mirror of
https://github.com/wassname/scikit-image.git
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emmanuelle
844858f01b
Modified comments in some gallery examples for compatibility with sphinx-gallery parsing. Also modified some links in the narrative doc since image file names have changed.
125 lines
3.5 KiB
Python
125 lines
3.5 KiB
Python
"""
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===============================
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Using geometric transformations
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===============================
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In this example, we will see how to use geometric transformations in the context
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of image processing.
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"""
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from __future__ import print_function
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import math
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import numpy as np
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import matplotlib.pyplot as plt
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from skimage import data
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from skimage import transform as tf
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margins = dict(hspace=0.01, wspace=0.01, top=1, bottom=0, left=0, right=1)
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######################################################################
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# Basics
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# ======
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#
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# Several different geometric transformation types are supported: similarity,
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# affine, projective and polynomial.
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#
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# Geometric transformations can either be created using the explicit
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# parameters (e.g. scale, shear, rotation and translation) or the
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# transformation matrix:
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#
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# First we create a transformation using explicit parameters:
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tform = tf.SimilarityTransform(scale=1, rotation=math.pi / 2,
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translation=(0, 1))
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print(tform.params)
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######################################################################
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# Alternatively you can define a transformation by the transformation matrix
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# itself:
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matrix = tform.params.copy()
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matrix[1, 2] = 2
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tform2 = tf.SimilarityTransform(matrix)
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######################################################################
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# These transformation objects can then be used to apply forward and inverse
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# coordinate transformations between the source and destination coordinate
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# systems:
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coord = [1, 0]
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print(tform2(coord))
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print(tform2.inverse(tform(coord)))
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######################################################################
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# Image warping
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# =============
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#
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# Geometric transformations can also be used to warp images:
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text = data.text()
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tform = tf.SimilarityTransform(scale=1, rotation=math.pi / 4,
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translation=(text.shape[0] / 2, -100))
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rotated = tf.warp(text, tform)
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back_rotated = tf.warp(rotated, tform.inverse)
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fig, (ax1, ax2, ax3) = plt.subplots(ncols=3, figsize=(8, 3))
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fig.subplots_adjust(**margins)
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plt.gray()
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ax1.imshow(text)
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ax1.axis('off')
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ax2.imshow(rotated)
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ax2.axis('off')
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ax3.imshow(back_rotated)
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ax3.axis('off')
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######################################################################
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# Parameter estimation
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# ====================
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#
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# In addition to the basic functionality mentioned above you can also
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# estimate the parameters of a geometric transformation using the least-
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# squares method.
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#
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# This can amongst other things be used for image registration or
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# rectification, where you have a set of control points or
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# homologous/corresponding points in two images.
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#
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# Let's assume we want to recognize letters on a photograph which was not
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# taken from the front but at a certain angle. In the simplest case of a
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# plane paper surface the letters are projectively distorted. Simple matching
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# algorithms would not be able to match such symbols. One solution to this
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# problem would be to warp the image so that the distortion is removed and
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# then apply a matching algorithm:
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text = data.text()
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src = np.array((
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(0, 0),
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(0, 50),
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(300, 50),
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(300, 0)
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))
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dst = np.array((
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(155, 15),
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(65, 40),
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(260, 130),
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(360, 95)
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))
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tform3 = tf.ProjectiveTransform()
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tform3.estimate(src, dst)
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warped = tf.warp(text, tform3, output_shape=(50, 300))
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fig, (ax1, ax2) = plt.subplots(nrows=2, figsize=(8, 3))
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fig.subplots_adjust(**margins)
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plt.gray()
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ax1.imshow(text)
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ax1.plot(dst[:, 0], dst[:, 1], '.r')
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ax1.axis('off')
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ax2.imshow(warped)
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ax2.axis('off')
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