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scikit-image/skimage/morphology/skel.py
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from __future__ import division, print_function, absolute_import
import numpy as np
def _prepare_image(img_in):
"""Convert to a binary image, pad the it w/ zeros, and ensure it's 3D.
"""
if img_in.ndim < 2 or img_in.ndim > 3:
raise ValueError('expect 2D, got ndim = %s' % img_in.ndim)
img = img_in.copy()
if img.ndim == 2:
img = img.reshape((1,) + img.shape)
# normalize to binary
img[img != 0] = 1
# pad w/ zeros to simplify dealing w/ neighborhood of a pixel
img_o = np.zeros(tuple(s + 2 for s in img.shape),
dtype=np.uint8)
img_o[1:-1, 1:-1, 1:-1] = img.astype(np.uint8)
return img_o
def _postprocess_image(img_o):
"""Clip the image (padding is an implementation detail), convert to b/w.
"""
img_oo = img_o[1:-1, 1:-1, 1:-1]
img_oo = img_oo.squeeze()
img_oo *= 255
return img_oo
def get_neighborhood(img, p, r, c):
"""Get the neighborhood of a pixel.
Assume zero boundary conditions. Image is already padded, so no
out-of-bounds checking.
"""
neighborhood = np.zeros(27, dtype=np.uint8)
neighborhood[0] = img[p-1, r-1, c-1]
neighborhood[1] = img[p-1, r, c-1]
neighborhood[2] = img[p-1, r+1, c-1]
neighborhood[ 3] = img[p-1, r-1, c]
neighborhood[ 4] = img[p-1, r, c]
neighborhood[ 5] = img[p-1, r+1, c]
neighborhood[ 6] = img[p-1, r-1, c+1]
neighborhood[ 7] = img[p-1, r, c+1]
neighborhood[ 8] = img[p-1, r+1, c+1]
neighborhood[ 9] = img[p, r-1, c-1]
neighborhood[10] = img[p, r, c-1]
neighborhood[11] = img[p, r+1, c-1]
neighborhood[12] = img[p, r-1, c]
neighborhood[13] = img[p, r, c]
neighborhood[14] = img[p, r+1, c]
neighborhood[15] = img[p, r-1, c+1]
neighborhood[16] = img[p, r, c+1]
neighborhood[17] = img[p, r+1, c+1]
neighborhood[18] = img[p+1, r-1, c-1]
neighborhood[19] = img[p+1, r, c-1]
neighborhood[20] = img[p+1, r+1, c-1]
neighborhood[21] = img[p+1, r-1, c]
neighborhood[22] = img[p+1, r, c]
neighborhood[23] = img[p+1, r+1, c]
neighborhood[24] = img[p+1, r-1, c+1]
neighborhood[25] = img[p+1, r, c+1]
neighborhood[26] = img[p+1, r+1, c+1]
return neighborhood
###### look-up tables
def fill_numpoints_LUT(n=256):
p = int(np.log2(n) + 1)
return np.sum(np.arange(n)[:, None] & (1 << np.arange(p)) != 0, axis=1)
NUMPOINTS_LUT = fill_numpoints_LUT()
def fill_Euler_LUT():
LUT = np.zeros(256, dtype=int)
LUT[1] = 1
LUT[3] = -1
LUT[5] = -1
LUT[7] = 1
LUT[9] = -3
LUT[11] = -1
LUT[13] = -1
LUT[15] = 1
LUT[17] = -1
LUT[19] = 1
LUT[21] = 1
LUT[23] = -1
LUT[25] = 3
LUT[27] = 1
LUT[29] = 1
LUT[31] = -1
LUT[33] = -3
LUT[35] = -1
LUT[37] = 3
LUT[39] = 1
LUT[41] = 1
LUT[43] = -1
LUT[45] = 3
LUT[47] = 1
LUT[49] = -1
LUT[51] = 1
LUT[53] = 1
LUT[55] = -1
LUT[57] = 3
LUT[59] = 1
LUT[61] = 1
LUT[63] = -1
LUT[65] = -3
LUT[67] = 3
LUT[69] = -1
LUT[71] = 1
LUT[73] = 1
LUT[75] = 3
LUT[77] = -1
LUT[79] = 1
LUT[81] = -1
LUT[83] = 1
LUT[85] = 1
LUT[87] = -1
LUT[89] = 3
LUT[91] = 1
LUT[93] = 1
LUT[95] = -1
LUT[97] = 1
LUT[99] = 3
LUT[101] = 3
LUT[103] = 1
LUT[105] = 5
LUT[107] = 3
LUT[109] = 3
LUT[111] = 1
LUT[113] = -1
LUT[115] = 1
LUT[117] = 1
LUT[119] = -1
LUT[121] = 3
LUT[123] = 1
LUT[125] = 1
LUT[127] = -1
LUT[129] = -7
LUT[131] = -1
LUT[133] = -1
LUT[135] = 1
LUT[137] = -3
LUT[139] = -1
LUT[141] = -1
LUT[143] = 1
LUT[145] = -1
LUT[147] = 1
LUT[149] = 1
LUT[151] = -1
LUT[153] = 3
LUT[155] = 1
LUT[157] = 1
LUT[159] = -1
LUT[161] = -3
LUT[163] = -1
LUT[165] = 3
LUT[167] = 1
LUT[169] = 1
LUT[171] = -1
LUT[173] = 3
LUT[175] = 1
LUT[177] = -1
LUT[179] = 1
LUT[181] = 1
LUT[183] = -1
LUT[185] = 3
LUT[187] = 1
LUT[189] = 1
LUT[191] = -1
LUT[193] = -3
LUT[195] = 3
LUT[197] = -1
LUT[199] = 1
LUT[201] = 1
LUT[203] = 3
LUT[205] = -1
LUT[207] = 1
LUT[209] = -1
LUT[211] = 1
LUT[213] = 1
LUT[215] = -1
LUT[217] = 3
LUT[219] = 1
LUT[221] = 1
LUT[223] = -1
LUT[225] = 1
LUT[227] = 3
LUT[229] = 3
LUT[231] = 1
LUT[233] = 5
LUT[235] = 3
LUT[237] = 3
LUT[239] = 1
LUT[241] = -1
LUT[243] = 1
LUT[245] = 1
LUT[247] = -1
LUT[249] = 3
LUT[251] = 1
LUT[253] = 1
LUT[255] = -1
return LUT
LUT = fill_Euler_LUT()
### Octants (indexOctantXXX functions)
OCTANTS = tuple(range(8))
NEB, NWB, SEB, SWB, NEU, NWU, SEU, SWU = OCTANTS
neib_idx = np.empty((8, 7), dtype=int)
neib_idx[NEB, ...] = [2, 1, 11, 10, 5, 4, 14]
neib_idx[NWB, ...] = [0, 9, 3, 12, 1, 10, 4]
neib_idx[SEB, ...] = [8, 7, 17, 16, 5, 4, 14]
neib_idx[SWB, ...] = [6, 15, 7, 16, 3, 12, 4]
neib_idx[NEU, ...] = [20, 23, 19, 22, 11, 14, 10]
neib_idx[NWU, ...] = [18, 21, 9, 12, 19, 22, 10]
neib_idx[SEU, ...] = [26, 23, 17, 14, 25, 22, 16]
neib_idx[SWU, ...] = [24, 25, 15, 16, 21, 22, 12]
def index_octants(octant, neighbors):
n = 1
for j, idx in enumerate(neib_idx[octant]):
if neighbors[idx] == 1:
n |= 2**(7 - j)
return n
def is_surfacepoint(neighbors, points_LUT):
for octant in OCTANTS:
n = index_octants(octabt, neighbors)
if n not in (240, 165, 170) and points_LUT[n] > 2:
return False
return True
def is_Euler_invariant(neighbors):
"""Check if a point is Euler invariant.
Calculate Euler characteristc for each octant and sum up.
Parameters
----------
neighbors : ndarray, shape (27,)
neighbors of a point
Returns
-------
bool
"""
euler_char = 0
for octant in OCTANTS:
n = index_octants(octant, neighbors)
euler_char += LUT[n]
return euler_char == 0
def is_simple_point(neighbors):
"""Check is a point is a Simple Point.
This method is named 'N(v)_labeling' in [Lee94].
Outputs the number of connected objects in a neighborhood of a point
after this point would have been removed.
Parameters
----------
neighbors : ndarray, shape(27,)
neighbors of the point
Returns
-------
bool
Whether the point is simple or not.
"""
# copy neighbors for labeling
# ignore center pixel (i=13) when counting (see [Lee94])
cube = np.r_[neighbors[:13], neighbors[14:]]
# set initial label
label = 2
# for all point in the neighborhood
for i in range(26):
if cube[i] == 1:
# voxel has not been labeled yet
# start recursion with any octant that contains the point i
if i in (0, 1, 3, 4, 9, 10, 12):
octree_labeling(1, label, cube)
elif i in (2, 5, 11, 13):
octree_labeling(2, label, cube)
elif i in (6, 7, 14, 15):
octree_labeling(3, label, cube)
elif i in (8, 16):
octree_labeling(4, label, cube)
elif i in (17, 18, 20, 21):
octree_labeling(5, label, cube)
elif i in (19, 22):
octree_labeling(6, label, cube)
elif i in (23, 24):
octree_labeling(7, label, cube)
elif i == 25:
octree_labeling(8, label, cube)
else:
raise ValueError("Never be here. i = %s" % i)
label += 1
if label - 2 >= 2:
return False
return True
def octree_labeling(octant, label, cube):
"""This is a recursive method that calculates the number of connected
components in the 3D neighborhood after the center pixel would
have been removed.
Parameters
----------
octant : int
octant index
label : int
the current label of the center point
cube : ndarray, shape(26,)
local neighborhood of the point
"""
# check if there are points in the octant with value 1
if octant == 1:
# set points in this octant to current label
# and recursive labeling of adjacent octants
if cube[0] == 1:
cube[0] = label
if cube[1] == 1:
cube[1] = label
octree_labeling(2, label, cube)
if cube[3] == 1:
cube[3] = label
octree_labeling(3, label, cube)
if cube[4] == 1:
cube[4] = label
octree_labeling(2, label, cube)
octree_labeling(3, label, cube)
octree_labeling(4, label, cube)
if cube[9] == 1:
cube[9] = label
octree_labeling(5, label, cube)
if cube[10] == 1:
cube[10] = label
octree_labeling(2, label, cube)
octree_labeling(5, label, cube)
octree_labeling(6, label, cube)
if cube[12] == 1:
cube[12] = label
octree_labeling(3, label, cube)
octree_labeling(5, label, cube)
octree_labeling(7, label, cube)
if octant == 2:
if cube[1] == 1:
cube[1] = label
octree_labeling(1, label, cube)
if cube[4] == 1:
cube[4] = label
octree_labeling(1, label, cube)
octree_labeling(3, label, cube)
octree_labeling(4, label, cube)
if cube[10] == 1:
cube[10] = label
octree_labeling(1, label, cube)
octree_labeling(5, label, cube)
octree_labeling(6, label, cube)
if cube[2] == 1:
cube[2] = label
if cube[5] == 1:
cube[5] = label
octree_labeling(4, label, cube)
if cube[11] == 1:
cube[11] = label
octree_labeling(6, label, cube)
if cube[13] == 1:
cube[13] = label
octree_labeling(4, label, cube)
octree_labeling(6, label, cube)
octree_labeling(8, label, cube)
if octant ==3:
if cube[3] == 1:
cube[3] = label
octree_labeling(1, label, cube)
if cube[4] == 1:
cube[4] = label
octree_labeling(1, label, cube)
octree_labeling(2, label, cube)
octree_labeling(4, label, cube)
if cube[12] == 1:
cube[12] = label
octree_labeling(1, label, cube)
octree_labeling(5, label, cube)
octree_labeling(7, label, cube)
if cube[6] == 1:
cube[6] = label
if cube[7] == 1:
cube[7] = label
octree_labeling(4, label, cube)
if cube[14] == 1:
cube[14] = label
octree_labeling(7, label, cube)
if cube[15] == 1:
cube[15] = label
octree_labeling(4, label, cube)
octree_labeling(7, label, cube)
octree_labeling(8, label, cube)
if octant == 4:
if cube[4] == 1:
cube[4] = label
octree_labeling(1, label, cube)
octree_labeling(2, label, cube)
octree_labeling(3, label, cube)
if cube[5] == 1:
cube[5] = label
octree_labeling(2, label, cube)
if cube[13] == 1:
cube[13] = label
octree_labeling(2, label, cube)
octree_labeling(6, label, cube)
octree_labeling(8, label, cube)
if cube[7] == 1:
cube[7] = label
octree_labeling(3, label, cube)
if cube[15] == 1:
cube[15] = label
octree_labeling(3, label, cube)
octree_labeling(7, label, cube)
octree_labeling(8, label, cube)
if cube[8] == 1:
cube[8] = label
if cube[16] == 1:
cube[16] = label
octree_labeling(8, label, cube)
if octant == 5:
if cube[9] == 1:
cube[9] = label
octree_labeling(1, label, cube)
if cube[10] == 1:
cube[10] = label
octree_labeling(1, label, cube)
octree_labeling(2, label, cube)
octree_labeling(6, label, cube)
if cube[12] == 1:
cube[12] = label
octree_labeling(1, label, cube)
octree_labeling(3, label, cube)
octree_labeling(7, label, cube)
if cube[17] == 1:
cube[17] = label
if cube[18] == 1:
cube[18] = label
octree_labeling(6, label, cube)
if cube[20] == 1:
cube[20] = label
octree_labeling(7, label, cube)
if cube[21] == 1:
cube[21] = label
octree_labeling(6, label, cube)
octree_labeling(7, label, cube)
octree_labeling(8, label, cube)
if octant == 6:
if cube[10] == 1:
cube[10] = label
octree_labeling(1, label, cube)
octree_labeling(2, label, cube)
octree_labeling(5, label, cube)
if cube[11] == 1:
cube[11] = label
octree_labeling(2, label, cube)
if cube[13] == 1:
cube[13] = label
octree_labeling(2, label, cube)
octree_labeling(4, label, cube)
octree_labeling(8, label, cube)
if cube[18] == 1:
cube[18] = label
octree_labeling(5, label, cube)
if cube[21] == 1:
cube[21] = label
octree_labeling(5, label, cube)
octree_labeling(7, label, cube)
octree_labeling(8, label, cube)
if cube[19] == 1:
cube[19] = label
if cube[22] == 1:
cube[22] = label
octree_labeling(8, label, cube)
if octant == 7:
if cube[12] == 1:
cube[12] = label
octree_labeling(1, label, cube)
octree_labeling(3, label, cube)
octree_labeling(5, label, cube)
if cube[14] == 1:
cube[14] = label
octree_labeling(3, label, cube)
if cube[15] == 1:
cube[15] = label
octree_labeling(3, label, cube)
octree_labeling(4, label, cube)
octree_labeling(8, label, cube)
if cube[20] == 1:
cube[20] = label
octree_labeling(5, label, cube)
if cube[21] == 1:
cube[21] = label
octree_labeling(5, label, cube)
octree_labeling(6, label, cube)
octree_labeling(8, label, cube)
if cube[23] == 1:
cube[23] = label
if cube[24] == 1:
cube[24] = label
octree_labeling(8, label, cube)
if octant == 8:
if cube[13] == 1:
cube[13] = label
octree_labeling(2, label, cube)
octree_labeling(4, label, cube)
octree_labeling(6, label, cube)
if cube[15] == 1:
cube[15] = label
octree_labeling(3, label, cube)
octree_labeling(4, label, cube)
octree_labeling(7, label, cube)
if cube[16] == 1:
cube[16] = label
octree_labeling(4, label, cube)
if cube[21] == 1:
cube[21] = label
octree_labeling(5, label, cube)
octree_labeling(6, label, cube)
octree_labeling(7, label, cube)
if cube[22] == 1:
cube[22] = label
octree_labeling(6, label, cube)
if cube[24] == 1:
cube[24] = label
octree_labeling(7, label, cube)
if cube[25] == 1:
cube[25] = label
def _loop_through(img, curr_border):
"""Inner loop of compute_thin_image.
return simple_border_points as a list to be rechecked sequentially.
"""
# loop through the image
# NB: each loop is from 1 to size-1: img is padded from all sides
simple_border_points = []
### XXX: 2D images
### if the original is 2D, img.shape[0] == 3, the algorithm removes too much
### because all points are considered 'boundary' in the 3rd direction.
### Hence just bail out
if img.shape[0] == 3 and curr_border in (5, 6):
print("skipping curr_border = ", curr_border)
return []
for p in range(1, img.shape[0] - 1):
for r in range(1, img.shape[1] - 1):
for c in range(1, img.shape[2] - 1):
# check if pixel is foreground
if img[p, r, c] != 1:
continue
is_border_pt = (curr_border == 1 and img[p, r, c-1] <= 0 or #N
curr_border == 2 and img[p, r, c+1] <= 0 or #S
curr_border == 3 and img[p, r+1, c] <= 0 or #E
curr_border == 4 and img[p, r-1, c] <= 0 or #W
curr_border == 5 and img[p+1, r, c] <= 0 or #U
curr_border == 6 and img[p-1, r, c] <= 0) #B
if not is_border_pt:
# current point is not deletable
continue
neighborhood = get_neighborhood(img, p, r, c)
# check if (p, r, c) is an endpoint. An endpoint has exactly
# one neighbor in the 26-neighborhood.
# The center pixel is counted, thus r.h.s. is 2
if neighborhood.sum() == 2:
continue
# check if point is Euler invariant (condition 1 in [Lee94])
# if it is not, it's not deletable
if not is_Euler_invariant(neighborhood):
continue
# check if point is simple (i.e., deletion does not
# change connectivity in the 3x3x3 neighborhood)
# this are conditions 2 and 3 in [Lee94]
if not is_simple_point(neighborhood):
continue
# ok, add (p, r, c) to the list of simple border points
simple_border_points.append((p, r, c))
return simple_border_points
def compute_thin_image(img_in):
### prepare
img = _prepare_image(img_in)
### compute
unchanged_borders = 0
# loop through the image several times until there is no change for all
# the six border types
while unchanged_borders < 6:
unchanged_borders = 0
for curr_border in (4, 3, 2, 1, 5, 6):
simple_border_points = _loop_through(img, curr_border)
print(curr_border, " : ", simple_border_points, '\n')
# sequential re-checking to preserve connectivity when deleting
# in a parallel way
no_change = True
for pt in simple_border_points:
p, r, c = pt
neighb = get_neighborhood(img, p, r, c)
if is_simple_point(neighb):
img[p, r, c] = 0
no_change = False
else:
print(" *** ", pt, is_simple_point(neighb))
if no_change:
unchanged_borders += 1
simple_border_points = []
img = _postprocess_image(img)
return img
if __name__ == "__main__":
pass
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