mirror of
https://github.com/wassname/scikit-image.git
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Stefan van der Walt
84 lines
2.5 KiB
Python
84 lines
2.5 KiB
Python
r"""
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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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from skimage import data
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from skimage.transform import swirl
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import matplotlib.pyplot as plt
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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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f, (ax0, ax1) = plt.subplots(1, 2, figsize=(8, 3))
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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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