def region_surface_areas(regions, voxel_size=1, strel=None):
r"""
Extracts the surface area of each region in a labeled image.
Optionally, it can also find the the interfacial area between all
adjoining regions.
Parameters
----------
regions : ND-array
An image of the pore space partitioned into individual pore regions.
Note that zeros in the image will not be considered for area
calculation.
voxel_size : scalar
The resolution of the image, expressed as the length of one side of a
voxel, so the volume of a voxel would be **voxel_size**-cubed. The
default is 1.
strel : array_like
The structuring element used to blur the region. If not provided,
then a spherical element (or disk) with radius 1 is used. See the
docstring for ``mesh_region`` for more details, as this argument is
passed to there.
Returns
-------
result : list
A list containing the surface area of each region, offset by 1, such
that the surface area of region 1 is stored in element 0 of the list.
"""
print('-' * 60)
print('Finding surface area of each region')
im = regions.copy()
# Get 'slices' into im for each pore region
slices = spim.find_objects(im)
# Initialize arrays
Ps = np.arange(1, np.amax(im) + 1)
sa = np.zeros_like(Ps, dtype=float)
# Start extracting marching cube area from im
for i in tqdm(Ps):
reg = i - 1
if slices[reg] is not None:
s = extend_slice(slices[reg], im.shape)
sub_im = im[s]
mask_im = sub_im == i
mesh = mesh_region(region=mask_im, strel=strel)
sa[reg] = mesh_surface_area(mesh)
result = sa * voxel_size**2
return result
def region_interface_areas(regions, areas, voxel_size=1, strel=None):
r"""
Calculates the interfacial area between all pairs of adjecent regions
Parameters
----------
regions : ND-array
An image of the pore space partitioned into individual pore regions.
Note that zeros in the image will not be considered for area
calculation.
areas : array_like
A list containing the areas of each regions, as determined by
``region_surface_area``. Note that the region number and list index
are offset by 1, such that the area for region 1 is stored in
``areas[0]``.
voxel_size : scalar
The resolution of the image, expressed as the length of one side of a
voxel, so the volume of a voxel would be **voxel_size**-cubed. The
default is 1.
strel : array_like
The structuring element used to blur the region. If not provided,
then a spherical element (or disk) with radius 1 is used. See the
docstring for ``mesh_region`` for more details, as this argument is
passed to there.
Returns
-------
result : named_tuple
A named-tuple containing 2 arrays. ``conns`` holds the connectivity
information and ``area`` holds the result for each pair. ``conns`` is
a N-regions by 2 array with each row containing the region number of an
adjacent pair of regions. For instance, if ``conns[0, 0]`` is 0 and
``conns[0, 1]`` is 5, then row 0 of ``area`` contains the interfacial
area shared by regions 0 and 5.
"""
print('-' * 60)
print('Finding interfacial areas between each region')
from skimage.morphology import disk, ball
im = regions.copy()
if im.ndim != im.squeeze().ndim:
warnings.warn('Input image conains a singleton axis:' + str(im.shape) +
' Reduce dimensionality with np.squeeze(im) to avoid' +
' unexpected behavior.')
# cube_elem = square if im.ndim == 2 else cube
ball_elem = disk if im.ndim == 2 else ball
# Get 'slices' into im for each region
slices = spim.find_objects(im)
# Initialize arrays
Ps = np.arange(1, np.amax(im) + 1)
sa = np.zeros_like(Ps, dtype=float)
sa_combined = [] # Difficult to preallocate since number of conns unknown
cn = []
# Start extracting area from im
for i in tqdm(Ps):
reg = i - 1
if slices[reg] is not None:
s = extend_slice(slices[reg], im.shape)
sub_im = im[s]
mask_im = sub_im == i
sa[reg] = areas[reg]
im_w_throats = spim.binary_dilation(input=mask_im,
structure=ball_elem(1))
im_w_throats = im_w_throats * sub_im
Pn = np.unique(im_w_throats)[1:] - 1
for j in Pn:
if j > reg:
cn.append([reg, j])
merged_region = im[(
min(slices[reg][0].start, slices[j][0].start)
):max(slices[reg][0].stop, slices[j][0].stop), (
min(slices[reg][1].start, slices[j][1].start)
):max(slices[reg][1].stop, slices[j][1].stop)]
merged_region = ((merged_region == reg + 1) +
(merged_region == j + 1))
mesh = mesh_region(region=merged_region, strel=strel)
sa_combined.append(mesh_surface_area(mesh))
# Interfacial area calculation
cn = np.array(cn)
ia = 0.5 * (sa[cn[:, 0]] + sa[cn[:, 1]] - sa_combined)
ia[ia <= 0] = 1
result = namedtuple('interfacial_areas', ('conns', 'area'))
result.conns = cn
result.area = ia * voxel_size**2
return result