# filters¶

Highlight Features of Interest

This module contains a variety of functions for altering images based on the structural characteristics, such as pore sizes. A definition of a filter is a function that returns an image the shape as the original image, but with altered values.

 porespy.filters.apply_chords(im[, spacing, …]) Adds chords to the void space in the specified direction. porespy.filters.apply_chords_3D(im[, …]) Adds chords to the void space in all three principle directions. porespy.filters.distance_transform_lin(im[, …]) Replaces each void voxel with the linear distance to the nearest solid voxel along the specified axis. porespy.filters.fill_blind_pores(im) Fills all pores that are not connected to the edges of the image. porespy.filters.find_disconnected_voxels(im) This identifies all pore (or solid) voxels that are not connected to the edge of the image. porespy.filters.find_dt_artifacts(dt) Finds points in a distance transform that are closer to wall than solid. porespy.filters.find_peaks(dt[, r_max, …]) Returns all local maxima in the distance transform porespy.filters.flood Floods/fills each region in an image with a single value based on the specific values in that region. porespy.filters.local_thickness(im[, sizes, …]) For each voxel, this functions calculates the radius of the largest sphere that both engulfs the voxel and fits entirely within the foreground. porespy.filters.porosimetry(im[, sizes, …]) Performs a porosimetry simulution on the image porespy.filters.region_size(im) Replace each voxel with size of region to which it belongs porespy.filters.snow_partitioning(im[, dt, …]) Partitions the void space into pore regions using a marker-based watershed algorithm, with specially filtered peaks as markers. porespy.filters.trim_disconnected_blobs(im, …) Removes foreground voxels not connected to specified inlets porespy.filters.trim_extrema(im, h[, mode]) Trims local extrema in greyscale values by a specified amount. porespy.filters.trim_floating_solid(im) Removes all solid that that is not attached to the edges of the image. porespy.filters.trim_nearby_peaks(peaks, dt) 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. porespy.filters.trim_nonpercolating_paths(im) Removes all nonpercolating paths between specified edges porespy.filters.trim_saddle_points(peaks, dt) 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.
porespy.filters.apply_chords(im, spacing=1, axis=0, trim_edges=True, label=False)[source]

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. image – A copy of im with non-zero values indicating the chords. ND-array
porespy.filters.apply_chords_3D(im, spacing=0, trim_edges=True)[source]

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 image – A copy of im with values of 1 indicating x-direction chords, 2 indicating y-direction chords, and 3 indicating z-direction chords. ND-array

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.

porespy.filters.distance_transform_lin(im, axis=0, mode='both')[source]

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. image – A copy of im with each foreground voxel containing the distance to the nearest background along the specified axis. ND-array
porespy.filters.fftmorphology(im, strel, mode='opening')[source]

Perform morphological operations on binary images using fft approach for improved performance

Parameters: im (nd-array) – The binary image on which to perform the morphological operation strel (nd-array) – The structuring element to use. Must have the same dims as im. mode (string) – The type of operation to perform. Options are ‘dilation’, ‘erosion’, ‘opening’ and ‘closing’. image – A copy of the image with the specified moropholgical operation applied using the fft-based methods available in scipy.fftconvolve. ND-array

Notes

This function uses scipy.signal.fftconvolve which can be more than 10x faster than the standard binary morphology operation in scipy.ndimage. This speed up may not always be realized, depending on the scipy distribution used.

Examples

>>> import porespy as ps
>>> from numpy import array_equal
>>> import scipy.ndimage as spim
>>> from skimage.morphology import disk
>>> im = ps.generators.blobs(shape=[100, 100], porosity=0.8)


Check that erosion, dilation, opening, and closing are all the same as the scipy.ndimage functions:

>>> result = ps.filters.fftmorphology(im, strel=disk(5), mode='erosion')
>>> temp = spim.binary_erosion(im, structure=disk(5))
>>> array_equal(result, temp)
True

>>> result = ps.filters.fftmorphology(im, strel=disk(5), mode='dilation')
>>> temp = spim.binary_dilation(im, structure=disk(5))
>>> array_equal(result, temp)
True

>>> result = ps.filters.fftmorphology(im, strel=disk(5), mode='opening')
>>> temp = spim.binary_opening(im, structure=disk(5))
>>> array_equal(result, temp)
True

>>> result = ps.filters.fftmorphology(im, strel=disk(5), mode='closing')
>>> temp = spim.binary_closing(im, structure=disk(5))
>>> array_equal(result, temp)
True

porespy.filters.fill_blind_pores(im)[source]

Fills all pores that are not connected to the edges of the image.

Parameters: im (ND-array) – The image of the porous material image – A version of im but with all the disconnected pores removed. ND-array
porespy.filters.find_disconnected_voxels(im, conn=None)[source]

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 image – 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. ND-array

Notes

image : ND-array
The returned array (e.g. holes) be used to trim blind pores from im using: im[holes] = False
porespy.filters.find_dt_artifacts(dt)[source]

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 image – 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. ND-array
porespy.filters.find_peaks(dt, r_max=4, footprint=None)[source]

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). image – An array of booleans with True values at the location of any local maxima. ND-array

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.

porespy.filters.flood()[source]

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 image – A copy of im with new values placed in each forground voxel based on the mode. ND-array

props_to_image()

porespy.filters.local_thickness(im, sizes=25, mode='hybrid')[source]

For each voxel, this functions 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. image – A copy of im with the pore size values in each voxel ND-array

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). 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.

porespy.filters.nphase_border(im, include_diagonals=False)[source]

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 image – A copy of im with voxel values equal to the number of uniquely different bordering values ND-array
porespy.filters.porosimetry(im, sizes=25, inlets=None, access_limited=True, mode='hybrid')[source]

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. image – 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. ND-array

Notes

There are many ways to perform this filter, and PoreSpy offer 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.

porespy.filters.region_size(im)[source]

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. image – 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. ND-array
porespy.filters.snow_partitioning(im, dt=None, r_max=4, sigma=0.4, return_all=False, mask=True, randomize=True)[source]

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. image – 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]. ND-array

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)

porespy.filters.snow_partitioning_n(im, r_max=4, sigma=0.4, return_all=True, mask=True, randomize=False, alias=None)[source]

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’,..}. 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)

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.

porespy.filters.trim_extrema(im, h, mode='maxima')[source]

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 image – A copy of the input image with all the peaks and/or valleys removed. ND-array

Notes

This function is referred to as imhmax or imhmin in Matlab.

porespy.filters.reduce_peaks(peaks)[source]

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 image – An array with the same number of isolated peaks as the original image, but fewer total voxels. ND-array

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.

porespy.filters.trim_disconnected_blobs(im, inlets)[source]

Removes foreground voxels not connected to specified inlets

Parameters: im (ND-array) – The array to be trimmed inlets (ND-array of tuple of indices) – The locations of the inlets. Any voxels not connected directly to the inlets will be trimmed image – An array of the same shape as im, but with all foreground voxels not connected to the inlets removed. ND-array
porespy.filters.trim_floating_solid(im)[source]

Removes all solid that that is not attached to the edges of the image.

Parameters: im (ND-array) – The image of the porous material image – A version of im but with all the disconnected solid removed. ND-array
porespy.filters.trim_nearby_peaks(peaks, dt)[source]

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. image – An array the same size as peaks containing a subset of the peaks in the original image. ND-array

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)

porespy.filters.trim_nonpercolating_paths(im, inlet_axis=0, outlet_axis=0)[source]

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. image – A copy of im with all the nonpercolating paths removed ND-array
porespy.filters.trim_saddle_points(peaks, dt, max_iters=10)[source]

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. image – An image with fewer peaks than the input image ND-array

References

[1] Gostick, J. “A versatile and efficient network extraction algorithm using marker-based watershed segmenation”. Physical Review E. (2017)