mirror of
https://github.com/wassname/scikit-image.git
synced 2026-06-28 16:30:54 +08:00
Neil Yager
141 lines
4.1 KiB
Python
141 lines
4.1 KiB
Python
"""Image projection.
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"""
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import numpy as np
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from scipy.ndimage import interpolation as ndii
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__all__ = ['homography']
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eps = np.finfo(float).eps
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def _stackcopy(a, b):
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"""a[:,:,0] = a[:,:,1] = ... = b"""
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if a.ndim == 3:
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a.transpose().swapaxes(1, 2)[:] = b
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else:
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a[:] = b
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def homography(image, H, output_shape=None, order=1,
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mode='constant', cval=0.):
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"""Perform a projective transformation (homography) on an image.
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For each pixel, given its homogeneous coordinate :math:`\mathbf{x}
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= [x, y, 1]^T`, its target position is calculated by multiplying
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with the given matrix, :math:`H`, to give :math:`H \mathbf{x}`.
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E.g., to rotate by theta degrees clockwise, the matrix should be
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::
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[[cos(theta) -sin(theta) 0]
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[sin(theta) cos(theta) 0]
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[0 0 1]]
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or, to translate x by 10 and y by 20,
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::
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[[1 0 10]
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[0 1 20]
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[0 0 1 ]].
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Parameters
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----------
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image : 2-D array
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Input image.
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H : array of shape ``(3, 3)``
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Transformation matrix H that defines the homography.
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output_shape : tuple (rows, cols)
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Shape of the output image generated.
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order : int
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Order of splines used in interpolation.
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mode : string
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How to handle values outside the image borders. Passed as-is
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to ndimage.
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cval : string
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Used in conjunction with mode 'constant', the value outside
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the image boundaries.
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Examples
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--------
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>>> # rotate by 90 degrees around origin and shift down by 2
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>>> x = np.arange(9, dtype=np.uint8).reshape((3, 3)) + 1
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>>> x
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array([[1, 2, 3],
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[4, 5, 6],
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[7, 8, 9]], dtype=uint8)
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>>> theta = -np.pi/2
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>>> M = np.array([[np.cos(theta),-np.sin(theta),0],
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... [np.sin(theta), np.cos(theta),2],
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... [0, 0, 1]])
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>>> x90 = homography(x, M, order=1)
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>>> x90
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array([[3, 6, 9],
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[2, 5, 8],
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[1, 4, 7]], dtype=uint8)
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>>> # translate right by 2 and down by 1
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>>> y = np.zeros((5,5), dtype=np.uint8)
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>>> y[1, 1] = 255
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>>> y
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array([[ 0, 0, 0, 0, 0],
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[ 0, 255, 0, 0, 0],
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[ 0, 0, 0, 0, 0],
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[ 0, 0, 0, 0, 0],
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[ 0, 0, 0, 0, 0]], dtype=uint8)
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>>> M = np.array([[ 1., 0., 2.],
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... [ 0., 1., 1.],
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... [ 0., 0., 1.]])
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>>> y21 = homography(y, M, order=1)
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>>> y21
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array([[ 0, 0, 0, 0, 0],
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[ 0, 0, 0, 0, 0],
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[ 0, 0, 0, 255, 0],
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[ 0, 0, 0, 0, 0],
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[ 0, 0, 0, 0, 0]], dtype=uint8)
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"""
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if image.ndim < 2:
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raise ValueError("Input must have more than 1 dimension.")
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image = np.atleast_3d(image)
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ishape = np.array(image.shape)
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bands = ishape[2]
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if output_shape is None:
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output_shape = ishape
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coords = np.empty(np.r_[3, output_shape], dtype=float)
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# Construct transformed coordinates
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rows, cols = output_shape[:2]
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rows, cols = np.mgrid[:rows, :cols]
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tf_coords = np.empty(shape=cols.shape,
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dtype=[('cols', float),
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('rows', float),
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('z', float)])
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tf_coords['cols'], tf_coords['rows'] = cols, rows
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tf_coords['z'] = 1
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tf_coords = tf_coords.view((float, 3))
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tf_coords = np.dot(tf_coords, np.linalg.inv(H).transpose())
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tf_coords[np.absolute(tf_coords) < eps] = 0.
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# normalize coordinates
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tf_coords[..., :2] /= tf_coords[..., 2, np.newaxis]
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# y-coordinate mapping
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_stackcopy(coords[0,...], tf_coords[...,1])
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# x-coordinate mapping
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_stackcopy(coords[1,...], tf_coords[...,0])
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# colour-coordinate mapping
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coords[2,...] = range(bands)
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# Prefilter not necessary for order 1 interpolation
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prefilter = order > 1
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mapped = ndii.map_coordinates(image, coords, prefilter=prefilter,
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mode=mode, order=order, cval=cval)
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return mapped.squeeze()
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