# Source code for porespy.filters.__funcs__

from collections import namedtuple
import scipy as sp
import numpy as np
import operator as op
import scipy.ndimage as spim
import scipy.spatial as sptl
import warnings
from scipy.signal import fftconvolve
from tqdm import tqdm
from numba import jit
from skimage.segmentation import clear_border
from skimage.morphology import ball, disk, square, cube, diamond, octahedron
from skimage.morphology import reconstruction, watershed
from porespy.tools import randomize_colors, fftmorphology
from porespy.tools import get_border, extend_slice, extract_subsection
from porespy.tools import ps_disk, ps_ball
from porespy.tools import _create_alias_map

[docs]def trim_small_clusters(im, size=1): r""" Remove isolated voxels or clusters smaller than a given size Parameters ---------- im : ND-array The binary image from which voxels are to be removed size : scalar The threshold size of clusters to trim. As clusters with this many voxels or fewer will be trimmed. The default is 1 so only single voxels are removed. Returns ------- im : ND-image A copy of im with clusters of voxels smaller than the given size removed. """ if im.dims == 2: strel = disk(1) elif im.ndims == 3: strel = ball(1) else: raise Exception('Only 2D or 3D images are accepted') filtered_array = sp.copy(im) labels, N = spim.label(filtered_array, structure=strel) id_sizes = sp.array(spim.sum(im, labels, range(N + 1))) area_mask = (id_sizes <= size) filtered_array[area_mask[labels]] = 0 return filtered_array
[docs]def hold_peaks(im, axis=-1): r""" Replaces each voxel with the highest value along the given axis Parameters ---------- im : ND-image A greyscale image whose peaks are to """ A = im B = np.swapaxes(A, axis, -1) updown = np.empty((*B.shape[:-1], B.shape[-1]+1), B.dtype) updown[..., 0], updown[..., -1] = -1, -1 np.subtract(B[..., 1:], B[..., :-1], out=updown[..., 1:-1]) chnidx = np.where(updown) chng = updown[chnidx] pkidx, = np.where((chng[:-1] > 0) & (chng[1:] < 0) | (chnidx[-1][:-1] == 0)) pkidx = (*map(op.itemgetter(pkidx), chnidx),) out = np.zeros_like(A) aux = out.swapaxes(axis, -1) aux[(*map(op.itemgetter(slice(1, None)), pkidx),)] = np.diff(B[pkidx]) aux[..., 0] = B[..., 0] result = out.cumsum(axis=axis) return result
[docs]def distance_transform_lin(im, axis=0, mode='both'): r""" Replaces each void voxel with the linear distance to the nearest solid voxel along the specified axis. Parameters ---------- im : ND-array The image of the porous material with True values indicating the void phase (or phase of interest) axis : int The direction along which the distance should be measured, the default is 0 (i.e. along the x-direction) mode : string Controls how the distance is measured. Options are: 'forward' - Distances are measured in the increasing direction along the specified axis 'reverse' - Distances are measured in the reverse direction. *'backward'* is also accepted. 'both' - Distances are calculated in both directions (by recursively calling itself), then reporting the minimum value of the two results. Returns ------- image : ND-array A copy of im with each foreground voxel containing the distance to the nearest background along the specified axis. """ 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.') if mode in ['backward', 'reverse']: im = sp.flip(im, axis) im = distance_transform_lin(im=im, axis=axis, mode='forward') im = sp.flip(im, axis) return im elif mode in ['both']: im_f = distance_transform_lin(im=im, axis=axis, mode='forward') im_b = distance_transform_lin(im=im, axis=axis, mode='backward') return sp.minimum(im_f, im_b) else: b = sp.cumsum(im > 0, axis=axis) c = sp.diff(b*(im == 0), axis=axis) d = sp.minimum.accumulate(c, axis=axis) if im.ndim == 1: e = sp.pad(d, pad_width=[1, 0], mode='constant', constant_values=0) elif im.ndim == 2: ax = [[[1, 0], [0, 0]], [[0, 0], [1, 0]]] e = sp.pad(d, pad_width=ax[axis], mode='constant', constant_values=0) elif im.ndim == 3: ax = [[[1, 0], [0, 0], [0, 0]], [[0, 0], [1, 0], [0, 0]], [[0, 0], [0, 0], [1, 0]]] e = sp.pad(d, pad_width=ax[axis], mode='constant', constant_values=0) f = im*(b + e) return f
[docs]def snow_partitioning(im, dt=None, r_max=4, sigma=0.4, return_all=False, mask=True, randomize=True): r""" Partitions the void space into pore regions using a marker-based watershed algorithm, with specially filtered peaks as markers. The SNOW network extraction algorithm (Sub-Network of an Over-segmented Watershed) was designed to handle to perculiarities of high porosity materials, but it applies well to other materials as well. Parameters ---------- im : array_like A boolean image of the domain, with True indicating the pore space and False elsewhere. dt : array_like, optional The distance transform of the pore space. This is done automatically if not provided, but if the distance transform has already been computed then supplying it can save some time. r_max : int The radius of the spherical structuring element to use in the Maximum filter stage that is used to find peaks. The default is 4 sigma : float The standard deviation of the Gaussian filter used in step 1. The default is 0.4. If 0 is given then the filter is not applied, which is useful if a distance transform is supplied as the im argument that has already been processed. return_all : boolean If set to True a named tuple is returned containing the original image, the distance transform, the filtered peaks, and the final pore regions. The default is False mask : boolean Apply a mask to the regions where the solid phase is. Default is True randomize : boolean If True (default), then the region colors will be randomized before returning. This is helpful for visualizing otherwise neighboring regions have simlar coloring are are hard to distinguish. Returns ------- image : ND-array An image the same shape as im with the void space partitioned into pores using a marker based watershed with the peaks found by the SNOW algorithm [1]. Notes ----- If return_all is True then a **named tuple** is returned containing all of the images used during the process. They can be access as attriutes with the following names: * im: The binary image of the void space * dt: The distance transform of the image * peaks: The peaks of the distance transform after applying the steps of the SNOW algorithm * regions: The void space partitioned into pores using a marker based watershed with the peaks found by the SNOW algorithm References ---------- [1] Gostick, J. "A versatile and efficient network extraction algorithm using marker-based watershed segmenation". Physical Review E. (2017) """ tup = namedtuple('results', field_names=['im', 'dt', 'peaks', 'regions']) print('_'*60) print("Beginning SNOW Algorithm") im_shape = sp.array(im.shape) if im.dtype is not bool: print('Converting supplied image (im) to boolean') im = im > 0 if dt is None: print('Peforming Distance Transform') if sp.any(im_shape == 1): ax = sp.where(im_shape == 1)[0][0] dt = spim.distance_transform_edt(input=im.squeeze()) dt = sp.expand_dims(dt, ax) else: dt = spim.distance_transform_edt(input=im) tup.im = im tup.dt = dt if sigma > 0: print('Applying Gaussian blur with sigma =', str(sigma)) dt = spim.gaussian_filter(input=dt, sigma=sigma) peaks = find_peaks(dt=dt, r_max=r_max) print('Initial number of peaks: ', spim.label(peaks)[1]) peaks = trim_saddle_points(peaks=peaks, dt=dt, max_iters=500) print('Peaks after trimming saddle points: ', spim.label(peaks)[1]) peaks = trim_nearby_peaks(peaks=peaks, dt=dt) peaks, N = spim.label(peaks) print('Peaks after trimming nearby peaks: ', N) tup.peaks = peaks if mask: mask_solid = im > 0 else: mask_solid = None regions = watershed(image=-dt, markers=peaks, mask=mask_solid) if randomize: regions = randomize_colors(regions) if return_all: tup.regions = regions return tup else: return regions
[docs]def snow_partitioning_n(im, r_max=4, sigma=0.4, return_all=True, mask=True, randomize=False, alias=None): r""" This function partitions an imaging oontain an arbitrary number of phases into regions using a marker-based watershed segmentation. Its an extension of snow_partitioning function with all phases partitioned together. Parameters ---------- im : ND-array Image of porous material where each phase is represented by unique integer starting from 1 (0's are ignored). r_max : scalar The radius of the spherical structuring element to use in the Maximum filter stage that is used to find peaks. The default is 4. sigma : scalar The standard deviation of the Gaussian filter used. The default is 0.4. If 0 is given then the filter is not applied, which is useful if a distance transform is supplied as the im argument that has already been processed. return_all : boolean (default is False) If set to True a named tuple is returned containing the original image, the combined distance transform, list of each phase max label, and the final combined regions of all phases. mask : boolean (default is True) Apply a mask to the regions which are not under concern. randomize : boolean If True (default), then the region colors will be randomized before returning. This is helpful for visualizing otherwise neighboring regions have similar coloring and are hard to distinguish. alias : dict (Optional) A dictionary that assigns unique image label to specific phases. For example {1: 'Solid'} will show all structural properties associated with label 1 as Solid phase properties. If None then default labelling will be used i.e {1: 'Phase1',..}. Returns ------- An image the same shape as im with the all phases partitioned into regions using a marker based watershed with the peaks found by the SNOW algorithm [1]. If return_all is True then a **named tuple** is returned with the following attribute: * im : The actual image of the porous material * dt : The combined distance transform of the image * phase_max_label : The list of max label of each phase in order to distinguish between each other * regions : The partitioned regions of n phases using a marker based watershed with the peaks found by the SNOW algorithm References ---------- [1] Gostick, J. "A versatile and efficient network extraction algorithm using marker-based watershed segmentation". Physical Review E. (2017) [2] Khan, ZA et al. "Dual network extraction algorithm to investigate multiple transport processes in porous materials: Image-based modeling of pore and grain-scale processes". Computers in Chemical Engineering. (2019) See Also ---------- snow_partitioning Notes ----- In principle it is possible to perform a distance transform on each phase separately, merge these into a single image, then apply the watershed only once. This, however, has been found to create edge artifacts between regions arising from the way watershed handles plateaus in the distance transform. To overcome this, this function applies the watershed to each of the distance transforms separately, then merges the segmented regions back into a single image. """ # Get alias if provided by user al = _create_alias_map(im=im, alias=alias) # Perform snow on each phase and merge all segmentation and dt together phases_num = sp.unique(im * 1) phases_num = sp.trim_zeros(phases_num) combined_dt = 0 combined_region = 0 num = [0] for i in phases_num: print('_' * 60) if alias is None: print('Processing Phase {}'.format(i)) else: print('Processing Phase {}'.format(al[i])) phase_snow = snow_partitioning(im == i, dt=None, r_max=r_max, sigma=sigma, return_all=return_all, mask=mask, randomize=randomize) if len(phases_num) == 1 and phases_num == 1: combined_dt = phase_snow.dt combined_region = phase_snow.regions else: combined_dt += phase_snow.dt phase_snow.regions *= phase_snow.im phase_snow.regions += num[i - 1] phase_ws = phase_snow.regions * phase_snow.im phase_ws[phase_ws == num[i - 1]] = 0 combined_region += phase_ws num.append(sp.amax(combined_region)) if return_all: tup = namedtuple('results', field_names=['im', 'dt', 'phase_max_label', 'regions']) tup.im = im tup.dt = combined_dt tup.phase_max_label = num[1:] tup.regions = combined_region return tup else: return combined_region
[docs]def find_peaks(dt, r_max=4, footprint=None): r""" Returns all local maxima in the distance transform Parameters ---------- dt : ND-array The distance transform of the pore space. This may be calculated and filtered using any means desired. r_max : scalar The size of the structuring element used in the maximum filter. This controls the localness of any maxima. The default is 4 voxels. footprint : ND-array Specifies the shape of the structuring element used to define the neighborhood when looking for peaks. If none is specified then a spherical shape is used (or circular in 2D). Returns ------- image : ND-array An array of booleans with True values at the location of any local maxima. Notes ----- It is also possible ot the peak_local_max function from the skimage.feature module as follows: peaks = peak_local_max(image=dt, min_distance=r, exclude_border=0, indices=False) This automatically uses a square structuring element which is significantly faster than using a circular or spherical element. """ im = dt > 0 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.') if footprint is None: if im.ndim == 2: footprint = disk elif im.ndim == 3: footprint = ball else: raise Exception("only 2-d and 3-d images are supported") mx = spim.maximum_filter(dt + 2*(~im), footprint=footprint(r_max)) peaks = (dt == mx)*im return peaks
[docs]def reduce_peaks(peaks): r""" Any peaks that are broad or elongated are replaced with a single voxel that is located at the center of mass of the original voxels. Parameters ---------- peaks : ND-image An image containing True values indicating peaks in the distance transform Returns ------- image : ND-array An array with the same number of isolated peaks as the original image, but fewer total voxels. Notes ----- The center of mass of a group of voxels is used as the new single voxel, so if the group has an odd shape (like a horse shoe), the new voxel may *not* lie on top of the original set. """ if peaks.ndim == 2: strel = square else: strel = cube markers, N = spim.label(input=peaks, structure=strel(3)) inds = spim.measurements.center_of_mass(input=peaks, labels=markers, index=sp.arange(1, N+1)) inds = sp.floor(inds).astype(int) # Centroid may not be on old pixel, so create a new peaks image peaks_new = sp.zeros_like(peaks, dtype=bool) peaks_new[tuple(inds.T)] = True return peaks_new
[docs]def trim_saddle_points(peaks, dt, max_iters=10): r""" Removes peaks that were mistakenly identified because they lied on a saddle or ridge in the distance transform that was not actually a true local peak. Parameters ---------- peaks : ND-array A boolean image containing True values to mark peaks in the distance transform (dt) dt : ND-array The distance transform of the pore space for which the true peaks are sought. max_iters : int The maximum number of iterations to run while eroding the saddle points. The default is 10, which is usually not reached; however, a warning is issued if the loop ends prior to removing all saddle points. Returns ------- image : ND-array An image with fewer peaks than the input image References ---------- [1] Gostick, J. "A versatile and efficient network extraction algorithm using marker-based watershed segmenation". Physical Review E. (2017) """ peaks = sp.copy(peaks) if dt.ndim == 2: from skimage.morphology import square as cube else: from skimage.morphology import cube labels, N = spim.label(peaks) slices = spim.find_objects(labels) for i in range(N): s = extend_slice(s=slices[i], shape=peaks.shape, pad=10) peaks_i = labels[s] == i+1 dt_i = dt[s] im_i = dt_i > 0 iters = 0 peaks_dil = sp.copy(peaks_i) while iters < max_iters: iters += 1 peaks_dil = spim.binary_dilation(input=peaks_dil, structure=cube(3)) peaks_max = peaks_dil*sp.amax(dt_i*peaks_dil) peaks_extended = (peaks_max == dt_i)*im_i if sp.all(peaks_extended == peaks_i): break # Found a true peak elif sp.sum(peaks_extended*peaks_i) == 0: peaks_i = False break # Found a saddle point peaks[s] = peaks_i if iters >= max_iters: print('Maximum number of iterations reached, consider' + 'running again with a larger value of max_iters') return peaks
[docs]def trim_nearby_peaks(peaks, dt): r""" Finds pairs of peaks that are nearer to each other than to the solid phase, and removes the peak that is closer to the solid. Parameters ---------- peaks : ND-array A boolean image containing True values to mark peaks in the distance transform (dt) dt : ND-array The distance transform of the pore space for which the true peaks are sought. Returns ------- image : ND-array An array the same size as peaks containing a subset of the peaks in the original image. Notes ----- Each pair of peaks is considered simultaneously, so for a triplet of peaks each pair is considered. This ensures that only the single peak that is furthest from the solid is kept. No iteration is required. References ---------- [1] Gostick, J. "A versatile and efficient network extraction algorithm using marker-based watershed segmenation". Physical Review E. (2017) """ peaks = sp.copy(peaks) if dt.ndim == 2: from skimage.morphology import square as cube else: from skimage.morphology import cube peaks, N = spim.label(peaks, structure=cube(3)) crds = spim.measurements.center_of_mass(peaks, labels=peaks, index=sp.arange(1, N+1)) crds = sp.vstack(crds).astype(int) # Convert to numpy array of ints # Get distance between each peak as a distance map tree = sptl.cKDTree(data=crds) temp = tree.query(x=crds, k=2) nearest_neighbor = temp[1][:, 1] dist_to_neighbor = temp[0][:, 1] del temp, tree # Free-up memory dist_to_solid = dt[tuple(crds.T)] # Get distance to solid for each peak hits = sp.where(dist_to_neighbor < dist_to_solid)[0] # Drop peak that is closer to the solid than it's neighbor drop_peaks = [] for peak in hits: if dist_to_solid[peak] < dist_to_solid[nearest_neighbor[peak]]: drop_peaks.append(peak) else: drop_peaks.append(nearest_neighbor[peak]) drop_peaks = sp.unique(drop_peaks) # Remove peaks from image slices = spim.find_objects(input=peaks) for s in drop_peaks: peaks[slices[s]] = 0 return (peaks > 0)
[docs]def find_disconnected_voxels(im, conn=None): r""" This identifies all pore (or solid) voxels that are not connected to the edge of the image. This can be used to find blind pores, or remove artifacts such as solid phase voxels that are floating in space. Parameters ---------- im : ND-image A Boolean image, with True values indicating the phase for which disconnected voxels are sought. conn : int For 2D the options are 4 and 8 for square and diagonal neighbors, while for the 3D the options are 6 and 26, similarily for square and diagonal neighbors. The default is max Returns ------- image : ND-array An ND-image the same size as im, with True values indicating voxels of the phase of interest (i.e. True values in the original image) that are not connected to the outer edges. Notes ----- image : ND-array The returned array (e.g. holes) be used to trim blind pores from im using: im[holes] = False """ 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.') if im.ndim == 2: if conn == 4: strel = disk(1) elif conn in [None, 8]: strel = square(3) elif im.ndim == 3: if conn == 6: strel = ball(1) elif conn in [None, 26]: strel = cube(3) labels, N = spim.label(input=im, structure=strel) holes = clear_border(labels=labels) > 0 return holes
[docs]def fill_blind_pores(im): r""" Fills all pores that are not connected to the edges of the image. Parameters ---------- im : ND-array The image of the porous material Returns ------- image : ND-array A version of im but with all the disconnected pores removed. See Also -------- find_disconnected_voxels """ im = sp.copy(im) holes = find_disconnected_voxels(im) im[holes] = False return im
[docs]def trim_floating_solid(im): r""" Removes all solid that that is not attached to the edges of the image. Parameters ---------- im : ND-array The image of the porous material Returns ------- image : ND-array A version of im but with all the disconnected solid removed. See Also -------- find_disconnected_voxels """ im = sp.copy(im) holes = find_disconnected_voxels(~im) im[holes] = True return im
[docs]def trim_nonpercolating_paths(im, inlet_axis=0, outlet_axis=0): r""" Removes all nonpercolating paths between specified edges This function is essential when performing transport simulations on an image, since image regions that do not span between the desired inlet and outlet do not contribute to the transport. Parameters ---------- im : ND-array The image of the porous material with True values indicating the phase of interest inlet_axis : int Inlet axis of boundary condition. For three dimensional image the number ranges from 0 to 2. For two dimensional image the range is between 0 to 1. outlet_axis : int Outlet axis of boundary condition. For three dimensional image the number ranges from 0 to 2. For two dimensional image the range is between 0 to 1. Returns ------- image : ND-array A copy of im with all the nonpercolating paths removed See Also -------- find_disconnected_voxels trim_floating_solid trim_blind_pores """ 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.') im = trim_floating_solid(~im) labels = spim.label(~im)[0] inlet = sp.zeros_like(im, dtype=int) outlet = sp.zeros_like(im, dtype=int) if im.ndim == 3: if inlet_axis == 0: inlet[0, :, :] = 1 elif inlet_axis == 1: inlet[:, 0, :] = 1 elif inlet_axis == 2: inlet[:, :, 0] = 1 if outlet_axis == 0: outlet[-1, :, :] = 1 elif outlet_axis == 1: outlet[:, -1, :] = 1 elif outlet_axis == 2: outlet[:, :, -1] = 1 if im.ndim == 2: if inlet_axis == 0: inlet[0, :] = 1 elif inlet_axis == 1: inlet[:, 0] = 1 if outlet_axis == 0: outlet[-1, :] = 1 elif outlet_axis == 1: outlet[:, -1] = 1 IN = sp.unique(labels*inlet) OUT = sp.unique(labels*outlet) new_im = sp.isin(labels, list(set(IN) ^ set(OUT)), invert=True) im[new_im == 0] = True return ~im
[docs]def trim_extrema(im, h, mode='maxima'): r""" Trims local extrema in greyscale values by a specified amount. This essentially decapitates peaks and/or floods valleys. Parameters ---------- im : ND-array The image whose extrema are to be removed h : float The height to remove from each peak or fill in each valley mode : string {'maxima' | 'minima' | 'extrema'} Specifies whether to remove maxima or minima or both Returns ------- image : ND-array A copy of the input image with all the peaks and/or valleys removed. Notes ----- This function is referred to as **imhmax** or **imhmin** in Matlab. """ result = im if mode in ['maxima', 'extrema']: result = reconstruction(seed=im - h, mask=im, method='dilation') elif mode in ['minima', 'extrema']: result = reconstruction(seed=im + h, mask=im, method='erosion') return result
[docs]@jit(forceobj=True) def flood(im, regions=None, mode='max'): r""" Floods/fills each region in an image with a single value based on the specific values in that region. The mode argument is used to determine how the value is calculated. Parameters ---------- im : array_like An ND image with isolated regions containing 0's elsewhere. regions : array_like An array the same shape as im with each region labeled. If None is supplied (default) then scipy.ndimage.label is used with its default arguments. mode : string Specifies how to determine which value should be used to flood each region. Options are: 'max' - Floods each region with the local maximum in that region 'min' - Floods each region the local minimum in that region 'size' - Floods each region with the size of that region Returns ------- image : ND-array A copy of im with new values placed in each forground voxel based on the mode. See Also -------- props_to_image """ mask = im > 0 if regions is None: labels, N = spim.label(mask) else: labels = sp.copy(regions) N = labels.max() I = im.flatten() L = labels.flatten() if mode.startswith('max'): V = sp.zeros(shape=N+1, dtype=float) for i in range(len(L)): if V[L[i]] < I[i]: V[L[i]] = I[i] elif mode.startswith('min'): V = sp.ones(shape=N+1, dtype=float)*sp.inf for i in range(len(L)): if V[L[i]] > I[i]: V[L[i]] = I[i] elif mode.startswith('size'): V = sp.zeros(shape=N+1, dtype=int) for i in range(len(L)): V[L[i]] += 1 im_flooded = sp.reshape(V[labels], newshape=im.shape) im_flooded = im_flooded*mask return im_flooded
[docs]def find_dt_artifacts(dt): r""" Finds points in a distance transform that are closer to wall than solid. These points could *potentially* be erroneously high since their distance values do not reflect the possibility that solid may have been present beyond the border of the image but lost by trimming. Parameters ---------- dt : ND-array The distance transform of the phase of interest Returns ------- image : ND-array An ND-array the same shape as dt with numerical values indicating the maximum amount of error in each volxel, which is found by subtracting the distance to nearest edge of image from the distance transform value. In other words, this is the error that would be found if there were a solid voxel lurking just beyond the nearest edge of the image. Obviously, voxels with a value of zero have no error. """ temp = sp.ones(shape=dt.shape)*sp.inf for ax in range(dt.ndim): dt_lin = distance_transform_lin(sp.ones_like(temp, dtype=bool), axis=ax, mode='both') temp = sp.minimum(temp, dt_lin) result = sp.clip(dt - temp, a_min=0, a_max=sp.inf) return result
[docs]def region_size(im): r""" Replace each voxel with size of region to which it belongs Parameters ---------- im : ND-array Either a boolean image wtih True indicating the features of interest, in which case scipy.ndimage.label will be applied to find regions, or a greyscale image with integer values indicating regions. Returns ------- image : ND-array A copy of im with each voxel value indicating the size of the region to which it belongs. This is particularly useful for finding chord sizes on the image produced by apply_chords. """ if im.dtype == bool: im = spim.label(im)[0] counts = sp.bincount(im.flatten()) counts[0] = 0 chords = counts[im] return chords
[docs]def apply_chords(im, spacing=1, axis=0, trim_edges=True, label=False): r""" Adds chords to the void space in the specified direction. The chords are separated by 1 voxel plus the provided spacing. Parameters ---------- im : ND-array An image of the porous material with void marked as True. spacing : int Separation between chords. The default is 1 voxel. This can be decreased to 0, meaning that the chords all touch each other, which automatically sets to the label argument to True. axis : int (default = 0) The axis along which the chords are drawn. trim_edges : bool (default = True) Whether or not to remove chords that touch the edges of the image. These chords are artifically shortened, so skew the chord length distribution. label : bool (default is False) If True the chords in the returned image are each given a unique label, such that all voxels lying on the same chord have the same value. This is automatically set to True if spacing is 0, but is False otherwise. Returns ------- image : ND-array A copy of im with non-zero values indicating the chords. See Also -------- apply_chords_3D """ 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.') if spacing < 0: raise Exception('Spacing cannot be less than 0') if spacing == 0: label = True result = sp.zeros(im.shape, dtype=int) # Will receive chords at end slxyz = [slice(None, None, spacing*(axis != i) + 1) for i in [0, 1, 2]] slices = tuple(slxyz[:im.ndim]) s = [[0, 1, 0], [0, 1, 0], [0, 1, 0]] # Straight-line structuring element if im.ndim == 3: # Make structuring element 3D if necessary s = sp.pad(sp.atleast_3d(s), pad_width=((0, 0), (0, 0), (1, 1)), mode='constant', constant_values=0) im = im[slices] s = sp.swapaxes(s, 0, axis) chords = spim.label(im, structure=s)[0] if trim_edges: # Label on border chords will be set to 0 chords = clear_border(chords) result[slices] = chords # Place chords into empty image created at top if label is False: # Remove label if not requested result = result > 0 return result
[docs]def apply_chords_3D(im, spacing=0, trim_edges=True): r""" Adds chords to the void space in all three principle directions. The chords are seprated by 1 voxel plus the provided spacing. Chords in the X, Y and Z directions are labelled 1, 2 and 3 resepctively. Parameters ---------- im : ND-array A 3D image of the porous material with void space marked as True. spacing : int (default = 0) Chords are automatically separed by 1 voxel on all sides, and this argument increases the separation. trim_edges : bool (default is True) Whether or not to remove chords that touch the edges of the image. These chords are artifically shortened, so skew the chord length distribution Returns ------- image : ND-array A copy of im with values of 1 indicating x-direction chords, 2 indicating y-direction chords, and 3 indicating z-direction chords. Notes ----- The chords are separated by a spacing of at least 1 voxel so that tools that search for connected components, such as scipy.ndimage.label can detect individual chords. See Also -------- apply_chords """ 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.') if im.ndim < 3: raise Exception('Must be a 3D image to use this function') if spacing < 0: raise Exception('Spacing cannot be less than 0') ch = sp.zeros_like(im, dtype=int) ch[:, ::4+2*spacing, ::4+2*spacing] = 1 # X-direction ch[::4+2*spacing, :, 2::4+2*spacing] = 2 # Y-direction ch[2::4+2*spacing, 2::4+2*spacing, :] = 3 # Z-direction chords = ch*im if trim_edges: temp = clear_border(spim.label(chords > 0)[0]) > 0 chords = temp*chords return chords
[docs]def local_thickness(im, sizes=25, mode='hybrid'): r""" For each voxel, this function calculates the radius of the largest sphere that both engulfs the voxel and fits entirely within the foreground. This is not the same as a simple distance transform, which finds the largest sphere that could be *centered* on each voxel. Parameters ---------- im : array_like A binary image with the phase of interest set to True sizes : array_like or scalar The sizes to invade. If a list of values of provided they are used directly. If a scalar is provided then that number of points spanning the min and max of the distance transform are used. mode : string Controls with method is used to compute the result. Options are: 'hybrid' - (default) Performs a distance tranform of the void space, thresholds to find voxels larger than sizes[i], trims the resulting mask if access_limitations is True, then dilates it using the efficient fft-method to obtain the non-wetting fluid configuration. 'dt' - Same as 'hybrid', except uses a second distance transform, relative to the thresholded mask, to find the invading fluid configuration. The choice of 'dt' or 'hybrid' depends on speed, which is system and installation specific. 'mio' - Using a single morphological image opening step to obtain the invading fluid confirguration directly, *then* trims if access_limitations is True. This method is not ideal and is included mostly for comparison purposes. Returns ------- image : ND-array A copy of im with the pore size values in each voxel See Also -------- porosimetry Notes ----- The term *foreground* is used since this function can be applied to both pore space or the solid, whichever is set to True. This function is identical to porosimetry with access_limited set to False. The way local thickness is found in PoreSpy differs from the traditional method (i.e. used in ImageJ <https://imagej.net/Local_Thickness>_). Our approach is probably slower, but it allows for the same code to be used for local_thickness and porosimetry, since we can 'trim' invaded regions that are not connected to the inlets in the porosimetry function. This is not needed in local_thickness however. """ im_new = porosimetry(im=im, sizes=sizes, access_limited=False, mode=mode) return im_new
[docs]def porosimetry(im, sizes=25, inlets=None, access_limited=True, mode='hybrid'): r""" Performs a porosimetry simulution on the image Parameters ---------- im : ND-array An ND image of the porous material containing True values in the pore space. sizes : array_like or scalar The sizes to invade. If a list of values of provided they are used directly. If a scalar is provided then that number of points spanning the min and max of the distance transform are used. inlets : ND-array, boolean A boolean mask with True values indicating where the invasion enters the image. By default all faces are considered inlets, akin to a mercury porosimetry experiment. Users can also apply solid boundaries to their image externally before passing it in, allowing for complex inlets like circular openings, etc. This argument is only used if access_limited is True. access_limited : Boolean This flag indicates if the intrusion should only occur from the surfaces (access_limited is True, which is the default), or if the invading phase should be allowed to appear in the core of the image. The former simulates experimental tools like mercury intrusion porosimetry, while the latter is useful for comparison to gauge the extent of shielding effects in the sample. mode : string Controls with method is used to compute the result. Options are: 'hybrid' - (default) Performs a distance tranform of the void space, thresholds to find voxels larger than sizes[i], trims the resulting mask if access_limitations is True, then dilates it using the efficient fft-method to obtain the non-wetting fluid configuration. 'dt' - Same as 'hybrid', except uses a second distance transform, relative to the thresholded mask, to find the invading fluid configuration. The choice of 'dt' or 'hybrid' depends on speed, which is system and installation specific. 'mio' - Using a single morphological image opening step to obtain the invading fluid confirguration directly, *then* trims if access_limitations is True. This method is not ideal and is included mostly for comparison purposes. The morphological operations are done using fft-based method implementations. Returns ------- image : ND-array A copy of im with voxel values indicating the sphere radius at which it becomes accessible from the inlets. This image can be used to find invading fluid configurations as a function of applied capillary pressure by applying a boolean comparison: inv_phase = im > r where r is the radius (in voxels) of the invading sphere. Of course, r can be converted to capillary pressure using your favorite model. Notes ----- There are many ways to perform this filter, and PoreSpy offers 3, which users can choose between via the mode argument. These methods all work in a similar way by finding which foreground voxels can accomodate a sphere of a given radius, then repeating for smaller radii. See Also -------- fftmorphology local_thickness """ 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.') dt = spim.distance_transform_edt(im > 0) if inlets is None: inlets = get_border(im.shape, mode='faces') if isinstance(sizes, int): sizes = sp.logspace(start=sp.log10(sp.amax(dt)), stop=0, num=sizes) else: sizes = sp.unique(sizes)[-1::-1] if im.ndim == 2: strel = ps_disk else: strel = ps_ball if mode == 'mio': pw = int(sp.floor(dt.max())) impad = sp.pad(im, mode='symmetric', pad_width=pw) inletspad = sp.pad(inlets, mode='symmetric', pad_width=pw) inlets = sp.where(inletspad) # sizes = sp.unique(sp.around(sizes, decimals=0).astype(int))[-1::-1] imresults = sp.zeros(sp.shape(impad)) for r in tqdm(sizes): imtemp = fftmorphology(impad, strel(r), mode='erosion') if access_limited: imtemp = trim_disconnected_blobs(imtemp, inlets) imtemp = fftmorphology(imtemp, strel(r), mode='dilation') if sp.any(imtemp): imresults[(imresults == 0)*imtemp] = r imresults = extract_subsection(imresults, shape=im.shape) elif mode == 'dt': inlets = sp.where(inlets) imresults = sp.zeros(sp.shape(im)) for r in tqdm(sizes): imtemp = dt >= r if access_limited: imtemp = trim_disconnected_blobs(imtemp, inlets) if sp.any(imtemp): imtemp = spim.distance_transform_edt(~imtemp) < r imresults[(imresults == 0)*imtemp] = r elif mode == 'hybrid': inlets = sp.where(inlets) imresults = sp.zeros(sp.shape(im)) for r in tqdm(sizes): imtemp = dt >= r if access_limited: imtemp = trim_disconnected_blobs(imtemp, inlets) if sp.any(imtemp): imtemp = fftconvolve(imtemp, strel(r), mode='same') > 0.0001 imresults[(imresults == 0)*imtemp] = r else: raise Exception('Unreckognized mode ' + mode) return imresults
[docs]def trim_disconnected_blobs(im, inlets): r""" Removes foreground voxels not connected to specified inlets Parameters ---------- im : ND-array The array to be trimmed inlets : ND-array or tuple of indices The locations of the inlets. Can either be a boolean mask the same shape as im, or a tuple of indices such as that returned by the where function. Any voxels *not* connected directly to the inlets will be trimmed. Returns ------- image : ND-array An array of the same shape as im, but with all foreground voxels not connected to the inlets removed. """ if type(inlets) == tuple: temp = sp.copy(inlets) inlets = sp.zeros_like(im, dtype=bool) inlets[temp] = True elif (inlets.shape == im.shape) and (inlets.max() == 1): inlets = inlets.astype(bool) else: raise Exception('inlets not valid, refer to docstring for info') labels = spim.label(inlets + (im > 0))[0] keep = sp.unique(labels[inlets]) keep = keep[keep > 0] if len(keep) > 0: im2 = sp.reshape(sp.in1d(labels, keep), newshape=im.shape) else: im2 = sp.zeros_like(im) im2 = im2*im return im2
def _get_axial_shifts(ndim=2, include_diagonals=False): r''' Helper function to generate the axial shifts that will be performed on the image to identify bordering pixels/voxels ''' if ndim == 2: if include_diagonals: neighbors = square(3) else: neighbors = diamond(1) neighbors[1, 1] = 0 x, y = np.where(neighbors) x -= 1 y -= 1 return np.vstack((x, y)).T else: if include_diagonals: neighbors = cube(3) else: neighbors = octahedron(1) neighbors[1, 1, 1] = 0 x, y, z = np.where(neighbors) x -= 1 y -= 1 z -= 1 return np.vstack((x, y, z)).T def _make_stack(im, include_diagonals=False): r''' Creates a stack of images with one extra dimension to the input image with length equal to the number of borders to search + 1. Image is rolled along the axial shifts so that the border pixel is overlapping the original pixel. First image in stack is the original. Stacking makes direct vectorized array comparisons possible. ''' ndim = len(np.shape(im)) axial_shift = _get_axial_shifts(ndim, include_diagonals) if ndim == 2: stack = np.zeros([np.shape(im)[0], np.shape(im)[1], len(axial_shift)+1]) stack[:, :, 0] = im for i in range(len(axial_shift)): ax0, ax1 = axial_shift[i] temp = np.roll(np.roll(im, ax0, 0), ax1, 1) stack[:, :, i+1] = temp return stack elif ndim == 3: stack = np.zeros([np.shape(im)[0], np.shape(im)[1], np.shape(im)[2], len(axial_shift)+1]) stack[:, :, :, 0] = im for i in range(len(axial_shift)): ax0, ax1, ax2 = axial_shift[i] temp = np.roll(np.roll(np.roll(im, ax0, 0), ax1, 1), ax2, 2) stack[:, :, :, i+1] = temp return stack
[docs]def nphase_border(im, include_diagonals=False): r''' Identifies the voxels in regions that border *N* other regions. Useful for finding triple-phase boundaries. Parameters ---------- im : ND-array An ND image of the porous material containing discrete values in the pore space identifying different regions. e.g. the result of a snow-partition include_diagonals : boolean When identifying bordering pixels (2D) and voxels (3D) include those shifted along more than one axis Returns ------- image : ND-array A copy of im with voxel values equal to the number of uniquely different bordering values ''' 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.') # Get dimension of image ndim = len(np.shape(im)) if ndim not in [2, 3]: raise NotImplementedError("Function only works for 2d and 3d images") # Pad image to handle edges im = np.pad(im, pad_width=1, mode='edge') # Stack rolled images for each neighbor to be inspected stack = _make_stack(im, include_diagonals) # Sort the stack along the last axis stack.sort() out = np.ones_like(im) # Run through stack recording when neighbor id changes # Number of changes is number of unique bordering regions for k in range(np.shape(stack)[ndim])[1:]: if ndim == 2: mask = stack[:, :, k] != stack[:, :, k-1] elif ndim == 3: mask = stack[:, :, :, k] != stack[:, :, :, k-1] out += mask # Un-pad if ndim == 2: return out[1:-1, 1:-1].copy() else: return out[1:-1, 1:-1, 1:-1].copy()
[docs]def prune_branches(skel, branch_points=None, iterations=1): r""" Removes all dangling ends or tails of a skeleton. Parameters ---------- skel : ND-image A image of a full or partial skeleton from which the tails should be trimmed. branch_points : ND-image, optional An image the same size skel` with True values indicating the branch points of the skeleton. If this is not provided it is calculated automatically. Returns ------- An ND-image containing the skeleton with tails removed. """ skel = skel > 0 if skel.ndim == 2: from skimage.morphology import square as cube else: from skimage.morphology import cube # Create empty image to house results im_result = sp.zeros_like(skel) # If branch points are not supplied, attempt to find them if branch_points is None: branch_points = spim.convolve(skel*1.0, weights=cube(3)) > 3 branch_points = branch_points*skel # Store original branch points before dilating pts_orig = branch_points # Find arcs of skeleton by deleting branch points arcs = skel*(~branch_points) # Label arcs arc_labels = spim.label(arcs, structure=cube(3))[0] # Dilate branch points so they overlap with the arcs branch_points = spim.binary_dilation(branch_points, structure=cube(3)) pts_labels = spim.label(branch_points, structure=cube(3))[0] # Now scan through each arc to see if it's connected to two branch points slices = spim.find_objects(arc_labels) label_num = 0 for s in slices: label_num += 1 # Find branch point labels the overlap current arc hits = pts_labels[s]*(arc_labels[s] == label_num) # If image contains 2 branch points, then it's not a tail. if len(sp.unique(hits)) == 3: im_result[s] += arc_labels[s] == label_num # Add missing branch points back to arc image to make complete skeleton im_result += skel*pts_orig if iterations > 1: iterations -= 1 im_temp = sp.copy(im_result) im_result = prune_branches(skel=im_result, branch_points=None, iterations=iterations) if sp.all(im_temp == im_result): iterations = 0 return im_result