mirror of
https://github.com/wassname/scikit-image.git
synced 2026-06-29 10:28:15 +08:00
Johannes Schönberger
135 lines
3.1 KiB
Python
135 lines
3.1 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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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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"""
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#: create using explicit parameters
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tform = tf.SimilarityTransformation()
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scale = 1
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rotation = math.pi/2
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translation = (0, 1)
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tform.from_params(scale, rotation, translation)
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print tform.matrix
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#: create using transformation matrix
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matrix = tform.matrix.copy()
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matrix[1, 2] = 2
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tform2 = tf.SimilarityTransformation(matrix)
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"""
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These transformation objects can be used to forward and reverse transform
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coordinates between the source and destination coordinate systems:
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"""
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coord = [1, 0]
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print tform2.forward(coord)
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print tform2.reverse(tform.forward(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.from_params(1, math.pi/4, (text.shape[0] / 2, -100))
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# uses tform.reverse, alternatively use tf.warp(text, tform.reverse)
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rotated = tf.warp(text, tform)
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back_rotated = tf.warp(rotated, tform.forward)
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plt.figure(figsize=(8, 3))
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plt.subplot(131)
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plt.imshow(text)
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plt.axis('off')
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plt.gray()
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plt.subplot(132)
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plt.imshow(rotated)
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plt.axis('off')
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plt.gray()
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plt.subplot(133)
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plt.imshow(back_rotated)
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plt.axis('off')
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plt.gray()
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plt.subplots_adjust(**margins)
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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 points in two 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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(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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dst = 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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tform3 = tf.estimate_transformation('projective', src, dst)
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warped = tf.warp(text, tform3, output_shape=(50, 300))
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plt.figure(figsize=(8, 3))
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plt.subplot(211)
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plt.imshow(text)
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plt.plot(src[:, 0], src[:, 1], '.r')
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plt.axis('off')
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plt.gray()
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plt.subplot(212)
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plt.imshow(warped)
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plt.axis('off')
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plt.gray()
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plt.subplots_adjust(**margins)
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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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