/
convex_hull.py
137 lines (111 loc) · 4.95 KB
/
convex_hull.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
"""Convex Hull."""
from itertools import product
import numpy as np
from scipy.spatial import ConvexHull
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 convex_hull_image(image, offset_coordinates=True, tolerance=1e-10):
"""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.
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=np.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(image.astype(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.
hull0 = ConvexHull(coords)
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
hull = ConvexHull(coords)
vertices = hull.points[hull.vertices]
# If 2D, use fast Cython function to locate convex hull pixels
if ndim == 2:
mask = grid_points_in_poly(image.shape, vertices)
else:
gridcoords = np.reshape(np.mgrid[tuple(map(slice, image.shape))],
(ndim, -1))
# A point is in the hull if it satisfies all of the hull's inequalities
coords_in_hull = np.all(hull.equations[:, :ndim].dot(gridcoords) +
hull.equations[:, ndim:] < tolerance, axis=0)
mask = np.reshape(coords_in_hull, image.shape)
return mask
def convex_hull_object(image, neighbors=8):
"""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) array
Binary input image.
neighbors : {4, 8}, int
Whether to use 4- or 8-connectivity.
Returns
-------
hull : ndarray of bool
Binary image with pixels in 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.
"""
if image.ndim > 2:
raise ValueError("Input must be a 2D image")
if neighbors != 4 and neighbors != 8:
raise ValueError('Neighbors must be either 4 or 8.')
labeled_im = label(image, neighbors, 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