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"""Convex Hull."""
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from itertools import product
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import numpy as np
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from scipy.spatial import ConvexHull, QhullError
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from ..measure.pnpoly import grid_points_in_poly
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from ._convex_hull import possible_hull
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from ..measure._label import label
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from ..util import unique_rows
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from .._shared.utils import warn
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__all__ = ['convex_hull_image', 'convex_hull_object']
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def _offsets_diamond(ndim):
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offsets = np.zeros((2 * ndim, ndim))
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for vertex, (axis, offset) in enumerate(product(range(ndim), (-0.5, 0.5))):
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offsets[vertex, axis] = offset
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return offsets
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def _check_coords_in_hull(gridcoords, hull_equations, tolerance):
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r"""Checks all the coordinates for inclusiveness in the convex hull.
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Parameters
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----------
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gridcoords : (M, N) ndarray
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Coordinates of ``N`` points in ``M`` dimensions.
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hull_equations : (M, N) ndarray
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Hyperplane equations of the facets of the convex hull.
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tolerance : float
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Tolerance when determining whether a point is inside the hull. Due
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to numerical floating point errors, a tolerance of 0 can result in
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some points erroneously being classified as being outside the hull.
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Returns
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-------
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coords_in_hull : ndarray of bool
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Binary 1D ndarray representing points in n-dimensional space
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with value ``True`` set for points inside the convex hull.
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Notes
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-----
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Checking the inclusiveness of coordinates in a convex hull requires
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intermediate calculations of dot products which are memory-intensive.
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Thus, the convex hull equations are checked individually with all
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coordinates to keep within the memory limit.
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References
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----------
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.. [1] https://github.com/scikit-image/scikit-image/issues/5019
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"""
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ndim, n_coords = gridcoords.shape
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n_hull_equations = hull_equations.shape[0]
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coords_in_hull = np.ones(n_coords, dtype=bool)
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# Pre-allocate arrays to cache intermediate results for reducing overheads
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dot_array = np.empty(n_coords, dtype=np.float64)
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test_ineq_temp = np.empty(n_coords, dtype=np.float64)
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coords_single_ineq = np.empty(n_coords, dtype=bool)
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# A point is in the hull if it satisfies all of the hull's inequalities
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for idx in range(n_hull_equations):
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# Tests a hyperplane equation on all coordinates of volume
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np.dot(hull_equations[idx, :ndim], gridcoords, out=dot_array)
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np.add(dot_array, hull_equations[idx, ndim:], out=test_ineq_temp)
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np.less(test_ineq_temp, tolerance, out=coords_single_ineq)
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coords_in_hull *= coords_single_ineq
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return coords_in_hull
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def convex_hull_image(image, offset_coordinates=True, tolerance=1e-10,
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include_borders=True):
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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 : array
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Binary input image. This array is cast to bool before processing.
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offset_coordinates : bool, optional
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If ``True``, a pixel at coordinate, e.g., (4, 7) will be represented
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by coordinates (3.5, 7), (4.5, 7), (4, 6.5), and (4, 7.5). This adds
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some "extent" to a pixel when computing the hull.
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tolerance : float, optional
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Tolerance when determining whether a point is inside the hull. Due
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to numerical floating point errors, a tolerance of 0 can result in
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some points erroneously being classified as being outside the hull.
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include_borders: bool, optional
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If ``False``, vertices/edges are excluded from the final hull mask.
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Returns
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-------
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hull : (M, N) array 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] https://blogs.mathworks.com/steve/2011/10/04/binary-image-convex-hull-algorithm-notes/
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"""
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ndim = image.ndim
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if np.count_nonzero(image) == 0:
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warn("Input image is entirely zero, no valid convex hull. "
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"Returning empty image", UserWarning)
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return np.zeros(image.shape, dtype=bool)
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# In 2D, 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 hull.
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if ndim == 2:
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coords = possible_hull(np.ascontiguousarray(image, dtype=np.uint8))
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else:
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coords = np.transpose(np.nonzero(image))
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if offset_coordinates:
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# when offsetting, we multiply number of vertices by 2 * ndim.
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# therefore, we reduce the number of coordinates by using a
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# convex hull on the original set, before offsetting.
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try:
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hull0 = ConvexHull(coords)
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except QhullError as err:
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warn(f"Failed to get convex hull image. "
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f"Returning empty image, see error message below:\n"
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f"{err}")
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return np.zeros(image.shape, dtype=bool)
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coords = hull0.points[hull0.vertices]
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# Add a vertex for the middle of each pixel edge
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if offset_coordinates:
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offsets = _offsets_diamond(image.ndim)
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coords = (coords[:, np.newaxis, :] + offsets).reshape(-1, ndim)
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# repeated coordinates can *sometimes* cause problems in
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# scipy.spatial.ConvexHull, so we remove them.
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coords = unique_rows(coords)
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# Find the convex hull
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try:
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hull = ConvexHull(coords)
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except QhullError as err:
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warn(f"Failed to get convex hull image. "
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f"Returning empty image, see error message below:\n"
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f"{err}")
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return np.zeros(image.shape, dtype=bool)
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vertices = hull.points[hull.vertices]
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# If 2D, use fast Cython function to locate convex hull pixels
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if ndim == 2:
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labels = grid_points_in_poly(image.shape, vertices, binarize=False)
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# If include_borders is True, we include vertices (2) and edge
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# points (3) in the mask, otherwise only the inside of the hull (1)
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mask = labels >= 1 if include_borders else labels == 1
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else:
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gridcoords = np.reshape(np.mgrid[tuple(map(slice, image.shape))],
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(ndim, -1))
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coords_in_hull = _check_coords_in_hull(gridcoords,
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hull.equations, tolerance)
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mask = np.reshape(coords_in_hull, image.shape)
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return mask
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def convex_hull_object(image, *, connectivity=2):
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r"""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 : (M, N) ndarray
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Binary input image.
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connectivity : {1, 2}, int, optional
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Determines the neighbors of each pixel. Adjacent elements
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within a squared distance of ``connectivity`` from pixel center
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are considered neighbors.::
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1-connectivity 2-connectivity
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[ ] [ ] [ ] [ ]
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| \ | /
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[ ]--[x]--[ ] [ ]--[x]--[ ]
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| / | \
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[ ] [ ] [ ] [ ]
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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 inside convex hull set to ``True``.
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Notes
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-----
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This function uses ``skimage.morphology.label`` to define unique objects,
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finds the convex hull of each using ``convex_hull_image``, and combines
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these regions with logical OR. Be aware the convex hulls of unconnected
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objects may overlap in the result. If this is suspected, consider using
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convex_hull_image separately on each object or adjust ``connectivity``.
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"""
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if image.ndim > 2:
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raise ValueError("Input must be a 2D image")
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if connectivity not in (1, 2):
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raise ValueError('`connectivity` must be either 1 or 2.')
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labeled_im = label(image, connectivity=connectivity, background=0)
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convex_obj = np.zeros(image.shape, dtype=bool)
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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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convex_obj = convex_hull_image(labeled_im == i)
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convex_img = np.logical_or(convex_img, convex_obj)
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return convex_img
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