mirror of
https://github.com/wassname/scikit-image.git
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emmanuelle
55f5103dd8
Modified travis_script.sh to account for the new structure of the gallery Added README.txt files in directories of gallery examples Fixed references to gallery images in user guide pages Fixed broken links
85 lines
2.6 KiB
Python
85 lines
2.6 KiB
Python
"""
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=====
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Swirl
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=====
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Image swirling is a non-linear image deformation that creates a whirlpool
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effect. This example describes the implementation of this transform in
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``skimage``, as well as the underlying warp mechanism.
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Image warping
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-------------
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When applying a geometric transformation on an image, we typically make use of
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a reverse mapping, i.e., for each pixel in the output image, we compute its
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corresponding position in the input. The reason is that, if we were to do it
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the other way around (map each input pixel to its new output position), some
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pixels in the output may be left empty. On the other hand, each output
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coordinate has exactly one corresponding location in (or outside) the input
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image, and even if that position is non-integer, we may use interpolation to
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compute the corresponding image value.
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Performing a reverse mapping
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----------------------------
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To perform a geometric warp in ``skimage``, you simply need to provide the
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reverse mapping to the ``skimage.transform.warp`` function. E.g., consider the
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case where we would like to shift an image 50 pixels to the left. The reverse
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mapping for such a shift would be::
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def shift_left(xy):
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xy[:, 0] += 50
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return xy
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The corresponding call to warp is::
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from skimage.transform import warp
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warp(image, shift_left)
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The swirl transformation
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------------------------
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Consider the coordinate :math:`(x, y)` in the output image. The reverse
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mapping for the swirl transformation first computes, relative to a center
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:math:`(x_0, y_0)`, its polar coordinates,
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.. math::
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\\theta = \\arctan(y/x)
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\\rho = \sqrt{(x - x_0)^2 + (y - y_0)^2},
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and then transforms them according to
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.. math::
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r = \ln(2) \, \mathtt{radius} / 5
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\phi = \mathtt{rotation}
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s = \mathtt{strength}
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\\theta' = \phi + s \, e^{-\\rho / r + \\theta}
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where ``strength`` is a parameter for the amount of swirl, ``radius`` indicates
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the swirl extent in pixels, and ``rotation`` adds a rotation angle. The
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transformation of ``radius`` into :math:`r` is to ensure that the
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transformation decays to :math:`\\approx 1/1000^{\mathsf{th}}` within the
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specified radius.
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"""
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import matplotlib.pyplot as plt
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from skimage import data
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from skimage.transform import swirl
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image = data.checkerboard()
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swirled = swirl(image, rotation=0, strength=10, radius=120, order=2)
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fig, (ax0, ax1) = plt.subplots(1, 2, figsize=(8, 3), sharex=True, sharey=True, subplot_kw={'adjustable':'box-forced'})
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ax0.imshow(image, cmap=plt.cm.gray, interpolation='none')
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ax0.axis('off')
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ax1.imshow(swirled, cmap=plt.cm.gray, interpolation='none')
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ax1.axis('off')
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plt.show()
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