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99 lines
3.1 KiB
Python
99 lines
3.1 KiB
Python
__all__ = ['convex_hull_image', 'convex_hull_object']
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import numpy as np
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from ._pnpoly import grid_points_inside_poly
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from ._convex_hull import possible_hull
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from .selem import square
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from skimage.morphology import label, dilation
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from skimage.util import img_as_ubyte, img_as_bool
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def convex_hull_image(image):
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"""Compute the convex hull image of a binary image.
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The convex hull is the set of pixels included in the smallest convex
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polygon that surround all white pixels in the input image.
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Parameters
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----------
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image : ndarray
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Binary input image. This array is cast to bool before processing.
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Returns
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-------
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hull : ndarray of bool
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Binary image with pixels in convex hull set to True.
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References
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----------
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.. [1] http://blogs.mathworks.com/steve/2011/10/04/binary-image-convex-hull-algorithm-notes/
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"""
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image = image.astype(bool)
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# Here we do an optimisation by choosing only pixels that are
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# the starting or ending pixel of a row or column. This vastly
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# limits the number of coordinates to examine for the virtual
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# hull.
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coords = possible_hull(image.astype(np.uint8))
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N = len(coords)
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# Add a vertex for the middle of each pixel edge
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coords_corners = np.empty((N * 4, 2))
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for i, (x_offset, y_offset) in enumerate(zip((0, 0, -0.5, 0.5),
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(-0.5, 0.5, 0, 0))):
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coords_corners[i * N:(i + 1) * N] = coords + [x_offset, y_offset]
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coords = coords_corners
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try:
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from scipy.spatial import Delaunay
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except ImportError:
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raise ImportError('Could not import scipy.spatial, only available in '
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'scipy >= 0.9.')
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# Find the convex hull
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chull = Delaunay(coords).convex_hull
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v = coords[np.unique(chull)]
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# Sort vertices clock-wise
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v_centred = v - v.mean(axis=0)
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angles = np.arctan2(v_centred[:, 0], v_centred[:, 1])
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v = v[np.argsort(angles)]
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# For each pixel coordinate, check whether that pixel
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# lies inside the convex hull
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mask = grid_points_inside_poly(image.shape[:2], v)
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return mask
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def convex_hull_object(image):
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"""Compute the convex hull image of individual objects in a binary image.
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The convex hull is the set of pixels included in the smallest convex
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polygon that surround all white pixels in the input image.
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Parameters
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----------
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image : ndarray
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Binary input image.
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Returns
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-------
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hull : ndarray of bool
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Binary image with pixels in convex hull set to True.
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"""
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# Add 1 to the output of label() so as to make the
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# background value 0 rather than -1
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labeled_im = label(image, neighbors=8, background=0) + 1
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convex_obj = np.zeros(image.shape, dtype=bool)
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mask = np.zeros(image.shape, dtype=np.uint8)
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convex_img = np.zeros(image.shape, dtype=bool)
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for i in range(1, labeled_im.max()+1):
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mask[:] = i
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mask = img_as_ubyte(np.logical_not(np.bitwise_xor(labeled_im, mask)))
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convex_obj = convex_hull_image(mask)
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convex_img = np.logical_or(convex_img, convex_obj)
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return convex_img
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