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