import logging
import heapq
import numpy as np
import scipy.ndimage as spim
import numpy.typing as npt
from edt import edt
from skimage.morphology import disk, ball
from porespy import settings
from porespy.tools import get_tqdm, ps_round, get_border, unpad
from porespy.tools import _insert_disk_at_point
from porespy.filters import trim_disconnected_blobs
from numba import njit
from typing import Literal, List
__all__ = [
"pseudo_gravity_packing",
"pseudo_electrostatic_packing",
"_random_spheres2",
]
tqdm = get_tqdm()
logger = logging.getLogger(__name__)
@njit
def _set_seed(a):
np.random.seed(a)
def _random_spheres2(
shape: List = None,
im: npt.ArrayLike = None,
r: int = 5,
clearance: int = 0,
protrusion: int = 0,
axis: int = 0,
edges: Literal['contained', 'extended'] = 'contained',
maxiter: int = 1000,
phi: float = 1.0,
seed: float = None,
smooth: bool = True,
value: int = 1,
) -> np.ndarray:
r"""
This is an alternative implementation of random_spheres that uses the same
machinery as the pseudo packing generators. It is not as fast as the original
though.
"""
if seed is not None:
_set_seed(seed) # Initialize rng so numba sees it
np.random.seed(seed) # Also initialize numpys rng
if im is None: # If shape is given instead of im
im = np.zeros(shape, dtype=bool)
im = np.swapaxes(im, 0, axis) # Move "axis" to x position for processing
if smooth: # Smooth balls are 1 pixel smaller, so increase r
r = r + 1
mask = im == 0 # Find mask of valid points
if protrusion > 0: # Dilate mask
dt = edt(~mask)
mask = dt <= protrusion
elif protrusion < 0: # Erode mask
dt = edt(mask)
mask = dt >= abs(protrusion)
# Deal with edge mode
if edges == 'contained':
border = get_border(im.shape, thickness=1, mode='faces')
mask[border] = False
# Generate mask of valid insertion points
mask = edt(mask > 0) > r
# Initialize the queue
tmp = np.arange(mask.size)[mask.flatten()]
inds = np.vstack(np.unravel_index(tmp, im.shape)).T
order = np.random.permutation(np.arange(len(tmp)))
q = inds[order, :]
# Compute maxiter
if phi < 1.0:
Vsph = 4/3*np.pi*(r**3) if im.ndim == 3 else np.pi*(r**2)
Vbulk = np.prod(im.shape)
maxiter = min(int(np.round(phi*Vbulk/Vsph)), maxiter)
# Finally run it
im_new = np.zeros_like(im, dtype=bool)
im_new, count = _do_packing(im_new, mask, q, r, True, clearance, smooth, maxiter)
logger.debug(f'A total of {count} spheres were added')
im_new = np.swapaxes(im_new, 0, axis)
im = np.copy(im).astype(type(value))
im[im_new] = value
return im
[docs]
def pseudo_gravity_packing(
shape: List = None,
im: npt.ArrayLike = None,
r: int = 5,
clearance: int = 0,
protrusion: int = 0,
axis: int = 0,
edges: Literal['contained', 'extended'] = 'contained',
maxiter: int = 1000,
phi: float = 1.0,
seed: int = None,
smooth: bool = True,
value: int = 1,
) -> np.ndarray:
r"""
Iteratively inserts spheres at the lowest accessible point in an image,
mimicking a gravity packing.
Parameters
----------
shape : list
The shape of the image to create. This is equivalent to passing an array
of `False` values of the desired size to `im`.
im : ndarray
Image with `False` indicating the voxels where spheres should be
inserted. This can be used to insert spheres into an image that already
has some features (e.g. half filled with larger spheres, or a cylindrical
plug).
r : int
The radius of the spheres to be added
clearance : int (default is 0)
The amount space to add between neighboring spheres. The value can be
negative for overlapping spheres, but ``abs(clearance) > r``.
protrusion : int (optional, default=0)
The amount that spheres are allowed to protrude beyond the active phase.
A negative number will create clearance between spheres and the background.
axis : int (default is 0)
The axis along which gravity acts, directed from the end (-1) towards the
start (0).
phi : float (default is 1.0)
The "solid volume fraction" of spheres to add (considering spheres as solid).
This is used to calculate the discrete number of spheres, *N*, required
based on the total volume of the image. If *N* is less than `maxiter` then
`maxiter` will be set to *N*. Note that this number is not quite accurate
when the `edges='extended'` since it's not possible to know how much of the
sphere will be cutoff by the edge.
maxiter : int (default is 1000)
The maximum number of spheres to add. This places a hard limit on the number
of spheres even if `phi` is specified.
edges : string (default is 'contained')
Controls how spheres at the edges of the image are handled. Options are:
============ ================================================================
edges description
============ ================================================================
'contained' Spheres are all completely within the image
'extended' Spheres are allowed to extend beyond the edge of the
image. In this mode the volume fraction will be less that
requested since some spheres extend beyond the image, but their
entire volume is counted as added for computational efficiency.
============ ================================================================
seed : int, optional, default = `None`
The seed to supply to the random number generator. Because this function
uses ``numba`` for speed, calling the normal ``numpy.random.seed(<seed>)``
has no effect. To get a repeatable image, the seed must be passed to the
function so it can be initialized the way ``numba`` requires. The default
is ``None``, which means each call will produce a new realization.
smooth : bool, default = `True`
Controls whether or not the spheres have the small pip each face.
value : int, default = 1
The value of insert for the spheres. The default is 1, which puts holes into
the background. Values other than 1 make it easy to add spheres repeatedly
and identify which were added on each step.
Returns
-------
spheres : ndarray
An image the same size as `im` with spheres indicated by `value`.
The spheres are only inserted at locations that are accessible
from the top of the image.
Examples
--------
`Click here
<https://porespy.org/examples/generators/reference/pseudo_gravity_packing.html>`_
to view online example.
"""
logger.debug(f'Adding spheres of radius {r}')
if seed is not None: # Initialize rng so numba sees it
_set_seed(seed)
np.random.seed(seed)
if im is None: # If shape was given, generate empty im
im = np.zeros(shape, dtype=bool)
im = np.swapaxes(im, 0, axis) # Move specified axis to 0 position
if smooth: # If smooth spheres are used, increase r to compensate
r = r + 1
# Shrink or grow mask to allow for clearance
mask = im == 0 # Find mask of valid points
if protrusion > 0: # Dilate mask
dt = edt(~mask)
mask = dt <= protrusion
elif protrusion < 0: # Erode mask
dt = edt(mask)
mask = dt >= abs(protrusion)
# Deal with edges
if edges == 'contained':
im_padded = np.pad(mask, pad_width=1, mode='constant', constant_values=False)
if smooth:
mask = unpad(edt(im_padded) >= r, 1)
else:
mask = unpad(edt(im_padded) > r, 1)
else:
mask = edt(mask) > r
# Finalize the mask of valid insertion points
inlets = np.zeros_like(im)
inlets[-r:, ...] = True
s = ball(1) if im.ndim == 3 else disk(1)
mask = trim_disconnected_blobs(im=mask, inlets=inlets, strel=s)
# Generate elevation values to initialize queue
from porespy.generators import ramp
tmp = np.arange(im.size)[mask.flatten()]
inds = np.vstack(np.unravel_index(tmp, im.shape)).T
vals = ramp(im.shape, inlet=0, outlet=im.shape[0], axis=0)*mask
vals = vals.flatten()[mask.flatten()]
order = _randomized_argsort(inds, vals)
q = inds[order, :]
# Compute maxiter
if phi < 1.0:
Vsph = 4/3*np.pi*(r**3) if im.ndim == 3 else np.pi*(r**2)
Vbulk = np.prod(im.shape)
maxiter = min(int(np.round(phi*Vbulk/Vsph)), maxiter)
# Finally insert spheres
im_new = np.zeros_like(im, dtype=bool)
im_new, count = _do_packing(im_new, mask, q, r, True, clearance, smooth, maxiter)
logger.debug(f'A total of {count} spheres were added')
im = np.copy(im).astype(type(value))
im[im_new] = value
im = np.swapaxes(im, 0, axis)
return im
[docs]
def pseudo_electrostatic_packing(
shape: List = None,
im: npt.ArrayLike = None,
r: int = 5,
sites=None,
clearance: int = 0,
protrusion: int = 0,
edges: Literal['extended', 'contained'] = 'extended',
phi: float = 1.0,
maxiter: int = 1000,
seed: int = None,
smooth: bool = True,
compactness: float = 1.0,
value: int = 1,
):
r"""
Iterativley inserts spheres as close to the given sites as possible.
Parameters
----------
shape : list
The shape of the image to create. This is equivalent to passing an array
of `False` values of the desired size to `im`.
im : ndarray
Image with `False` indicating the voxels where spheres should be
inserted. This can be used to insert spheres into an image that already
has some features (e.g. half filled with larger spheres, or a cylindrical
plug).
r : int
Radius of spheres to insert.
sites : ndarray (optional)
An image with ``True`` values indicating the electrostatic attraction
points. If this is not given then the peaks in the distance transform of
`im` are used, which corresponds to the center of the image for a blank
input.
clearance : int (optional, default=0)
The amount of space to put between each sphere. Negative values are
acceptable to create overlaps, but ``abs(clearance) < r``.
protrusion : int (optional, default=0)
The amount that spheres are allowed to protrude beyond the active phase.
A negative number will create clearance between spheres and the background.
maxiter : int (optional, default=1000)
The maximum number of spheres to insert.
phi : float (default is 1.0)
The "solid volume fraction" of spheres to add (considering spheres as solid).
This is used to calculate the discrete number of spheres, *N*, required
based on the total volume of the image. If *N* is less than `maxiter` then
`maxiter` will be set to *N*. Note that this number is not quite accurate
when the `edges='extended'` since it's not possible to know how much of the
sphere will be cutoff by the edge.
edges : string (default is 'contained')
Controls how spheres at the edges of the image are handled. Options are:
============ ================================================================
edges description
============ ================================================================
'contained' Spheres are all completely within the image
'extended' Spheres are allowed to extend beyond the edge of the
image. In this mode the volume fraction will be less that
requested since some spheres extend beyond the image, but their
entire volume is counted as added for computational efficiency.
============ ================================================================
seed : int, optional, default = `None`
The seed to supply to the random number generator. Because this function
uses ``numba`` for speed, calling the normal ``numpy.random.seed(<seed>)``
has no effect. To get a repeatable image, the seed must be passed to the
function so it can be initialized the way ``numba`` requires. The default
is ``None``, which means each call will produce a new realization.
compactness : float
Controls how tightly the spheres are grouped together. A value of 1.0
(default) results in the tighest possible grouping while values < 1.0
give more loosely or imperfectly packed spheres.
value : int, default = 1
The value of insert for the spheres. The default is 1, which puts holes
into to the background. Values other than 1 (Foreground) make
it easy to add spheres repeated and identify which were added on each step.
Returns
-------
im : ndarray
An image with inserted spheres indicated by ``True``
Examples
--------
`Click here
<https://porespy.org/examples/generators/reference/pseudo_electrostatic_packing.html>`_
to view online example.
"""
if seed is not None: # Initialize rng so numba sees it
_set_seed(seed)
np.random.seed(seed)
if im is None: # If shape was given, generate empty im
im = np.zeros(shape, dtype=bool)
if smooth: # If smooth spheres are used, increase r to compensate
r = r + 1
mask = im == 0 # Find mask of valid points
if protrusion > 0: # Dilate mask
dt = edt(~mask)
mask = dt <= protrusion
elif protrusion < 0: # Erode mask
dt = edt(mask)
mask = dt >= abs(protrusion)
if edges == 'contained':
borders = get_border(mask.shape, thickness=1, mode='faces')
mask[borders] = 0
if sites is None:
dt = edt(mask)
dt = spim.gaussian_filter(dt, sigma=0.5)
strel = ps_round(r, ndim=im.ndim, smooth=True)
sites = (spim.maximum_filter(dt, footprint=strel) == dt)*(mask > 0)
if np.any(dt == np.inf): # In case above method failed.
sites = np.zeros_like(im)
inds = tuple((np.array(im.shape)/2).astype(int))
sites[inds] = True
dt2 = edt(~sites) # Where spheres are attracted to
dt = edt(mask + sites) # Where spheres can fit
mask = mask * (dt2 > r) * (dt > r)
mask = mask.astype(bool)
# Initialize queue
tmp = np.arange(im.size)[mask.flatten()]
inds = np.vstack(np.unravel_index(tmp, im.shape)).T
vals = np.digitize(dt2[mask], bins=np.arange(1, dt2.max(), int(1/compactness)))
order = _randomized_argsort(inds, vals)
q = inds[order, :]
# Compute maxiter
if phi < 1.0:
Vsph = 4/3*np.pi*(r**3) if im.ndim == 3 else np.pi*(r**2)
Vbulk = np.prod(im.shape)
maxiter = min(int(np.round(phi*Vbulk/Vsph)), maxiter)
# Finally run it
im_new = np.zeros_like(im, dtype=bool)
im_new, count = _do_packing(im_new, mask, q, r, True, clearance, smooth, maxiter)
logger.debug(f'A total of {count} spheres were added')
im = np.copy(im).astype(type(value))
im[im_new] = value
return im
def _randomized_argsort(inds, vals):
r"""
A utility function to take a sorted list and randomize the order of the elements
with the same value. So if the list is [21, 44, 16, 21, 44, 37], np.argsort
would return [2, 0, 3, 5, 1, 4], this function will return and alternative set of
args [2, 0|3, 3|0, 1|5, 5|1, 4].
"""
order = np.argsort(vals)
_, counts = np.unique(vals[order], return_counts=True)
counts = np.cumsum(np.hstack(([0], counts)))
for i in range(len(counts)-1):
orig_order = order[counts[i]:counts[i+1]]
new_order = np.random.permutation(orig_order)
order[counts[i]:counts[i+1]] = new_order
return order
# @njit
def _do_packing(im, mask, q, r, value, clearance, smooth, maxiter):
count = 0
for i in range(len(q)):
cen = tuple(q[i, :])
if mask[cen]:
count += 1
im = _insert_disk_at_point(
im=im,
coords=cen,
r=r,
v=value,
overwrite=True,
smooth=smooth,
)
mask = _insert_disk_at_point(
im=mask,
coords=cen,
r=2*r + clearance,
v=False,
overwrite=True,
smooth=smooth,
)
if count >= maxiter:
break
return im, count
if __name__ == "__main__":
import porespy as ps
import matplotlib.pyplot as plt
import scipy.ndimage as spim
shape = [200, 200]
# %% Electrostatic packing
fig, ax = plt.subplots(2, 2)
if 1:
sites = np.zeros([300, 300], dtype=bool)
sites[150, 150] = True
im = ps.generators.pseudo_electrostatic_packing(
shape=[300, 300],
r=15,
sites=sites,
maxiter=30,
edges='contained',
clearance=0,
smooth=False,
compactness=0.1,
)
ax[0][0].imshow(im)
if 1:
blobs = ps.generators.blobs([400, 400], porosity=0.75, seed=0)
im = ps.generators.pseudo_electrostatic_packing(
im=~blobs,
r=10,
clearance=0,
protrusion=0,
edges='contained',
seed=0,
phi=.3,
smooth=True,
value=2,
)
im2 = ps.generators.pseudo_electrostatic_packing(
im=im,
sites=im == 2,
r=5,
clearance=1,
protrusion=0,
edges='extended',
seed=0,
phi=1.0,
smooth=True,
value=3,
)
ax[0][1].imshow(im2 + (im == 2)*2, origin='lower')
# %% Gravity packing
if 1:
im = pseudo_gravity_packing(
shape=shape,
r=16,
clearance=0,
edges='contained',
phi=.2,
smooth=False,
value=2,
)
im = pseudo_gravity_packing(
im=im,
r=8,
clearance=2,
protrusion=-2,
edges='extended',
seed=0,
phi=0.25,
maxiter=1000,
smooth=False,
value=3,
)
im = pseudo_gravity_packing(
im=im,
r=12,
clearance=4,
protrusion=-4,
edges='contained',
seed=0,
smooth=True,
value=4,
)
ax[1][0].imshow(im, origin='lower')
# %% Random packing
if 1:
im = _random_spheres2(
shape=shape,
r=16,
clearance=5,
edges='extended',
seed=0,
phi=.25,
smooth=False,
value=3,
)
im = _random_spheres2(
im=im,
r=8,
clearance=5,
protrusion=5,
edges='contained',
seed=0,
phi=0.1,
maxiter=1000,
smooth=False,
value=2,
)
im = _random_spheres2(
im=im,
r=12,
clearance=5,
protrusion=5,
edges='contained',
seed=0,
smooth=True,
value=1
)
ax[1][1].imshow(im, origin='lower')