mirror of
https://github.com/wassname/scikit-image.git
synced 2026-06-28 03:19:12 +08:00
Johannes Schönberger
135 lines
3.2 KiB
Python
135 lines
3.2 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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Several different geometric transformation types are supported: similarity,
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affine, projective and polynomial.
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Geometric transformations can either be created using the explicit parameters
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(e.g. scale, shear, rotation and translation) or the transformation matrix:
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First we create a transformation using explicit parameters:
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"""
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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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"""
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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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"""
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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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Geometric transformations can also be used to warp images:
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"""
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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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.. image:: PLOT2RST.current_figure
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Parameter estimation
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====================
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In addition to the basic functionality mentioned above you can also estimate the
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parameters of a geometric transformation using the least-squares method.
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This can amongst other things be used for image registration or rectification,
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where you have a set of control points or homologous/corresponding points in two
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images.
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Let's assume we want to recognize letters on a photograph which was not taken
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from the front but at a certain angle. In the simplest case of a plane paper
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surface the letters are projectively distorted. Simple matching algorithms would
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not be able to match such symbols. One solution to this problem would be to warp
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the image so that the distortion is removed and then apply a matching algorithm:
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"""
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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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"""
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.. image:: PLOT2RST.current_figure
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"""
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plt.show()
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