648 lines
22 KiB
Python
648 lines
22 KiB
Python
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"""
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Algorithms for computing the skeleton of a binary image
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"""
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import numpy as np
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from ..util import img_as_ubyte, crop
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from scipy import ndimage as ndi
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from .._shared.utils import check_nD, warn
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from ._skeletonize_cy import (_fast_skeletonize, _skeletonize_loop,
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_table_lookup_index)
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from ._skeletonize_3d_cy import _compute_thin_image
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def skeletonize(image, *, method=None):
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"""Compute the skeleton of a binary image.
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Thinning is used to reduce each connected component in a binary image
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to a single-pixel wide skeleton.
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Parameters
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----------
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image : ndarray, 2D or 3D
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A binary image containing the objects to be skeletonized. Zeros
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represent background, nonzero values are foreground.
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method : {'zhang', 'lee'}, optional
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Which algorithm to use. Zhang's algorithm [Zha84]_ only works for
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2D images, and is the default for 2D. Lee's algorithm [Lee94]_
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works for 2D or 3D images and is the default for 3D.
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Returns
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-------
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skeleton : ndarray
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The thinned image.
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See also
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--------
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medial_axis
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References
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----------
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.. [Lee94] T.-C. Lee, R.L. Kashyap and C.-N. Chu, Building skeleton models
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via 3-D medial surface/axis thinning algorithms.
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Computer Vision, Graphics, and Image Processing, 56(6):462-478, 1994.
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.. [Zha84] A fast parallel algorithm for thinning digital patterns,
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T. Y. Zhang and C. Y. Suen, Communications of the ACM,
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March 1984, Volume 27, Number 3.
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Examples
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--------
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>>> X, Y = np.ogrid[0:9, 0:9]
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>>> ellipse = (1./3 * (X - 4)**2 + (Y - 4)**2 < 3**2).astype(np.uint8)
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>>> ellipse
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array([[0, 0, 0, 1, 1, 1, 0, 0, 0],
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[0, 0, 1, 1, 1, 1, 1, 0, 0],
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[0, 0, 1, 1, 1, 1, 1, 0, 0],
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[0, 0, 1, 1, 1, 1, 1, 0, 0],
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[0, 0, 1, 1, 1, 1, 1, 0, 0],
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[0, 0, 1, 1, 1, 1, 1, 0, 0],
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[0, 0, 1, 1, 1, 1, 1, 0, 0],
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[0, 0, 1, 1, 1, 1, 1, 0, 0],
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[0, 0, 0, 1, 1, 1, 0, 0, 0]], dtype=uint8)
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>>> skel = skeletonize(ellipse)
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>>> skel.astype(np.uint8)
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array([[0, 0, 0, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 1, 0, 0, 0, 0],
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[0, 0, 0, 0, 1, 0, 0, 0, 0],
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[0, 0, 0, 0, 1, 0, 0, 0, 0],
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[0, 0, 0, 0, 1, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0, 0, 0]], dtype=uint8)
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"""
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if image.ndim == 2 and (method is None or method == 'zhang'):
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skeleton = skeletonize_2d(image)
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elif image.ndim == 3 and method == 'zhang':
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raise ValueError('skeletonize method "zhang" only works for 2D '
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'images.')
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elif image.ndim == 3 or (image.ndim == 2 and method == 'lee'):
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skeleton = skeletonize_3d(image)
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else:
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raise ValueError('skeletonize requires a 2D or 3D image as input, '
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'got {}D.'.format(image.ndim))
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return skeleton
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def skeletonize_2d(image):
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"""Return the skeleton of a 2D binary image.
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Thinning is used to reduce each connected component in a binary image
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to a single-pixel wide skeleton.
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Parameters
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----------
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image : numpy.ndarray
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A binary image containing the objects to be skeletonized. '1'
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represents foreground, and '0' represents background. It
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also accepts arrays of boolean values where True is foreground.
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Returns
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-------
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skeleton : ndarray
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A matrix containing the thinned image.
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See also
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--------
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medial_axis
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Notes
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-----
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The algorithm [Zha84]_ works by making successive passes of the image,
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removing pixels on object borders. This continues until no
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more pixels can be removed. The image is correlated with a
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mask that assigns each pixel a number in the range [0...255]
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corresponding to each possible pattern of its 8 neighbouring
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pixels. A look up table is then used to assign the pixels a
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value of 0, 1, 2 or 3, which are selectively removed during
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the iterations.
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Note that this algorithm will give different results than a
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medial axis transform, which is also often referred to as
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"skeletonization".
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References
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----------
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.. [Zha84] A fast parallel algorithm for thinning digital patterns,
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T. Y. Zhang and C. Y. Suen, Communications of the ACM,
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March 1984, Volume 27, Number 3.
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Examples
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--------
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>>> X, Y = np.ogrid[0:9, 0:9]
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>>> ellipse = (1./3 * (X - 4)**2 + (Y - 4)**2 < 3**2).astype(np.uint8)
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>>> ellipse
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array([[0, 0, 0, 1, 1, 1, 0, 0, 0],
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[0, 0, 1, 1, 1, 1, 1, 0, 0],
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[0, 0, 1, 1, 1, 1, 1, 0, 0],
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[0, 0, 1, 1, 1, 1, 1, 0, 0],
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[0, 0, 1, 1, 1, 1, 1, 0, 0],
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[0, 0, 1, 1, 1, 1, 1, 0, 0],
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[0, 0, 1, 1, 1, 1, 1, 0, 0],
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[0, 0, 1, 1, 1, 1, 1, 0, 0],
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[0, 0, 0, 1, 1, 1, 0, 0, 0]], dtype=uint8)
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>>> skel = skeletonize(ellipse)
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>>> skel.astype(np.uint8)
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array([[0, 0, 0, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 1, 0, 0, 0, 0],
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[0, 0, 0, 0, 1, 0, 0, 0, 0],
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[0, 0, 0, 0, 1, 0, 0, 0, 0],
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[0, 0, 0, 0, 1, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0, 0, 0]], dtype=uint8)
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"""
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# convert to unsigned int (this should work for boolean values)
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image = image.astype(np.uint8)
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# check some properties of the input image:
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# - 2D
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# - binary image with only 0's and 1's
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if image.ndim != 2:
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raise ValueError('Skeletonize requires a 2D array')
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if not np.all(np.in1d(image.flat, (0, 1))):
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raise ValueError('Image contains values other than 0 and 1')
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return _fast_skeletonize(image)
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# --------- Skeletonization and thinning based on Guo and Hall 1989 ---------
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def _generate_thin_luts():
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"""generate LUTs for thinning algorithm (for reference)"""
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def nabe(n):
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return np.array([n >> i & 1 for i in range(0, 9)]).astype(np.bool)
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def G1(n):
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s = 0
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bits = nabe(n)
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for i in (0, 2, 4, 6):
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if not(bits[i]) and (bits[i + 1] or bits[(i + 2) % 8]):
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s += 1
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return s == 1
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g1_lut = np.array([G1(n) for n in range(256)])
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def G2(n):
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n1, n2 = 0, 0
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bits = nabe(n)
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for k in (1, 3, 5, 7):
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if bits[k] or bits[k - 1]:
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n1 += 1
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if bits[k] or bits[(k + 1) % 8]:
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n2 += 1
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return min(n1, n2) in [2, 3]
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g2_lut = np.array([G2(n) for n in range(256)])
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g12_lut = g1_lut & g2_lut
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def G3(n):
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bits = nabe(n)
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return not((bits[1] or bits[2] or not(bits[7])) and bits[0])
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def G3p(n):
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bits = nabe(n)
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return not((bits[5] or bits[6] or not(bits[3])) and bits[4])
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g3_lut = np.array([G3(n) for n in range(256)])
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g3p_lut = np.array([G3p(n) for n in range(256)])
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g123_lut = g12_lut & g3_lut
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g123p_lut = g12_lut & g3p_lut
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return g123_lut, g123p_lut
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G123_LUT = np.array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
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0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1,
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0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
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0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
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1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0,
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0, 1, 1, 0, 0, 1, 0, 0, 0], dtype=np.bool)
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G123P_LUT = np.array([0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0,
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0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
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1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1,
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0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0], dtype=np.bool)
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def thin(image, max_iter=None):
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"""
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Perform morphological thinning of a binary image.
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Parameters
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----------
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image : binary (M, N) ndarray
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The image to be thinned.
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max_iter : int, number of iterations, optional
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Regardless of the value of this parameter, the thinned image
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is returned immediately if an iteration produces no change.
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If this parameter is specified it thus sets an upper bound on
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the number of iterations performed.
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Returns
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-------
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out : ndarray of bool
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Thinned image.
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See also
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--------
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skeletonize, medial_axis
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Notes
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-----
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This algorithm [1]_ works by making multiple passes over the image,
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removing pixels matching a set of criteria designed to thin
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connected regions while preserving eight-connected components and
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2 x 2 squares [2]_. In each of the two sub-iterations the algorithm
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correlates the intermediate skeleton image with a neighborhood mask,
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then looks up each neighborhood in a lookup table indicating whether
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the central pixel should be deleted in that sub-iteration.
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References
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----------
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.. [1] Z. Guo and R. W. Hall, "Parallel thinning with
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two-subiteration algorithms," Comm. ACM, vol. 32, no. 3,
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pp. 359-373, 1989. :DOI:`10.1145/62065.62074`
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.. [2] Lam, L., Seong-Whan Lee, and Ching Y. Suen, "Thinning
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Methodologies-A Comprehensive Survey," IEEE Transactions on
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Pattern Analysis and Machine Intelligence, Vol 14, No. 9,
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p. 879, 1992. :DOI:`10.1109/34.161346`
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Examples
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--------
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>>> square = np.zeros((7, 7), dtype=np.uint8)
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>>> square[1:-1, 2:-2] = 1
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>>> square[0, 1] = 1
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>>> square
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array([[0, 1, 0, 0, 0, 0, 0],
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[0, 0, 1, 1, 1, 0, 0],
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[0, 0, 1, 1, 1, 0, 0],
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[0, 0, 1, 1, 1, 0, 0],
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[0, 0, 1, 1, 1, 0, 0],
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[0, 0, 1, 1, 1, 0, 0],
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[0, 0, 0, 0, 0, 0, 0]], dtype=uint8)
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>>> skel = thin(square)
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>>> skel.astype(np.uint8)
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array([[0, 1, 0, 0, 0, 0, 0],
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[0, 0, 1, 0, 0, 0, 0],
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||
|
|
[0, 0, 0, 1, 0, 0, 0],
|
||
|
|
[0, 0, 0, 1, 0, 0, 0],
|
||
|
|
[0, 0, 0, 1, 0, 0, 0],
|
||
|
|
[0, 0, 0, 0, 0, 0, 0],
|
||
|
|
[0, 0, 0, 0, 0, 0, 0]], dtype=uint8)
|
||
|
|
"""
|
||
|
|
# check that image is 2d
|
||
|
|
check_nD(image, 2)
|
||
|
|
|
||
|
|
# convert image to uint8 with values in {0, 1}
|
||
|
|
skel = np.asanyarray(image, dtype=bool).astype(np.uint8)
|
||
|
|
|
||
|
|
# neighborhood mask
|
||
|
|
mask = np.array([[ 8, 4, 2],
|
||
|
|
[16, 0, 1],
|
||
|
|
[32, 64, 128]], dtype=np.uint8)
|
||
|
|
|
||
|
|
# iterate until convergence, up to the iteration limit
|
||
|
|
max_iter = max_iter or np.inf
|
||
|
|
n_iter = 0
|
||
|
|
n_pts_old, n_pts_new = np.inf, np.sum(skel)
|
||
|
|
while n_pts_old != n_pts_new and n_iter < max_iter:
|
||
|
|
n_pts_old = n_pts_new
|
||
|
|
|
||
|
|
# perform the two "subiterations" described in the paper
|
||
|
|
for lut in [G123_LUT, G123P_LUT]:
|
||
|
|
# correlate image with neighborhood mask
|
||
|
|
N = ndi.correlate(skel, mask, mode='constant')
|
||
|
|
# take deletion decision from this subiteration's LUT
|
||
|
|
D = np.take(lut, N)
|
||
|
|
# perform deletion
|
||
|
|
skel[D] = 0
|
||
|
|
|
||
|
|
n_pts_new = np.sum(skel) # count points after thinning
|
||
|
|
n_iter += 1
|
||
|
|
|
||
|
|
return skel.astype(np.bool)
|
||
|
|
|
||
|
|
|
||
|
|
# --------- Skeletonization by medial axis transform --------
|
||
|
|
|
||
|
|
_eight_connect = ndi.generate_binary_structure(2, 2)
|
||
|
|
|
||
|
|
|
||
|
|
def medial_axis(image, mask=None, return_distance=False):
|
||
|
|
"""
|
||
|
|
Compute the medial axis transform of a binary image
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
image : binary ndarray, shape (M, N)
|
||
|
|
The image of the shape to be skeletonized.
|
||
|
|
mask : binary ndarray, shape (M, N), optional
|
||
|
|
If a mask is given, only those elements in `image` with a true
|
||
|
|
value in `mask` are used for computing the medial axis.
|
||
|
|
return_distance : bool, optional
|
||
|
|
If true, the distance transform is returned as well as the skeleton.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
out : ndarray of bools
|
||
|
|
Medial axis transform of the image
|
||
|
|
dist : ndarray of ints, optional
|
||
|
|
Distance transform of the image (only returned if `return_distance`
|
||
|
|
is True)
|
||
|
|
|
||
|
|
See also
|
||
|
|
--------
|
||
|
|
skeletonize
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
This algorithm computes the medial axis transform of an image
|
||
|
|
as the ridges of its distance transform.
|
||
|
|
|
||
|
|
The different steps of the algorithm are as follows
|
||
|
|
* A lookup table is used, that assigns 0 or 1 to each configuration of
|
||
|
|
the 3x3 binary square, whether the central pixel should be removed
|
||
|
|
or kept. We want a point to be removed if it has more than one neighbor
|
||
|
|
and if removing it does not change the number of connected components.
|
||
|
|
|
||
|
|
* The distance transform to the background is computed, as well as
|
||
|
|
the cornerness of the pixel.
|
||
|
|
|
||
|
|
* The foreground (value of 1) points are ordered by
|
||
|
|
the distance transform, then the cornerness.
|
||
|
|
|
||
|
|
* A cython function is called to reduce the image to its skeleton. It
|
||
|
|
processes pixels in the order determined at the previous step, and
|
||
|
|
removes or maintains a pixel according to the lookup table. Because
|
||
|
|
of the ordering, it is possible to process all pixels in only one
|
||
|
|
pass.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> square = np.zeros((7, 7), dtype=np.uint8)
|
||
|
|
>>> square[1:-1, 2:-2] = 1
|
||
|
|
>>> square
|
||
|
|
array([[0, 0, 0, 0, 0, 0, 0],
|
||
|
|
[0, 0, 1, 1, 1, 0, 0],
|
||
|
|
[0, 0, 1, 1, 1, 0, 0],
|
||
|
|
[0, 0, 1, 1, 1, 0, 0],
|
||
|
|
[0, 0, 1, 1, 1, 0, 0],
|
||
|
|
[0, 0, 1, 1, 1, 0, 0],
|
||
|
|
[0, 0, 0, 0, 0, 0, 0]], dtype=uint8)
|
||
|
|
>>> medial_axis(square).astype(np.uint8)
|
||
|
|
array([[0, 0, 0, 0, 0, 0, 0],
|
||
|
|
[0, 0, 1, 0, 1, 0, 0],
|
||
|
|
[0, 0, 0, 1, 0, 0, 0],
|
||
|
|
[0, 0, 0, 1, 0, 0, 0],
|
||
|
|
[0, 0, 0, 1, 0, 0, 0],
|
||
|
|
[0, 0, 1, 0, 1, 0, 0],
|
||
|
|
[0, 0, 0, 0, 0, 0, 0]], dtype=uint8)
|
||
|
|
|
||
|
|
"""
|
||
|
|
global _eight_connect
|
||
|
|
if mask is None:
|
||
|
|
masked_image = image.astype(np.bool)
|
||
|
|
else:
|
||
|
|
masked_image = image.astype(bool).copy()
|
||
|
|
masked_image[~mask] = False
|
||
|
|
#
|
||
|
|
# Build lookup table - three conditions
|
||
|
|
# 1. Keep only positive pixels (center_is_foreground array).
|
||
|
|
# AND
|
||
|
|
# 2. Keep if removing the pixel results in a different connectivity
|
||
|
|
# (if the number of connected components is different with and
|
||
|
|
# without the central pixel)
|
||
|
|
# OR
|
||
|
|
# 3. Keep if # pixels in neighbourhood is 2 or less
|
||
|
|
# Note that table is independent of image
|
||
|
|
center_is_foreground = (np.arange(512) & 2**4).astype(bool)
|
||
|
|
table = (center_is_foreground # condition 1.
|
||
|
|
&
|
||
|
|
(np.array([ndi.label(_pattern_of(index), _eight_connect)[1] !=
|
||
|
|
ndi.label(_pattern_of(index & ~ 2**4),
|
||
|
|
_eight_connect)[1]
|
||
|
|
for index in range(512)]) # condition 2
|
||
|
|
|
|
||
|
|
np.array([np.sum(_pattern_of(index)) < 3 for index in range(512)]))
|
||
|
|
# condition 3
|
||
|
|
)
|
||
|
|
|
||
|
|
# Build distance transform
|
||
|
|
distance = ndi.distance_transform_edt(masked_image)
|
||
|
|
if return_distance:
|
||
|
|
store_distance = distance.copy()
|
||
|
|
|
||
|
|
# Corners
|
||
|
|
# The processing order along the edge is critical to the shape of the
|
||
|
|
# resulting skeleton: if you process a corner first, that corner will
|
||
|
|
# be eroded and the skeleton will miss the arm from that corner. Pixels
|
||
|
|
# with fewer neighbors are more "cornery" and should be processed last.
|
||
|
|
# We use a cornerness_table lookup table where the score of a
|
||
|
|
# configuration is the number of background (0-value) pixels in the
|
||
|
|
# 3x3 neighbourhood
|
||
|
|
cornerness_table = np.array([9 - np.sum(_pattern_of(index))
|
||
|
|
for index in range(512)])
|
||
|
|
corner_score = _table_lookup(masked_image, cornerness_table)
|
||
|
|
|
||
|
|
# Define arrays for inner loop
|
||
|
|
i, j = np.mgrid[0:image.shape[0], 0:image.shape[1]]
|
||
|
|
result = masked_image.copy()
|
||
|
|
distance = distance[result]
|
||
|
|
i = np.ascontiguousarray(i[result], dtype=np.intp)
|
||
|
|
j = np.ascontiguousarray(j[result], dtype=np.intp)
|
||
|
|
result = np.ascontiguousarray(result, np.uint8)
|
||
|
|
|
||
|
|
# Determine the order in which pixels are processed.
|
||
|
|
# We use a random # for tiebreaking. Assign each pixel in the image a
|
||
|
|
# predictable, random # so that masking doesn't affect arbitrary choices
|
||
|
|
# of skeletons
|
||
|
|
#
|
||
|
|
generator = np.random.RandomState(0)
|
||
|
|
tiebreaker = generator.permutation(np.arange(masked_image.sum()))
|
||
|
|
order = np.lexsort((tiebreaker,
|
||
|
|
corner_score[masked_image],
|
||
|
|
distance))
|
||
|
|
order = np.ascontiguousarray(order, dtype=np.int32)
|
||
|
|
|
||
|
|
table = np.ascontiguousarray(table, dtype=np.uint8)
|
||
|
|
# Remove pixels not belonging to the medial axis
|
||
|
|
_skeletonize_loop(result, i, j, order, table)
|
||
|
|
|
||
|
|
result = result.astype(bool)
|
||
|
|
if mask is not None:
|
||
|
|
result[~mask] = image[~mask]
|
||
|
|
if return_distance:
|
||
|
|
return result, store_distance
|
||
|
|
else:
|
||
|
|
return result
|
||
|
|
|
||
|
|
|
||
|
|
def _pattern_of(index):
|
||
|
|
"""
|
||
|
|
Return the pattern represented by an index value
|
||
|
|
Byte decomposition of index
|
||
|
|
"""
|
||
|
|
return np.array([[index & 2**0, index & 2**1, index & 2**2],
|
||
|
|
[index & 2**3, index & 2**4, index & 2**5],
|
||
|
|
[index & 2**6, index & 2**7, index & 2**8]], bool)
|
||
|
|
|
||
|
|
|
||
|
|
def _table_lookup(image, table):
|
||
|
|
"""
|
||
|
|
Perform a morphological transform on an image, directed by its
|
||
|
|
neighbors
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
image : ndarray
|
||
|
|
A binary image
|
||
|
|
table : ndarray
|
||
|
|
A 512-element table giving the transform of each pixel given
|
||
|
|
the values of that pixel and its 8-connected neighbors.
|
||
|
|
border_value : bool
|
||
|
|
The value of pixels beyond the border of the image.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
result : ndarray of same shape as `image`
|
||
|
|
Transformed image
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
The pixels are numbered like this::
|
||
|
|
|
||
|
|
|
||
|
|
0 1 2
|
||
|
|
3 4 5
|
||
|
|
6 7 8
|
||
|
|
|
||
|
|
The index at a pixel is the sum of 2**<pixel-number> for pixels
|
||
|
|
that evaluate to true.
|
||
|
|
"""
|
||
|
|
#
|
||
|
|
# We accumulate into the indexer to get the index into the table
|
||
|
|
# at each point in the image
|
||
|
|
#
|
||
|
|
if image.shape[0] < 3 or image.shape[1] < 3:
|
||
|
|
image = image.astype(bool)
|
||
|
|
indexer = np.zeros(image.shape, int)
|
||
|
|
indexer[1:, 1:] += image[:-1, :-1] * 2**0
|
||
|
|
indexer[1:, :] += image[:-1, :] * 2**1
|
||
|
|
indexer[1:, :-1] += image[:-1, 1:] * 2**2
|
||
|
|
|
||
|
|
indexer[:, 1:] += image[:, :-1] * 2**3
|
||
|
|
indexer[:, :] += image[:, :] * 2**4
|
||
|
|
indexer[:, :-1] += image[:, 1:] * 2**5
|
||
|
|
|
||
|
|
indexer[:-1, 1:] += image[1:, :-1] * 2**6
|
||
|
|
indexer[:-1, :] += image[1:, :] * 2**7
|
||
|
|
indexer[:-1, :-1] += image[1:, 1:] * 2**8
|
||
|
|
else:
|
||
|
|
indexer = _table_lookup_index(np.ascontiguousarray(image, np.uint8))
|
||
|
|
image = table[indexer]
|
||
|
|
return image
|
||
|
|
|
||
|
|
|
||
|
|
def skeletonize_3d(image):
|
||
|
|
"""Compute the skeleton of a binary image.
|
||
|
|
|
||
|
|
Thinning is used to reduce each connected component in a binary image
|
||
|
|
to a single-pixel wide skeleton.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
image : ndarray, 2D or 3D
|
||
|
|
A binary image containing the objects to be skeletonized. Zeros
|
||
|
|
represent background, nonzero values are foreground.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
skeleton : ndarray
|
||
|
|
The thinned image.
|
||
|
|
|
||
|
|
See also
|
||
|
|
--------
|
||
|
|
skeletonize, medial_axis
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
The method of [Lee94]_ uses an octree data structure to examine a 3x3x3
|
||
|
|
neighborhood of a pixel. The algorithm proceeds by iteratively sweeping
|
||
|
|
over the image, and removing pixels at each iteration until the image
|
||
|
|
stops changing. Each iteration consists of two steps: first, a list of
|
||
|
|
candidates for removal is assembled; then pixels from this list are
|
||
|
|
rechecked sequentially, to better preserve connectivity of the image.
|
||
|
|
|
||
|
|
The algorithm this function implements is different from the algorithms
|
||
|
|
used by either `skeletonize` or `medial_axis`, thus for 2D images the
|
||
|
|
results produced by this function are generally different.
|
||
|
|
|
||
|
|
References
|
||
|
|
----------
|
||
|
|
.. [Lee94] T.-C. Lee, R.L. Kashyap and C.-N. Chu, Building skeleton models
|
||
|
|
via 3-D medial surface/axis thinning algorithms.
|
||
|
|
Computer Vision, Graphics, and Image Processing, 56(6):462-478, 1994.
|
||
|
|
|
||
|
|
"""
|
||
|
|
# make sure the image is 3D or 2D
|
||
|
|
if image.ndim < 2 or image.ndim > 3:
|
||
|
|
raise ValueError("skeletonize_3d can only handle 2D or 3D images; "
|
||
|
|
"got image.ndim = %s instead." % image.ndim)
|
||
|
|
image = np.ascontiguousarray(image)
|
||
|
|
image = img_as_ubyte(image, force_copy=False)
|
||
|
|
|
||
|
|
# make an in image 3D and pad it w/ zeros to simplify dealing w/ boundaries
|
||
|
|
# NB: careful here to not clobber the original *and* minimize copying
|
||
|
|
image_o = image
|
||
|
|
if image.ndim == 2:
|
||
|
|
image_o = image[np.newaxis, ...]
|
||
|
|
image_o = np.pad(image_o, pad_width=1, mode='constant')
|
||
|
|
|
||
|
|
# normalize to binary
|
||
|
|
maxval = image_o.max()
|
||
|
|
image_o[image_o != 0] = 1
|
||
|
|
|
||
|
|
# do the computation
|
||
|
|
image_o = np.asarray(_compute_thin_image(image_o))
|
||
|
|
|
||
|
|
# crop it back and restore the original intensity range
|
||
|
|
image_o = crop(image_o, crop_width=1)
|
||
|
|
if image.ndim == 2:
|
||
|
|
image_o = image_o[0]
|
||
|
|
image_o *= maxval
|
||
|
|
|
||
|
|
return image_o
|