixels, based on Fourier-space cross-correlation. This method is implemented by :func:skimage.registration.phase_cross_correlation and explained in the :ref:sphx_glr_auto_examples_registration_plot_register_translation.py tutorial.

.. image:: ../auto_examples/registration/images/sphx_glr_plot_register_translation_001.png :target: ../auto_examples/registration/plot_register_translation.html :align: center :width: 80%

Bear in mind that the estimation can fail, in which case from_estimate returns a special FailedEstimation object instead of a valid transform. See the :ref:sphx_glr_auto_examples_transform_plot_geometric.py tutorial for more detail on testing for such estimation failures.

The :ref:sphx_glr_auto_examples_registration_plot_register_rotation.py tutorial explains a variant of this full-field method for estimating a rotation, by using first a log-polar transformation.