.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/transform/plot_geometric.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code or to run this example in your browser via Binder. .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_transform_plot_geometric.py: =============================== Using geometric transformations =============================== In this example, we will see how to use geometric transformations in the context of image processing. .. GENERATED FROM PYTHON SOURCE LINES 9-17 .. code-block:: Python import math import numpy as np import matplotlib.pyplot as plt from skimage import data from skimage import transform .. GENERATED FROM PYTHON SOURCE LINES 18-30 Basics ====== Several different geometric transformation types are supported: similarity, affine, projective and polynomial. For a tutorial on the available types of transformations, see :ref:`sphx_glr_auto_examples_transform_plot_transform_types.py`. Geometric transformations can either be created using the explicit parameters (e.g. scale, shear, rotation and translation) or the transformation matrix. First we create a transformation using explicit parameters: .. GENERATED FROM PYTHON SOURCE LINES 30-34 .. code-block:: Python tform = transform.SimilarityTransform(scale=1, rotation=math.pi / 2, translation=(0, 1)) print(tform.params) .. rst-class:: sphx-glr-script-out .. code-block:: none [[ 6.123234e-17 -1.000000e+00 0.000000e+00] [ 1.000000e+00 6.123234e-17 1.000000e+00] [ 0.000000e+00 0.000000e+00 1.000000e+00]] .. GENERATED FROM PYTHON SOURCE LINES 35-37 Alternatively you can define a transformation by the transformation matrix itself: .. GENERATED FROM PYTHON SOURCE LINES 37-42 .. code-block:: Python matrix = tform.params.copy() matrix[1, 2] = 2 tform2 = transform.SimilarityTransform(matrix) .. GENERATED FROM PYTHON SOURCE LINES 43-46 These transformation objects can then be used to apply forward and inverse coordinate transformations between the source and destination coordinate systems: .. GENERATED FROM PYTHON SOURCE LINES 46-51 .. code-block:: Python coord = [1, 0] print(tform2(coord)) print(tform2.inverse(tform(coord))) .. rst-class:: sphx-glr-script-out .. code-block:: none [[6.123234e-17 3.000000e+00]] [[ 0.000000e+00 -6.123234e-17]] .. GENERATED FROM PYTHON SOURCE LINES 52-56 Image warping ============= Geometric transformations can also be used to warp images: .. GENERATED FROM PYTHON SOURCE LINES 56-77 .. code-block:: Python text = data.text() tform = transform.SimilarityTransform( scale=1, rotation=math.pi / 4, translation=(text.shape[0] / 2, -100) ) rotated = transform.warp(text, tform) back_rotated = transform.warp(rotated, tform.inverse) fig, ax = plt.subplots(nrows=3) ax[0].imshow(text, cmap=plt.cm.gray) ax[1].imshow(rotated, cmap=plt.cm.gray) ax[2].imshow(back_rotated, cmap=plt.cm.gray) for a in ax: a.axis('off') plt.tight_layout() .. image-sg:: /auto_examples/transform/images/sphx_glr_plot_geometric_001.png :alt: plot geometric :srcset: /auto_examples/transform/images/sphx_glr_plot_geometric_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 78-95 Parameter estimation ==================== In addition to the basic functionality mentioned above you can also generate a transform by estimating the parameters of a geometric transformation using the least squares method. This can amongst other things be used for image registration or rectification, where you have a set of control points or homologous/corresponding points in two images. Let's assume we want to recognize letters on a photograph which was not taken from the front but at a certain angle. In the simplest case of a plane paper surface the letters are projectively distorted. Simple matching algorithms would not be able to match such symbols. One solution to this problem would be to warp the image so that the distortion is removed and then apply a matching algorithm: .. GENERATED FROM PYTHON SOURCE LINES 95-103 .. code-block:: Python text = 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 = transform.ProjectiveTransform.from_estimate(src, dst) .. GENERATED FROM PYTHON SOURCE LINES 104-119 .. note:: For many transform types, including the ``ProjectiveTransform``, it is possible for the estimation to fail. If this is the case, ``from_estimate`` returns a special object of type ``FailedEstimation``. This object describes the reason for the failure and can be tested for. The following is a typical pattern to handle failed estimations explicitly: .. code-block:: python if not tform3: # If result is *falsey*, we have a failed estimation. raise RuntimeError(f'Failed estimation: {tform3}') See :ref:`failed-estimation` below for more details. .. GENERATED FROM PYTHON SOURCE LINES 119-134 .. code-block:: Python warped = transform.warp(text, tform3, output_shape=(50, 300)) fig, ax = plt.subplots(nrows=2, figsize=(8, 3)) ax[0].imshow(text, cmap=plt.cm.gray) ax[0].plot(dst[:, 0], dst[:, 1], '.r') ax[1].imshow(warped, cmap=plt.cm.gray) for a in ax: a.axis('off') plt.tight_layout() plt.show() .. image-sg:: /auto_examples/transform/images/sphx_glr_plot_geometric_002.png :alt: plot geometric :srcset: /auto_examples/transform/images/sphx_glr_plot_geometric_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 135-145 The above estimation relies on accurate knowledge of the location of points and an accurate selection of their correspondence. If point locations have an uncertainty associated with them, then weighting can be provided so that the resulting transform prioritises an accurate fit to those points with the highest weighting. An alternative approach called the `RANSAC algorithm `_ is useful when the correspondence points are not perfectly accurate. See the :ref:`sphx_glr_auto_examples_transform_plot_matching.py` tutorial for an in-depth description of how to use this approach in scikit-image. .. GENERATED FROM PYTHON SOURCE LINES 147-159 .. _failed-estimation: Failed estimation ==================== There are situations where transform classes can fail to estimate a valid transformation, and we recommend that you always check for this possible case. If estimation succeeds, the result you get back will be a valid estimated transform. You can check if you have a valid transform by truth testing. E.g., the estimation from the previous section ``tform3`` is valid and *truthy*: .. GENERATED FROM PYTHON SOURCE LINES 159-162 .. code-block:: Python bool(tform3) .. rst-class:: sphx-glr-script-out .. code-block:: none True .. GENERATED FROM PYTHON SOURCE LINES 163-166 However, if estimation failed, the ``from_estimate`` method returns a special object of type ``FailedEstimation``. Here is an example of a failed estimation, where all the input points are the same: .. GENERATED FROM PYTHON SOURCE LINES 166-172 .. code-block:: Python # Repeat last point 4 times, for four identical points. bad_src = np.tile(src[-1, :], (4, 1)) bad_tform = transform.ProjectiveTransform.from_estimate(bad_src, dst) bad_tform .. rst-class:: sphx-glr-script-out .. code-block:: none /opt/hostedtoolcache/Python/3.12.12/x64/lib/python3.12/site-packages/numpy/_core/numeric.py:475: RuntimeWarning: invalid value encountered in cast FailedEstimation('ProjectiveTransform: Scaling generated NaN values') .. GENERATED FROM PYTHON SOURCE LINES 173-174 This object type is *falsey*---meaning that: .. GENERATED FROM PYTHON SOURCE LINES 174-177 .. code-block:: Python bool(bad_tform) .. rst-class:: sphx-glr-script-out .. code-block:: none False .. GENERATED FROM PYTHON SOURCE LINES 178-179 You can access the raw message string of the failure with .. GENERATED FROM PYTHON SOURCE LINES 179-182 .. code-block:: Python str(bad_tform) .. rst-class:: sphx-glr-script-out .. code-block:: none 'ProjectiveTransform: Scaling generated NaN values' .. GENERATED FROM PYTHON SOURCE LINES 183-195 We recommend that you put in a routine check to confirm the estimation succeeded: .. code-block:: python if not bad_tform: raise RuntimeError(f'Failed estimation: {bad_tform}') Of course, there may be times, where you did not check the *truthiness* of the estimation, and you nevertheless try to use the returned estimate. In this case, you'll get a :class:`~.FailedEstimationAccessError`---a custom subclass of a :class:`AttributeError`. .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.630 seconds) .. _sphx_glr_download_auto_examples_transform_plot_geometric.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: binder-badge .. image:: images/binder_badge_logo.svg :target: https://mybinder.org/v2/gh/scikit-image/scikit-image/v0.26.0?filepath=notebooks/auto_examples/transform/plot_geometric.ipynb :alt: Launch binder :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_geometric.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_geometric.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_geometric.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_