snow2#
The SNOW algorithm uses a standard marker-based watershed segementation function to identify pores. The key to the SNOW algorithm is in how the markers are identified. Finding peaks in the distance transform which truly correspond to pore centers requires several careful steps. Each of these steps can be done manually, but the snow2 function was created to combine them all in a single function for ease of use.
In addition to the original SNOW algorithm, snow2 also incorporates a few new developements such as multiphase extractions and parallelized processing. The new snow2 function also handles boundaries better, and returns a different set of geometrical properties. For instance it no longer returns ‘pore.diameter’, which was an opinionated choice that was not appropriate for every case. Instead it returns several different diameters, like ‘pore.equivalent_diameter’ and ‘pore.inscribed_diameter’, and the user must decide which of these they wish to declare as the offical ‘pore.diameter’.
The snow2 function has quite a few arguments, which will be explored and explained in this example.
import matplotlib.pyplot as plt
import numpy as np
import openpnm as op
import scipy.ndimage as spim
from edt import edt
import porespy as ps
---------------------------------------------------------------------------
ModuleNotFoundError Traceback (most recent call last)
Cell In[1], line 3
1 import matplotlib.pyplot as plt
2 import numpy as np
----> 3 import openpnm as op
4 import scipy.ndimage as spim
5 from edt import edt
ModuleNotFoundError: No module named 'openpnm'
im = ~ps.generators.random_spheres([400, 400], r=15, clearance=5)
ps.imshow(im);
phases#
One of the main features of snow2 is the ability to extract networks from multiple phases simultaneously, and have them be interconnected. This is quite useful for modeling electrochemial devices for instance, since transport occurs in the solid and void phases simultaneously, and the processes are coupled. For a powerful example, see Khan et al. where the transient discharage of a Li-ion battery was modelled using PNMs. Li-ion batteries contain 3 distinct phases: liquid electrolyte, solid active material, and carbonaceous binder.
Note that snow2 does not need to operate on mulitphase phases, only that it can if needed. It accomplishes this flexibility by ignoring all 0’s in the input images, and treating all voxels with values of 1, 2, 3, etc. as distinct phases. Therefore supplying an image of 0’s and 1’s will result in a standard single phase extraction, while supplying an image of 1’s and 2’s will create a dual phase network.
A few additional notes:
It should also be mentioned that the image can contain 0’s as well as values (ie. 1, 2, 3), so can have multiple phases and have some regions ignored
The voxels values do not have be integers or sequential. Each unique numerical value in the image is treated as phase.
Let’s explore this:
im.min()
False
net1 = ps.networks.snow2(phases=im, boundary_width=0)
net2 = ps.networks.snow2(phases=im.astype(int) + 1, boundary_width=0)
The “object” returned by the snow2 function is a dataclass-like object, meaning it has data attached to it as attributes. These attributes are the segmented image called regions, the OpenPNM compatible network called network, and a copy of the input image called phases which will be padded to be the same size as regions if any boundaries were added.
fig, ax = plt.subplots(1, 2, figsize=[12, 6])
ax[0].imshow(net1.regions, origin='lower', interpolation='none')
ax[1].imshow(net2.regions, origin='lower', interpolation='none');
On the left we can see that the spherical particles are all purple, which indicates 0, because they have not been labelled by the function. On the right the particles each have a unique greyscale value because they have been labelled as distinct regions.
The returned objects (net1 and net2) also contain the pore networks, in OpenPNM format. We can overlay these networks with the above images. Let’s start with the single phase network:
pn1 = op.io.network_from_porespy(net1.network)
ax = op.visualization.plot_connections(pn1, c='k')
ax = op.visualization.plot_coordinates(pn1, markersize=50, ax=ax)
fig, ax = plt.gcf(), plt.gca()
ax.imshow(net1.regions.T)
ax.axis(False);
The image needed to be rotated so that the x and y directions lined up with the OpenPNM network. The agreement between the image and network is pretty good. Clearly the the red pore centers lie within each labelled regions and the black throat connections follow the topology quite well.
Now let’s do the same for the multiphase network:
pn2 = op.io.network_from_porespy(net2.network)
ax = op.visualization.plot_connections(pn2, c='k')
ax = op.visualization.plot_coordinates(pn2, markersize=50, ax=ax)
fig, ax = plt.gcf(), plt.gca()
ax.imshow(net2.regions.T)
ax.axis(False);
The above shows the additional network comprised of the solids (although they don’t actually connect in this 2D example) as well as the void-solid connections. We can improve this plot by coloring the different types of pores and throats differently. If we print pn2 we can see that snow2 has created some labels for us, by assuming phase names of “phase1” and “phase2”.
print(pn2)
throat.conns
[[ 0 82]
[ 0 83]
[ 0 90]
...
[183 187]
[184 188]
[186 188]]
<class 'numpy.ndarray'>
int32
pore.coords
[[ 16. 80. 0. ]
[ 16. 251. 0. ]
[ 25. 144. 0. ]
[ 25. 181. 0. ]
[ 33. 379. 0. ]
[ 34. 320. 0. ]
[ 37. 19. 0. ]
[ 40. 109. 0. ]
[ 49. 58. 0. ]
[ 53. 234. 0. ]
[ 59. 197. 0. ]
[ 61. 272. 0. ]
[ 64. 139. 0. ]
[ 71. 316. 0. ]
[ 72. 87. 0. ]
[ 74. 24. 0. ]
[ 74. 367. 0. ]
[ 89. 225. 0. ]
[ 95. 57. 0. ]
[107. 151. 0. ]
[108. 327. 0. ]
[111. 18. 0. ]
[111. 113. 0. ]
[118. 189. 0. ]
[124. 255. 0. ]
[125. 364. 0. ]
[126. 293. 0. ]
[128. 78. 0. ]
[143. 218. 0. ]
[144. 152. 0. ]
[148. 329. 0. ]
[151. 47. 0. ]
[157. 116. 0. ]
[165. 294. 0. ]
[169. 370. 0. ]
[171. 256. 0. ]
[173. 177. 0. ]
[185. 16. 0. ]
[189. 54. 0. ]
[198. 347. 0. ]
[202. 298. 0. ]
[206. 91. 0. ]
[206. 228. 0. ]
[215. 174. 0. ]
[215. 381. 0. ]
[221. 135. 0. ]
[226. 261. 0. ]
[238. 16. 0. ]
[240. 306. 0. ]
[242. 80. 0. ]
[242. 346. 0. ]
[258. 383. 0. ]
[262. 244. 0. ]
[263. 154. 0. ]
[263. 196. 0. ]
[264. 49. 0. ]
[272. 118. 0. ]
[279. 350. 0. ]
[282. 310. 0. ]
[284. 17. 0. ]
[284. 82. 0. ]
[298. 257. 0. ]
[298. 383. 0. ]
[300. 190. 0. ]
[313. 333. 0. ]
[315. 224. 0. ]
[318. 154. 0. ]
[319. 68. 0. ]
[322. 22. 0. ]
[324. 292. 0. ]
[339. 103. 0. ]
[339. 382. 0. ]
[351. 214. 0. ]
[359. 173. 0. ]
[360. 351. 0. ]
[361. 309. 0. ]
[363. 24. 0. ]
[368. 251. 0. ]
[379. 383. 0. ]
[380. 115. 0. ]
[382. 61. 0. ]
[ 13.6402214 8.38929889 0. ]
[ 16.95243978 45.06670784 0. ]
[ 11.97881356 114.99661017 0. ]
[ 7.94285714 162.5 0. ]
[ 21.47852194 213.90808314 0. ]
[ 26.96234613 289.51737871 0. ]
[ 14.15455665 348.89593596 0. ]
[ 12.02626263 390.41616162 0. ]
[ 47.01476793 165.32067511 0. ]
[ 44.01197605 83.39221557 0. ]
[ 41.99463807 252.90884718 0. ]
[ 42.9488189 131.06692913 0. ]
[ 56.65789474 389.17251462 0. ]
[ 52.03517964 346.89296407 0. ]
[ 57.24271845 6.6092233 0. ]
[ 53.36577181 34.5704698 0. ]
[ 75.50932836 112.99813433 0. ]
[ 67.55102041 217.95510204 0. ]
[ 85.64050633 250.21772152 0. ]
[ 72.25609756 54.96493902 0. ]
[ 83.83201941 171.28562765 0. ]
[ 94.43589744 288.27672956 0. ]
[ 89.02554745 202.08394161 0. ]
[ 83.51102941 338.70220588 0. ]
[ 89.7238806 6.6318408 0. ]
[100.17904903 385.71768202 0. ]
[ 91.40268456 133.92170022 0. ]
[100.8411215 85.18457944 0. ]
[ 94.01831502 33.63003663 0. ]
[100.89081456 353.32582322 0. ]
[116.80811078 222.5776459 0. ]
[121.77202073 47.80103627 0. ]
[130.32232497 130.89035667 0. ]
[147.36301793 15.2436611 0. ]
[123.51973684 165.34210526 0. ]
[126.82727273 340.2 0. ]
[127.93602694 316.003367 0. ]
[133.21162791 102.63023256 0. ]
[146.82551143 272.91576414 0. ]
[145.75247525 386.81287129 0. ]
[145.1476378 184.75885827 0. ]
[146.84773663 243.35185185 0. ]
[147.79049676 354.16414687 0. ]
[145.69387755 305.51360544 0. ]
[167.09887006 81.39500942 0. ]
[186.70990566 137.57985175 0. ]
[174.02823529 217.22176471 0. ]
[179.37522124 320.02743363 0. ]
[171.56455142 346.64770241 0. ]
[174.16455696 38.11075949 0. ]
[193.08434959 274.45934959 0. ]
[188.18994413 389.81564246 0. ]
[199.50105708 250.02536998 0. ]
[193.84693878 367.58843537 0. ]
[211.44580777 6.73619632 0. ]
[198.25240055 196.12482853 0. ]
[221.12957198 47.73307393 0. ]
[218.59006816 325.37877313 0. ]
[219.4 357.54647887 0. ]
[234.84110535 215.86183074 0. ]
[237.01089494 108.41400778 0. ]
[223.16995074 287. 0. ]
[235.30508475 392.88418079 0. ]
[235.20491803 154.69262295 0. ]
[237.8125 369.94270833 0. ]
[244.94165316 174.69854133 0. ]
[262.79564411 277.99258573 0. ]
[249.28730512 134.50556793 0. ]
[261.64082687 6.20155039 0. ]
[260.71827411 326.93527919 0. ]
[261.25428571 26.4 0. ]
[259.54230769 360.39230769 0. ]
[263.35294118 70.85661765 0. ]
[264.55882353 93.45454545 0. ]
[278. 393.32713755 0. ]
[284.98479613 221.96406358 0. ]
[275.91420912 178.3538874 0. ]
[287.68421053 143.06791171 0. ]
[278.40310078 372.10077519 0. ]
[296.35091278 47.40162272 0. ]
[291.95294118 165.0907563 0. ]
[307.04719101 111.03505618 0. ]
[291.01532567 331.02681992 0. ]
[305.61748634 6.22131148 0. ]
[310.40641711 360.84278075 0. ]
[300.36998255 285.69458988 0. ]
[306.24585635 310.7320442 0. ]
[319.15789474 393.06578947 0. ]
[333.37347561 252.06097561 0. ]
[330.06184896 188.7890625 0. ]
[333.86480687 312.37339056 0. ]
[345.93449782 46.92212518 0. ]
[343.50704225 7.79225352 0. ]
[342.4457429 330.89983306 0. ]
[335.88076923 355.18461538 0. ]
[349.14293785 137.18587571 0. ]
[348.64447236 75.91331658 0. ]
[351.80164159 282.27770178 0. ]
[358.29824561 393.44210526 0. ]
[359.07758621 372.67241379 0. ]
[367.0311174 91.54879774 0. ]
[382.17356688 210.19785032 0. ]
[385.22014309 340.11172262 0. ]
[386.34341085 22.78682171 0. ]
[384.42998761 281.366171 0. ]
[385.4726477 149.26185266 0. ]
[394.28873239 393.14788732 0. ]
[391.6601626 89.10243902 0. ]]
<class 'numpy.ndarray'>
float64
pore.region_label
[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72
73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108
109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126
127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144
145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162
163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180
181 182 183 184 185 186 187 188 189]
<class 'numpy.ndarray'>
int32
pore.phase
[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2]
<class 'numpy.ndarray'>
int32
throat.phases
[[1 2]
[1 2]
[1 2]
...
[2 2]
[2 2]
[2 2]]
<class 'numpy.ndarray'>
int32
pore.region_volume
[ 793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793.
793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793.
793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793.
793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793.
793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793.
793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793.
793. 793. 793. 793. 793. 793. 793. 793. 793. 542. 1619. 1180.
560. 2165. 2762. 1624. 495. 948. 668. 373. 254. 684. 1336. 412.
298. 1072. 245. 1185. 656. 1649. 2067. 548. 544. 402. 1346. 447.
856. 273. 577. 1011. 965. 757. 1617. 304. 330. 297. 430. 831.
1010. 1016. 486. 463. 294. 2124. 2968. 1700. 1130. 457. 316. 984.
716. 473. 294. 489. 729. 2570. 1027. 355. 2316. 1285. 406. 354.
488. 384. 617. 2158. 449. 387. 788. 350. 260. 272. 374. 269.
1447. 373. 589. 258. 1479. 595. 2225. 261. 366. 935. 573. 362.
304. 1968. 1536. 466. 1374. 568. 599. 520. 1770. 796. 731. 285.
232. 707. 2512. 1817. 1290. 1614. 1371. 142. 615.]
<class 'numpy.ndarray'>
float64
pore.equivalent_diameter
[31.77544585 31.77544585 31.77544585 31.77544585 31.77544585 31.77544585
31.77544585 31.77544585 31.77544585 31.77544585 31.77544585 31.77544585
31.77544585 31.77544585 31.77544585 31.77544585 31.77544585 31.77544585
31.77544585 31.77544585 31.77544585 31.77544585 31.77544585 31.77544585
31.77544585 31.77544585 31.77544585 31.77544585 31.77544585 31.77544585
31.77544585 31.77544585 31.77544585 31.77544585 31.77544585 31.77544585
31.77544585 31.77544585 31.77544585 31.77544585 31.77544585 31.77544585
31.77544585 31.77544585 31.77544585 31.77544585 31.77544585 31.77544585
31.77544585 31.77544585 31.77544585 31.77544585 31.77544585 31.77544585
31.77544585 31.77544585 31.77544585 31.77544585 31.77544585 31.77544585
31.77544585 31.77544585 31.77544585 31.77544585 31.77544585 31.77544585
31.77544585 31.77544585 31.77544585 31.77544585 31.77544585 31.77544585
31.77544585 31.77544585 31.77544585 31.77544585 31.77544585 31.77544585
31.77544585 31.77544585 31.77544585 26.26967516 45.40236583 38.76109729
26.70232471 52.50298672 59.30166627 45.47242044 25.10485162 34.74235295
29.16374489 21.79262146 17.98340469 29.51094456 41.24376355 22.90359562
19.47884453 36.94472617 17.66192765 38.84313145 28.90060798 45.82108695
51.30093702 26.41467907 26.31809857 22.62393195 41.39783119 23.85661494
33.01352829 18.6438836 27.10459772 35.87819923 35.05247724 31.04581027
45.3743137 19.67396304 20.49802551 19.44613444 23.39856842 32.52786593
35.86045092 35.96680939 24.87557876 24.27982515 19.34767237 52.00346905
61.47336796 46.52426492 37.93099901 24.12199146 20.05850683 35.3958714
30.19336871 24.5406256 19.34767237 24.95223712 30.46623751 57.20337079
36.16098744 21.26029253 54.30306424 40.44889139 22.73621022 21.23032734
24.92671053 22.11162557 28.02835705 52.41804019 23.90992588 22.19783106
31.67511265 21.11004123 18.19456737 18.60970597 21.82181454 18.50679436
42.92292652 21.79262146 27.38499757 18.12445317 43.3949454 27.52412631
53.22553886 18.22952334 21.58716455 34.50331831 27.01048424 21.46887783
19.67396304 50.05732138 44.22325113 24.35835848 41.82620153 26.89237924
27.61648941 25.73100393 47.47245511 31.83549399 30.50800071 19.0492328
17.18695943 30.00300582 56.55420176 48.09860968 40.52750933 45.33220296
41.78051479 13.44618962 27.98289335]
<class 'numpy.ndarray'>
float64
pore.local_peak
[[ 17. 81.]
[ 17. 252.]
[ 26. 145.]
[ 26. 182.]
[ 34. 380.]
[ 35. 321.]
[ 38. 20.]
[ 41. 110.]
[ 50. 59.]
[ 54. 235.]
[ 60. 198.]
[ 62. 273.]
[ 65. 140.]
[ 72. 317.]
[ 73. 88.]
[ 75. 25.]
[ 75. 368.]
[ 90. 226.]
[ 96. 58.]
[108. 152.]
[109. 328.]
[112. 19.]
[112. 114.]
[119. 190.]
[125. 256.]
[126. 365.]
[127. 294.]
[129. 79.]
[144. 219.]
[145. 153.]
[149. 330.]
[152. 48.]
[158. 117.]
[166. 295.]
[170. 371.]
[172. 257.]
[174. 178.]
[186. 17.]
[190. 55.]
[199. 348.]
[203. 299.]
[207. 92.]
[207. 229.]
[216. 175.]
[216. 382.]
[222. 136.]
[227. 262.]
[239. 17.]
[241. 307.]
[243. 81.]
[243. 347.]
[259. 384.]
[263. 245.]
[264. 155.]
[264. 197.]
[265. 50.]
[273. 119.]
[280. 351.]
[283. 311.]
[285. 18.]
[285. 83.]
[299. 258.]
[299. 384.]
[301. 191.]
[314. 334.]
[316. 225.]
[319. 155.]
[320. 69.]
[323. 23.]
[325. 293.]
[340. 104.]
[340. 383.]
[352. 215.]
[360. 174.]
[361. 352.]
[362. 310.]
[364. 25.]
[369. 252.]
[380. 384.]
[381. 116.]
[383. 62.]
[ 10. 10.]
[ 18. 48.]
[ 13. 109.]
[ 9. 163.]
[ 20. 217.]
[ 21. 288.]
[ 18. 350.]
[ 10. 390.]
[ 49. 164.]
[ 43. 84.]
[ 40. 254.]
[ 44. 132.]
[ 59. 390.]
[ 51. 348.]
[ 59. 8.]
[ 55. 36.]
[ 83. 115.]
[ 69. 218.]
[ 82. 253.]
[ 73. 49.]
[ 80. 171.]
[ 93. 289.]
[ 94. 202.]
[ 84. 341.]
[ 91. 8.]
[102. 385.]
[ 89. 136.]
[101. 86.]
[ 96. 35.]
[101. 355.]
[118. 229.]
[123. 46.]
[134. 129.]
[144. 17.]
[125. 167.]
[128. 342.]
[129. 317.]
[135. 104.]
[147. 274.]
[145. 387.]
[147. 188.]
[149. 245.]
[150. 355.]
[146. 307.]
[166. 82.]
[185. 142.]
[176. 219.]
[180. 323.]
[168. 346.]
[174. 38.]
[196. 272.]
[190. 389.]
[196. 251.]
[192. 370.]
[210. 9.]
[200. 197.]
[225. 50.]
[217. 325.]
[221. 358.]
[231. 205.]
[242. 112.]
[225. 287.]
[237. 393.]
[239. 155.]
[238. 371.]
[244. 176.]
[265. 280.]
[248. 136.]
[262. 9.]
[260. 326.]
[262. 26.]
[260. 362.]
[264. 72.]
[264. 94.]
[279. 394.]
[285. 221.]
[274. 176.]
[288. 145.]
[279. 373.]
[296. 48.]
[291. 166.]
[308. 119.]
[292. 332.]
[306. 8.]
[315. 361.]
[300. 289.]
[307. 310.]
[320. 394.]
[334. 256.]
[332. 189.]
[337. 314.]
[345. 50.]
[344. 9.]
[342. 333.]
[336. 353.]
[351. 138.]
[350. 78.]
[352. 284.]
[360. 394.]
[360. 374.]
[370. 91.]
[383. 199.]
[385. 331.]
[389. 12.]
[383. 283.]
[385. 150.]
[396. 396.]
[391. 87.]]
<class 'numpy.ndarray'>
float64
pore.global_peak
[[ 16. 80.]
[ 16. 251.]
[ 25. 144.]
[ 25. 181.]
[ 33. 379.]
[ 34. 320.]
[ 37. 19.]
[ 40. 109.]
[ 49. 58.]
[ 53. 234.]
[ 59. 197.]
[ 61. 272.]
[ 64. 139.]
[ 71. 316.]
[ 72. 87.]
[ 74. 24.]
[ 74. 367.]
[ 89. 225.]
[ 95. 57.]
[107. 151.]
[108. 327.]
[111. 18.]
[111. 113.]
[118. 189.]
[124. 255.]
[125. 364.]
[126. 293.]
[128. 78.]
[143. 218.]
[144. 152.]
[148. 329.]
[151. 47.]
[157. 116.]
[165. 294.]
[169. 370.]
[171. 256.]
[173. 177.]
[185. 16.]
[189. 54.]
[198. 347.]
[202. 298.]
[206. 91.]
[206. 228.]
[215. 174.]
[215. 381.]
[221. 135.]
[226. 261.]
[238. 16.]
[240. 306.]
[242. 80.]
[242. 346.]
[258. 383.]
[262. 244.]
[263. 154.]
[263. 196.]
[264. 49.]
[272. 118.]
[279. 350.]
[282. 310.]
[284. 17.]
[284. 82.]
[298. 257.]
[298. 383.]
[300. 190.]
[313. 333.]
[315. 224.]
[318. 154.]
[319. 68.]
[322. 22.]
[324. 292.]
[339. 103.]
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float64
pore.geometric_centroid
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<class 'numpy.ndarray'>
float64
throat.global_peak
[[ 0. 75. 0.]
[ 0. 81. 0.]
[ 27. 92. 0.]
...
[399. 383. 0.]
[399. 62. 0.]
[399. 115. 0.]]
<class 'numpy.ndarray'>
float64
pore.inscribed_diameter
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32. 32. 32. 32. 32. 32.
32. 32. 32. 32. 32. 32.
32. 32. 32. 32. 32. 32.
32. 32. 32. 32. 32. 32.
32. 32. 32. 32. 32. 32.
32. 32. 32. 32. 32. 32.
32. 32. 32. 32. 32. 32.
32. 32. 32. 32. 32. 32.
32. 32. 32. 32. 32. 32.
32. 32. 32. 32. 32. 32.
32. 32. 32. 32. 32. 32.
32. 32. 32. 32. 32. 32.
32. 32. 32. 20. 36. 26.
18. 40. 40.2492218 34.05877304 20. 26.07680893
20.39607811 15.62049961 12.80624866 22. 31.1126976 15.62049961
14.42220497 26. 12.64911079 24.73863411 17.88854408 35.6089859
38. 18. 20.88061333 15.62049961 31.1126976 18.
26. 14.14213562 22.36067963 24.16609192 26.83281517 21.54065895
32.55764008 14.14213562 15.62049961 14.42220497 18.86796188 25.45584488
26.90724754 26. 20.39607811 19.79899025 14.42220497 40.44749832
42.42640686 33.10589218 31.24099922 18. 15.62049961 24.33105087
22.36067963 17.88854408 14. 18. 22. 40.
26.90724754 17.08800697 35.77708817 31.1126976 18.86796188 16.
19.79899025 17.88854408 22. 40. 18.11077118 17.08800697
22.62741661 17.08800697 14. 14. 16.12451553 13.41640759
32. 15.2315464 18.97366524 14. 32. 22.09072113
39.39543152 13.41640759 14.14213562 24. 20. 17.88854408
14. 40. 32. 16.4924221 31.24099922 18.
22. 20. 39.84971619 24.08318901 24.16609192 13.41640759
12.64911079 23.32380676 36. 31.1126976 24. 36.
32. 8.48528099 20. ]
<class 'numpy.ndarray'>
float64
pore.extended_diameter
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32. 32. 32. 32. 32. 32.
32. 32. 32. 32. 32. 32.
32. 32. 32. 32. 32. 32.
32. 32. 32. 32. 32. 32.
32. 32. 32. 32. 32. 32.
32. 32. 32. 32. 32. 32.
32. 32. 32. 32. 32. 32.
32. 32. 32. 32. 32. 32.
32. 32. 32. 32. 32. 32.
32. 32. 32. 32. 32. 32.
32. 32. 32. 32. 32. 32.
32. 32. 32. 32. 32. 32.
32. 32. 32. 51.88448715 53.66563034 45.25483322
32. 49.67897034 56.46237564 58. 45.65084839 32.
20.39607811 18.86796188 20. 37.20215225 32.24903107 32.
22. 27.85677719 23.32380676 34.92849731 17.88854408 35.6089859
38. 28.07133675 24.16609192 32. 52.34500885 22.62741661
26. 17.88854408 24.16609192 24.16609192 26.83281517 32.
49.1934967 22. 18. 16. 19.69771576 32.
46.69047165 26. 20.59126091 19.79899025 16. 40.44749832
42.42640686 36.22154236 31.24099922 22.36067963 26. 30.
35.77708817 24.08318901 17.08800697 32. 30.4630928 40.
32. 17.08800697 35.77708817 31.1126976 18.86796188 32.
22. 18. 26. 40. 23.32380676 32.
32. 17.08800697 18. 14. 20. 32.
32. 28. 28.84440994 16. 32. 25.29822159
40. 18. 32. 32. 26. 18.
32. 40. 32. 22.80350876 34.92849731 32.
25.45584488 25.45584488 40.49691391 34. 34. 32.
14. 34. 67.20118713 56.35601044 54.91812134 59.36328888
56.35601044 32. 32.80244064]
<class 'numpy.ndarray'>
float64
throat.inscribed_diameter
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2. 2. 2. 2. 2. 2.
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2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
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2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
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2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 2. 2.
2. 2. 2. 2. 44. 8.
2. 7.21110249 8.24621105 20. 5.65685415 5.65685415
20. 6. 2. 6.3245554 8.24621105 6.
38. 17.88854408 6. 14. 36. 28.
10. 8. 28. 7.21110249 5.65685415 8.
7.21110249 10.19803905 34. 20. 6. 18.
10. 21.54065895 14.42220497 6. 8.48528099 32.98484421
14.14213562 5.65685415 7.21110249 28. 12.16552544 8.
6. 6.3245554 8. 14.14213562 19.79899025 6.
6. 20. 40. 8. 7.21110249 7.21110249
10. 8.24621105 5.65685415 10. 17.20465088 5.65685415
6. 16. 6. 14.14213562 2. 12.80624866
10. 8.94427204 10. 15.62049961 16. 8.
8. 14. 28. 5.65685415 18.43908882 14.42220497
14.42220497 6.3245554 23.32380676 8. 8.94427204 12.
14.14213562 8. 12.80624866 27.78488731 20.88061333 6.
18. 5.65685415 8. 24. 11.66190338 16.
6. 6.3245554 5.65685415 22. 2. 24.
6. 10. 5.65685415 14. 8. 10.
11.31370831 21.54065895 8.24621105 18. 20.88061333 16.97056198
14.56021976 12. 2. 19.69771576 13.41640759 8.24621105
12. 12. 6. 22.80350876 6. 16.
4. 6. 10. 5.65685415 7.21110249 12.
6.3245554 6.3245554 10. 2. 6. 4.47213602
4.47213602 19.79899025 24. 25.61249733 6.3245554 5.65685415
8. 16. 8.94427204 22.36067963 8.24621105 5.65685415
5.65685415 14. 10. 23.32380676 14.42220497 11.31370831
10. 4. 6. 28.28427124 8.24621105 12.64911079
10. 21.54065895 8.94427204 10. 32. 10.
18. 17.88854408 12. 4.47213602 10.19803905 29.73213768
28.28427124 28. 10. 2. 5.65685415 24.
32. 50. 46. 10. 4. 8. ]
<class 'numpy.ndarray'>
float64
throat.total_length
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33.05521097 35.2504025 28.75624347 42.06131525 34.6644879 32.28830769
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47.47360858 39.41195917 27.78114742 40.17455455 35.25038109 45.61421233
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42.31973412 31.40785162 22.58310498 40.60710342 31.79407204 34.26415839
24.12994565 38.34461444 28.97577777 35.5007564 43.04504296 26.64893031
37.01251444 26.69578326 48.30869584 35.49875057 31.12360584 26.98130299
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28.66875876 32.11659231 36.44127443 30.34461985 38.93805818 32.33080671
39.9810112 29.77490364 39.18124167 39.12360827 45.48080797 37.05318593
37.03795803 29.31988193 37.72535252 26.66028507 30.00310654 36.92560859
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31.82356115 38.81226441 26.39091912 43.29023799 52.95440042 47.24137753
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34.30526897 25.43935765 30.74526791 35.77017252 27.09147238 36.56158243
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39.30221846 30.78763952 47.75267699 36.35773706 44.46154422 40.70352413
28.39133094 27.11918718 34.05264162 28.47261081 30.02794561 35.98624015
25.67488415 27.93812884 25.84353397 27.99182655 36.78897228 25.74613332
42.45149182 46.03313629 38.82954819 29.85999757 28.23530833 25.92236301
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30.74429716 30.97394364 25.36893056 27.56998968 43.56681423 37.29957247
24.46606068 28.9524191 46.31071698 48.41571928 49.08056995 44.65905051
33.14626826 44.95866965 27.07473566 23.67236264 38.10091387 37.04444335
45.25962118 27.22970771 29.52149534 42.92186236 23.469616 38.66959078
28.70805375 33.28871986 35.86353336 31.8828829 31.0882636 46.01215928
45.34596335 32.25923155 30.2708387 47.24380038 45.0150486 37.88543147
33.71946151 52.71661009 41.57081177 36.69357376 45.17539865 27.54852832
42.51392143 36.61643158 24.50393712 27.0743418 50.85724729 32.2578611
32.13203474 37.36414207 45.63440737 39.42220265 32.31628637 37.24851443
27.71381533 33.05982608 35.82918778 27.12709318 49.86401668 37.56851857
46.2781622 41.24939513 43.77560762 49.95974192 36.06478808 28.29863549
29.02189094 27.78393331 40.78490694 30.69525457 28.73167147 35.0045701
44.54784566 39.13906454 38.94687599 28.50248965 42.82446691 36.35087829
36.24511009 50.90989023 40.443077 27.45181456 23.37883157 49.29581039
31.47191565 47.74376044 33.1290575 42.69702152 30.57772359 38.78650096
37.32974579 35.24747702 43.30240715 32.15908664 48.173627 46.11490109
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59.51927028 39.33957467 89.87839487 56.47746609 44.40401066 46.30011284
72.87241622 39.58148304 66.57255541 68.30031538 49.8476002 38.17698816
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28.09164828 26.65114724 38.25035719 37.4909524 27.22400938 39.94328414
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51.70536503 43.6582874 55.49642974 35.92784065 23.17229422 27.33966858
61.71464966 32.56734459 52.24651695 39.04893539 42.8782133 36.78280249
31.16497168 29.09484118 47.3179675 36.7724061 41.58822038 56.55871733
35.22033335 28.68317273 56.79360078 35.26311872 67.8970308 29.11381245
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25.12470472 36.89260742 60.98306175 44.12628991 65.82180453 59.67485934
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49.53806482 51.42834925 27.47667578 42.63287002 51.83598398 41.74201585
64.29105027 45.4442762 48.14203525 32.23068171 38.65879878 42.1589835
22.22385827 43.03294579 69.35705425 50.53369246 28.8395517 31.46982728
40.82620585 23.10933924 44.29349148 22.35770791 24.71567401 23.76068779
31.438006 48.99685548 61.2045399 38.36728536 39.68694651 20.22088642
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27.84812126 40.79312154 63.42135415 35.40284322 64.36217696 55.09958048
57.11175685 20.55803024 35.16785565 39.51823699 29.52655691 50.90158299
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25.06738532 32.8714111 20.79151355 37.84284639 42.83116468 25.12963739
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31.78049716 25.13961018 30.62678566 22.11334439 25.13961018 33.07567082
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35.02855978 32.37282811 25.63201124 32.86335345 23.70653918 22.56102835
28.63564213 25.90366769 22.22611077 35.70714214 34.55430509 25.84569597
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28.21347196 26.21068484 32.03123476 28.87905816 24.12467616 23.15167381
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33.58571125 24.2693222 27.44084547 38.63935817 44.50842617 33.19638535
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24.79919354 31.90611227 23.06512519 28.91366459 23.3023604 28.0713377
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38.88444419 28.75760769 29.10326442 28.89636655 41.71330723 40.22437072
31.65438358 37.62977544 24.59674775 28. 48.07286137 35.05709629
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24.45403852 21.65640783 27.45906044 27.33130074 28.68797658 28.24889378
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35.21363372 43.17406629 34.51086785 23.17326045 22.4053565 43.32435804
18.30300522 38. 26.77685568 34.66987165 28.37252192 38.70400496
36.52396474 34.0147027 38.44476557 29.69848481 36.81032464 43.63484846
70.09992867 46.9041576 37.88139385 47.66550115 44.98888752 34.88552709
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27.76688675 26.2488095 37.60319135 36.97296309 26.68332813 39.05124838
41.64132563 41.59326869 30.46309242 31.20897307 38.11823711 40.1248053
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35.09985755 28.39013913 56.77147171 35.21363372 64.63745044 29.05167809
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24.12467616 32.61901286 20.76053949 35.98610843 41.74925149 24.71841419
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float64
throat.perimeter
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24. 24. 23. 28. 25. 16. 28. 23. 18. 23. 28. 23. 17. 24. 33. 20. 16. 23.
28. 18. 14. 17. 15. 38. 9. 19. 26. 18. 15. 22. 20. 17. 19. 22. 33. 18.
24. 24. 19. 25. 20. 14. 22. 21. 15. 17. 27. 13. 24. 11. 16. 30. 23. 23.
26. 24. 17. 25. 34. 20. 20. 18. 26. 17. 19. 15. 15. 25. 13. 19. 35. 23.
10. 20. 23. 16. 21. 8. 22. 17. 24. 20. 16. 21. 21. 14. 22. 16. 19. 19.
16. 37. 19. 23. 13. 26. 23. 19. 24. 27. 22. 20. 23. 29. 12. 24. 27. 13.
11. 22. 18. 23. 5. 24. 23. 30. 15. 19. 10. 23. 40. 26. 15. 30. 21. 25.
11. 23. 18. 15. 20. 12. 23. 23. 14. 22. 34. 23. 13. 34. 14. 24. 20. 35.
18. 39. 15. 20. 21. 21. 15. 23. 33. 20. 16. 27. 19. 25. 21. 23. 21. 16.
32. 27. 17. 17. 11. 20. 29. 10. 19. 22. 12. 37. 21. 17. 17. 13. 12. 24.
18. 25. 23. 34. 24. 11. 27. 13. 32. 20. 38. 29. 14. 11. 22. 11. 19. 26.
14. 23. 15. 18. 24. 12. 31. 33. 28. 19. 14. 18. 11. 18. 12. 33. 13. 26.
20. 25. 21. 19. 27. 19. 11. 17. 16. 29. 23. 15. 19. 14. 21. 29. 23. 14.
7. 19. 23. 14. 30. 25. 12. 18. 26. 36. 22. 24. 19. 27. 24. 14. 31. 23.
28. 14. 20. 30. 19. 26. 17. 7. 20. 3. 31. 37. 24. 12. 14. 21. 22. 23.
31. 26. 18. 17. 24. 21. 24. 23. 20. 9. 23. 21. 19. 26. 28. 21. 17. 11.
23. 21. 23. 14. 26. 31. 35. 28. 24. 26. 14. 15. 22. 18. 37. 20. 11. 18.
24. 19. 33. 23. 36. 26. 8. 32. 26. 24. 13. 32. 23. 18. 18. 33. 23. 17.
9. 10. 32. 24. 1. 1. 1. 3. 2. 1. 2. 2. 1. 2. 1. 2. 3. 2.
1. 2. 2. 2. 1. 2. 1. 2. 2. 3. 2. 2. 2. 2. 1. 2. 2. 1.
3. 2. 2. 2. 3. 2. 2. 3. 2. 2. 2. 2. 2. 3. 2. 2. 2. 2.
1. 2. 1. 2. 2. 2. 2. 3. 2. 3. 2. 3. 2. 2. 2. 2. 1. 2.
2. 3. 3. 2. 2. 2. 2. 2. 1. 2. 2. 2. 2. 3. 3. 2. 2. 2.
3. 2. 2. 2. 2. 2. 2. 2. 2. 2. 3. 2. 1. 2. 2. 2. 1. 2.
2. 3. 2. 2. 2. 2. 2. 3. 3. 2. 3. 2. 3. 2. 1. 2. 3. 2.
2. 2. 2. 2. 2. 2. 1. 2. 2. 2. 2. 2. 2. 3. 2. 1. 2. 3.
3. 2. 2. 2. 3. 3. 2. 2. 3. 3. 2. 2. 3. 1. 2. 2. 3. 3.
2. 1. 2. 2. 3. 2. 2. 3. 2. 2. 2. 3. 1. 3. 2. 2. 2. 3.
2. 2. 2. 1. 2. 2. 1. 1. 1. 1. 1. 1.]
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float64
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793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793.
793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793.
793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793.
793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793.
793. 793. 793. 793. 793. 793. 793. 793. 793. 542. 1619. 1180.
560. 2165. 2762. 1624. 495. 948. 668. 373. 254. 684. 1336. 412.
298. 1072. 245. 1185. 656. 1649. 2067. 548. 544. 402. 1346. 447.
856. 273. 577. 1011. 965. 757. 1617. 304. 330. 297. 430. 831.
1010. 1016. 486. 463. 294. 2124. 2968. 1700. 1130. 457. 316. 984.
716. 473. 294. 489. 729. 2570. 1027. 355. 2316. 1285. 406. 354.
488. 384. 617. 2158. 449. 387. 788. 350. 260. 272. 374. 269.
1447. 373. 589. 258. 1479. 595. 2225. 261. 366. 935. 573. 362.
304. 1968. 1536. 466. 1374. 568. 599. 520. 1770. 796. 731. 285.
232. 707. 2512. 1817. 1290. 1614. 1371. 142. 615.]
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float64
pore.surface_area
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-4. -4. -4. -4. -4. -4. -4. -4. -4. -4. -4. -4. -4. -4.
-4. -4. -4. -4. -4. -4. -4. -4. -4. -4. -4. 75. 164. 144.
90. 202. 195. 119. 90. 94. 101. 71. 57. 87. 127. 80. 57. 100.
47. 98. 102. 113. 177. 77. 69. 86. 109. 79. 111. 54. 79. 113.
104. 91. 176. 56. 52. 56. 62. 89. 101. 107. 68. 69. 60. 154.
211. 121. 92. 82. 60. 96. 103. 79. 62. 86. 80. 210. 100. 59.
158. 105. 63. 80. 50. 66. 87. 158. 80. 84. 104. 67. 57. 46.
67. 74. 150. 57. 46. 56. 141. 81. 168. 52. 87. 95. 66. 62.
87. 149. 147. 54. 99. 98. 66. 89. 127. 83. 71. 79. 54. 71.
183. 175. 179. 162. 157. 57. 124.]
<class 'numpy.ndarray'>
float64
throat.cross_sectional_area
[36. 33. 23. 37. 37. 18. 29. 24. 24. 15. 24. 38. 30. 23. 23. 29. 17. 44.
24. 24. 23. 28. 25. 16. 28. 23. 18. 23. 28. 23. 17. 24. 33. 20. 16. 23.
28. 18. 14. 17. 15. 38. 9. 19. 26. 18. 15. 22. 20. 17. 19. 22. 33. 18.
24. 24. 19. 25. 20. 14. 22. 21. 15. 17. 27. 13. 24. 11. 16. 30. 23. 23.
26. 24. 17. 25. 34. 20. 20. 18. 26. 17. 19. 15. 15. 25. 13. 19. 35. 23.
10. 20. 23. 16. 21. 8. 22. 17. 24. 20. 16. 21. 21. 14. 22. 16. 19. 19.
16. 37. 19. 23. 13. 26. 23. 19. 24. 27. 22. 20. 23. 29. 12. 24. 27. 13.
11. 22. 18. 23. 5. 24. 23. 30. 15. 19. 10. 23. 40. 26. 15. 30. 21. 25.
11. 23. 18. 15. 20. 12. 23. 23. 14. 22. 34. 23. 13. 34. 14. 24. 20. 35.
18. 39. 15. 20. 21. 21. 15. 23. 33. 20. 16. 27. 19. 25. 21. 23. 21. 16.
32. 27. 17. 17. 11. 20. 29. 10. 19. 22. 12. 37. 21. 17. 17. 13. 12. 24.
18. 25. 23. 34. 24. 11. 27. 13. 32. 20. 38. 29. 14. 11. 22. 11. 19. 26.
14. 23. 15. 18. 24. 12. 31. 33. 28. 19. 14. 18. 11. 18. 12. 33. 13. 26.
20. 25. 21. 19. 27. 19. 11. 17. 16. 29. 23. 15. 19. 14. 21. 29. 23. 14.
7. 19. 23. 14. 30. 25. 12. 18. 26. 36. 22. 24. 19. 27. 24. 14. 31. 23.
28. 14. 20. 30. 19. 26. 17. 7. 20. 3. 31. 37. 24. 12. 14. 21. 22. 23.
31. 26. 18. 17. 24. 21. 24. 23. 20. 9. 23. 21. 19. 26. 28. 21. 17. 11.
23. 21. 23. 14. 26. 31. 35. 28. 24. 26. 14. 15. 22. 18. 37. 20. 11. 18.
24. 19. 33. 23. 36. 26. 8. 32. 26. 24. 13. 32. 23. 18. 18. 33. 23. 17.
9. 10. 32. 24. 22. 4. 1. 8. 8. 10. 4. 6. 10. 6. 1. 5. 9. 6.
19. 19. 6. 13. 18. 28. 5. 8. 27. 7. 3. 7. 5. 10. 17. 20. 6. 9.
11. 25. 16. 5. 7. 35. 12. 5. 7. 28. 12. 7. 6. 7. 7. 13. 17. 6.
3. 20. 20. 7. 7. 7. 10. 9. 4. 10. 17. 6. 6. 15. 6. 11. 1. 14.
9. 11. 11. 15. 16. 8. 7. 13. 14. 4. 18. 15. 15. 7. 26. 7. 9. 11.
15. 8. 12. 29. 22. 6. 18. 3. 7. 24. 14. 15. 3. 6. 6. 22. 1. 23.
5. 10. 4. 13. 7. 9. 12. 23. 8. 17. 23. 16. 16. 12. 1. 21. 15. 8.
11. 11. 6. 24. 5. 15. 2. 6. 9. 5. 7. 11. 6. 6. 9. 1. 6. 5.
5. 15. 24. 23. 6. 6. 7. 15. 9. 25. 8. 6. 6. 7. 10. 27. 15. 12.
10. 2. 5. 23. 9. 14. 10. 25. 9. 10. 32. 10. 9. 20. 11. 4. 10. 32.
21. 27. 9. 1. 5. 23. 16. 25. 23. 5. 2. 4.]
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float64
throat.equivalent_diameter
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5.52790639 5.52790639 5.41151638 5.97082132 5.64189584 4.51351667
5.97082132 5.41151638 4.78730736 5.41151638 5.97082132 5.41151638
4.65242649 5.52790639 6.48204481 5.04626504 4.51351667 5.41151638
5.97082132 4.78730736 4.22200825 4.65242649 4.37019372 6.95579634
3.3851375 4.91849076 5.75362739 4.78730736 4.37019372 5.29256743
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5.52790639 5.52790639 4.91849076 5.64189584 5.04626504 4.22200825
5.29256743 5.17088295 4.37019372 4.65242649 5.86323014 4.06842895
5.52790639 3.74241032 4.51351667 6.18038723 5.41151638 5.41151638
5.75362739 5.52790639 4.65242649 5.64189584 6.57952464 5.04626504
5.04626504 4.78730736 5.75362739 4.65242649 4.91849076 4.37019372
4.37019372 5.64189584 4.06842895 4.91849076 6.67558118 5.41151638
3.56824823 5.04626504 5.41151638 4.51351667 5.17088295 3.19153824
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5.17088295 4.22200825 5.29256743 4.51351667 4.91849076 4.91849076
4.51351667 6.86366252 4.91849076 5.41151638 4.06842895 5.75362739
5.41151638 4.91849076 5.52790639 5.86323014 5.29256743 5.04626504
5.41151638 6.07650778 3.9088201 5.52790639 5.86323014 4.06842895
3.74241032 5.29256743 4.78730736 5.41151638 2.52313252 5.52790639
5.41151638 6.18038723 4.37019372 4.91849076 3.56824823 5.41151638
7.13649646 5.75362739 4.37019372 6.18038723 5.17088295 5.64189584
3.74241032 5.41151638 4.78730736 4.37019372 5.04626504 3.9088201
5.41151638 5.41151638 4.22200825 5.29256743 6.57952464 5.41151638
4.06842895 6.57952464 4.22200825 5.52790639 5.04626504 6.67558118
4.78730736 7.04672564 4.37019372 5.04626504 5.17088295 5.17088295
4.37019372 5.41151638 6.48204481 5.04626504 4.51351667 5.86323014
4.91849076 5.64189584 5.17088295 5.41151638 5.17088295 4.51351667
6.38307649 5.86323014 4.65242649 4.65242649 3.74241032 5.04626504
6.07650778 3.56824823 4.91849076 5.29256743 3.9088201 6.86366252
5.17088295 4.65242649 4.65242649 4.06842895 3.9088201 5.52790639
4.78730736 5.64189584 5.41151638 6.57952464 5.52790639 3.74241032
5.86323014 4.06842895 6.38307649 5.04626504 6.95579634 6.07650778
4.22200825 3.74241032 5.29256743 3.74241032 4.91849076 5.75362739
4.22200825 5.41151638 4.37019372 4.78730736 5.52790639 3.9088201
6.28254931 6.48204481 5.97082132 4.91849076 4.22200825 4.78730736
3.74241032 4.78730736 3.9088201 6.48204481 4.06842895 5.75362739
5.04626504 5.64189584 5.17088295 4.91849076 5.86323014 4.91849076
3.74241032 4.65242649 4.51351667 6.07650778 5.41151638 4.37019372
4.91849076 4.22200825 5.17088295 6.07650778 5.41151638 4.22200825
2.98541066 4.91849076 5.41151638 4.22200825 6.18038723 5.64189584
3.9088201 4.78730736 5.75362739 6.770275 5.29256743 5.52790639
4.91849076 5.86323014 5.52790639 4.22200825 6.28254931 5.41151638
5.97082132 4.22200825 5.04626504 6.18038723 4.91849076 5.75362739
4.65242649 2.98541066 5.04626504 1.95441005 6.28254931 6.86366252
5.52790639 3.9088201 4.22200825 5.17088295 5.29256743 5.41151638
6.28254931 5.75362739 4.78730736 4.65242649 5.52790639 5.17088295
5.52790639 5.41151638 5.04626504 3.3851375 5.41151638 5.17088295
4.91849076 5.75362739 5.97082132 5.17088295 4.65242649 3.74241032
5.41151638 5.17088295 5.41151638 4.22200825 5.75362739 6.28254931
6.67558118 5.97082132 5.52790639 5.75362739 4.22200825 4.37019372
5.29256743 4.78730736 6.86366252 5.04626504 3.74241032 4.78730736
5.52790639 4.91849076 6.48204481 5.41151638 6.770275 5.75362739
3.19153824 6.38307649 5.75362739 5.52790639 4.06842895 6.38307649
5.41151638 4.78730736 4.78730736 6.48204481 5.41151638 4.65242649
3.3851375 3.56824823 6.38307649 5.52790639 5.29256743 2.25675833
1.12837917 3.19153824 3.19153824 3.56824823 2.25675833 2.7639532
3.56824823 2.7639532 1.12837917 2.52313252 3.3851375 2.7639532
4.91849076 4.91849076 2.7639532 4.06842895 4.78730736 5.97082132
2.52313252 3.19153824 5.86323014 2.98541066 1.95441005 2.98541066
2.52313252 3.56824823 4.65242649 5.04626504 2.7639532 3.3851375
3.74241032 5.64189584 4.51351667 2.52313252 2.98541066 6.67558118
3.9088201 2.52313252 2.98541066 5.97082132 3.9088201 2.98541066
2.7639532 2.98541066 2.98541066 4.06842895 4.65242649 2.7639532
1.95441005 5.04626504 5.04626504 2.98541066 2.98541066 2.98541066
3.56824823 3.3851375 2.25675833 3.56824823 4.65242649 2.7639532
2.7639532 4.37019372 2.7639532 3.74241032 1.12837917 4.22200825
3.3851375 3.74241032 3.74241032 4.37019372 4.51351667 3.19153824
2.98541066 4.06842895 4.22200825 2.25675833 4.78730736 4.37019372
4.37019372 2.98541066 5.75362739 2.98541066 3.3851375 3.74241032
4.37019372 3.19153824 3.9088201 6.07650778 5.29256743 2.7639532
4.78730736 1.95441005 2.98541066 5.52790639 4.22200825 4.37019372
1.95441005 2.7639532 2.7639532 5.29256743 1.12837917 5.41151638
2.52313252 3.56824823 2.25675833 4.06842895 2.98541066 3.3851375
3.9088201 5.41151638 3.19153824 4.65242649 5.41151638 4.51351667
4.51351667 3.9088201 1.12837917 5.17088295 4.37019372 3.19153824
3.74241032 3.74241032 2.7639532 5.52790639 2.52313252 4.37019372
1.59576912 2.7639532 3.3851375 2.52313252 2.98541066 3.74241032
2.7639532 2.7639532 3.3851375 1.12837917 2.7639532 2.52313252
2.52313252 4.37019372 5.52790639 5.41151638 2.7639532 2.7639532
2.98541066 4.37019372 3.3851375 5.64189584 3.19153824 2.7639532
2.7639532 2.98541066 3.56824823 5.86323014 4.37019372 3.9088201
3.56824823 1.59576912 2.52313252 5.41151638 3.3851375 4.22200825
3.56824823 5.64189584 3.3851375 3.56824823 6.38307649 3.56824823
3.3851375 5.04626504 3.74241032 2.25675833 3.56824823 6.38307649
5.17088295 5.86323014 3.3851375 1.12837917 2.52313252 5.41151638
4.51351667 5.64189584 5.41151638 2.52313252 1.59576912 2.25675833]
<class 'numpy.ndarray'>
float64
══════════════════════════════════════════════════════════════════════════════
net : <openpnm.network.Network at 0x18f436b9860>
――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――
# Properties Valid Values
――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――
2 throat.conns 534 / 534
3 pore.coords 189 / 189
4 pore.region_label 189 / 189
5 pore.phase 189 / 189
6 throat.phases 534 / 534
7 pore.region_volume 189 / 189
8 pore.equivalent_diameter 189 / 189
9 pore.local_peak 189 / 189
10 pore.global_peak 189 / 189
11 pore.geometric_centroid 189 / 189
12 throat.global_peak 534 / 534
13 pore.inscribed_diameter 189 / 189
14 pore.extended_diameter 189 / 189
15 throat.inscribed_diameter 534 / 534
16 throat.total_length 534 / 534
17 throat.direct_length 534 / 534
18 throat.perimeter 534 / 534
19 pore.volume 189 / 189
20 pore.surface_area 189 / 189
21 throat.cross_sectional_area 534 / 534
22 throat.equivalent_diameter 534 / 534
――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――
# Labels Assigned Locations
――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――
2 pore.all 189
3 throat.all 534
4 pore.phase1 81
5 throat.phase1_phase2 346
6 pore.phase2 108
7 throat.phase2_phase1 346
8 throat.phase2_phase2 188
――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――
ax = op.visualization.plot_connections(pn2, throats=pn2['throat.phase2_phase2'], c='k')
ax = op.visualization.plot_connections(pn2, throats=pn2['throat.phase2_phase1'], c='grey', ax=ax)
ax = op.visualization.plot_coordinates(pn2, pores=pn2['pore.phase2'], c='r', markersize=50, ax=ax)
ax = op.visualization.plot_coordinates(pn2, pores=pn2['pore.phase1'], c='g', markersize=50, ax=ax)
fig, ax = plt.gcf(), plt.gca()
ax.imshow(net2.regions.T)
ax.axis(False);
Now can see the particles are indicated by a green marker, the void pores by a red marker, the solid-void interconnections are in grey, and the void-void throats are black.
phase_alias#
In the previous section the default phase names created by snow2 were the uncreative “phase1” and “phase2”. The snow2 function allows for these to be given more desriptive names. This is done by supplying a dictionary with the voxels value as the key and the desired phase name as the value.
net3 = ps.networks.snow2(phases=im.astype(int) + 1, phase_alias={1: 'solid', 2: 'void'}, boundary_width=0)
pn3 = op.io.network_from_porespy(net3.network)
print(pn3)
throat.conns
[[ 0 82]
[ 0 83]
[ 0 90]
...
[183 187]
[184 188]
[186 188]]
<class 'numpy.ndarray'>
int32
pore.coords
[[ 16. 80. 0. ]
[ 16. 251. 0. ]
[ 25. 144. 0. ]
[ 25. 181. 0. ]
[ 33. 379. 0. ]
[ 34. 320. 0. ]
[ 37. 19. 0. ]
[ 40. 109. 0. ]
[ 49. 58. 0. ]
[ 53. 234. 0. ]
[ 59. 197. 0. ]
[ 61. 272. 0. ]
[ 64. 139. 0. ]
[ 71. 316. 0. ]
[ 72. 87. 0. ]
[ 74. 24. 0. ]
[ 74. 367. 0. ]
[ 89. 225. 0. ]
[ 95. 57. 0. ]
[107. 151. 0. ]
[108. 327. 0. ]
[111. 18. 0. ]
[111. 113. 0. ]
[118. 189. 0. ]
[124. 255. 0. ]
[125. 364. 0. ]
[126. 293. 0. ]
[128. 78. 0. ]
[143. 218. 0. ]
[144. 152. 0. ]
[148. 329. 0. ]
[151. 47. 0. ]
[157. 116. 0. ]
[165. 294. 0. ]
[169. 370. 0. ]
[171. 256. 0. ]
[173. 177. 0. ]
[185. 16. 0. ]
[189. 54. 0. ]
[198. 347. 0. ]
[202. 298. 0. ]
[206. 91. 0. ]
[206. 228. 0. ]
[215. 174. 0. ]
[215. 381. 0. ]
[221. 135. 0. ]
[226. 261. 0. ]
[238. 16. 0. ]
[240. 306. 0. ]
[242. 80. 0. ]
[242. 346. 0. ]
[258. 383. 0. ]
[262. 244. 0. ]
[263. 154. 0. ]
[263. 196. 0. ]
[264. 49. 0. ]
[272. 118. 0. ]
[279. 350. 0. ]
[282. 310. 0. ]
[284. 17. 0. ]
[284. 82. 0. ]
[298. 257. 0. ]
[298. 383. 0. ]
[300. 190. 0. ]
[313. 333. 0. ]
[315. 224. 0. ]
[318. 154. 0. ]
[319. 68. 0. ]
[322. 22. 0. ]
[324. 292. 0. ]
[339. 103. 0. ]
[339. 382. 0. ]
[351. 214. 0. ]
[359. 173. 0. ]
[360. 351. 0. ]
[361. 309. 0. ]
[363. 24. 0. ]
[368. 251. 0. ]
[379. 383. 0. ]
[380. 115. 0. ]
[382. 61. 0. ]
[ 13.6402214 8.38929889 0. ]
[ 16.95243978 45.06670784 0. ]
[ 11.97881356 114.99661017 0. ]
[ 7.94285714 162.5 0. ]
[ 21.47852194 213.90808314 0. ]
[ 26.96234613 289.51737871 0. ]
[ 14.15455665 348.89593596 0. ]
[ 12.02626263 390.41616162 0. ]
[ 47.01476793 165.32067511 0. ]
[ 44.01197605 83.39221557 0. ]
[ 41.99463807 252.90884718 0. ]
[ 42.9488189 131.06692913 0. ]
[ 56.65789474 389.17251462 0. ]
[ 52.03517964 346.89296407 0. ]
[ 57.24271845 6.6092233 0. ]
[ 53.36577181 34.5704698 0. ]
[ 75.50932836 112.99813433 0. ]
[ 67.55102041 217.95510204 0. ]
[ 85.64050633 250.21772152 0. ]
[ 72.25609756 54.96493902 0. ]
[ 83.83201941 171.28562765 0. ]
[ 94.43589744 288.27672956 0. ]
[ 89.02554745 202.08394161 0. ]
[ 83.51102941 338.70220588 0. ]
[ 89.7238806 6.6318408 0. ]
[100.17904903 385.71768202 0. ]
[ 91.40268456 133.92170022 0. ]
[100.8411215 85.18457944 0. ]
[ 94.01831502 33.63003663 0. ]
[100.89081456 353.32582322 0. ]
[116.80811078 222.5776459 0. ]
[121.77202073 47.80103627 0. ]
[130.32232497 130.89035667 0. ]
[147.36301793 15.2436611 0. ]
[123.51973684 165.34210526 0. ]
[126.82727273 340.2 0. ]
[127.93602694 316.003367 0. ]
[133.21162791 102.63023256 0. ]
[146.82551143 272.91576414 0. ]
[145.75247525 386.81287129 0. ]
[145.1476378 184.75885827 0. ]
[146.84773663 243.35185185 0. ]
[147.79049676 354.16414687 0. ]
[145.69387755 305.51360544 0. ]
[167.09887006 81.39500942 0. ]
[186.70990566 137.57985175 0. ]
[174.02823529 217.22176471 0. ]
[179.37522124 320.02743363 0. ]
[171.56455142 346.64770241 0. ]
[174.16455696 38.11075949 0. ]
[193.08434959 274.45934959 0. ]
[188.18994413 389.81564246 0. ]
[199.50105708 250.02536998 0. ]
[193.84693878 367.58843537 0. ]
[211.44580777 6.73619632 0. ]
[198.25240055 196.12482853 0. ]
[221.12957198 47.73307393 0. ]
[218.59006816 325.37877313 0. ]
[219.4 357.54647887 0. ]
[234.84110535 215.86183074 0. ]
[237.01089494 108.41400778 0. ]
[223.16995074 287. 0. ]
[235.30508475 392.88418079 0. ]
[235.20491803 154.69262295 0. ]
[237.8125 369.94270833 0. ]
[244.94165316 174.69854133 0. ]
[262.79564411 277.99258573 0. ]
[249.28730512 134.50556793 0. ]
[261.64082687 6.20155039 0. ]
[260.71827411 326.93527919 0. ]
[261.25428571 26.4 0. ]
[259.54230769 360.39230769 0. ]
[263.35294118 70.85661765 0. ]
[264.55882353 93.45454545 0. ]
[278. 393.32713755 0. ]
[284.98479613 221.96406358 0. ]
[275.91420912 178.3538874 0. ]
[287.68421053 143.06791171 0. ]
[278.40310078 372.10077519 0. ]
[296.35091278 47.40162272 0. ]
[291.95294118 165.0907563 0. ]
[307.04719101 111.03505618 0. ]
[291.01532567 331.02681992 0. ]
[305.61748634 6.22131148 0. ]
[310.40641711 360.84278075 0. ]
[300.36998255 285.69458988 0. ]
[306.24585635 310.7320442 0. ]
[319.15789474 393.06578947 0. ]
[333.37347561 252.06097561 0. ]
[330.06184896 188.7890625 0. ]
[333.86480687 312.37339056 0. ]
[345.93449782 46.92212518 0. ]
[343.50704225 7.79225352 0. ]
[342.4457429 330.89983306 0. ]
[335.88076923 355.18461538 0. ]
[349.14293785 137.18587571 0. ]
[348.64447236 75.91331658 0. ]
[351.80164159 282.27770178 0. ]
[358.29824561 393.44210526 0. ]
[359.07758621 372.67241379 0. ]
[367.0311174 91.54879774 0. ]
[382.17356688 210.19785032 0. ]
[385.22014309 340.11172262 0. ]
[386.34341085 22.78682171 0. ]
[384.42998761 281.366171 0. ]
[385.4726477 149.26185266 0. ]
[394.28873239 393.14788732 0. ]
[391.6601626 89.10243902 0. ]]
<class 'numpy.ndarray'>
float64
pore.region_label
[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72
73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108
109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126
127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144
145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162
163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180
181 182 183 184 185 186 187 188 189]
<class 'numpy.ndarray'>
int32
pore.phase
[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2]
<class 'numpy.ndarray'>
int32
throat.phases
[[1 2]
[1 2]
[1 2]
...
[2 2]
[2 2]
[2 2]]
<class 'numpy.ndarray'>
int32
pore.region_volume
[ 793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793.
793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793.
793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793.
793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793.
793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793.
793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793.
793. 793. 793. 793. 793. 793. 793. 793. 793. 542. 1619. 1180.
560. 2165. 2762. 1624. 495. 948. 668. 373. 254. 684. 1336. 412.
298. 1072. 245. 1185. 656. 1649. 2067. 548. 544. 402. 1346. 447.
856. 273. 577. 1011. 965. 757. 1617. 304. 330. 297. 430. 831.
1010. 1016. 486. 463. 294. 2124. 2968. 1700. 1130. 457. 316. 984.
716. 473. 294. 489. 729. 2570. 1027. 355. 2316. 1285. 406. 354.
488. 384. 617. 2158. 449. 387. 788. 350. 260. 272. 374. 269.
1447. 373. 589. 258. 1479. 595. 2225. 261. 366. 935. 573. 362.
304. 1968. 1536. 466. 1374. 568. 599. 520. 1770. 796. 731. 285.
232. 707. 2512. 1817. 1290. 1614. 1371. 142. 615.]
<class 'numpy.ndarray'>
float64
pore.equivalent_diameter
[31.77544585 31.77544585 31.77544585 31.77544585 31.77544585 31.77544585
31.77544585 31.77544585 31.77544585 31.77544585 31.77544585 31.77544585
31.77544585 31.77544585 31.77544585 31.77544585 31.77544585 31.77544585
31.77544585 31.77544585 31.77544585 31.77544585 31.77544585 31.77544585
31.77544585 31.77544585 31.77544585 31.77544585 31.77544585 31.77544585
31.77544585 31.77544585 31.77544585 31.77544585 31.77544585 31.77544585
31.77544585 31.77544585 31.77544585 31.77544585 31.77544585 31.77544585
31.77544585 31.77544585 31.77544585 31.77544585 31.77544585 31.77544585
31.77544585 31.77544585 31.77544585 31.77544585 31.77544585 31.77544585
31.77544585 31.77544585 31.77544585 31.77544585 31.77544585 31.77544585
31.77544585 31.77544585 31.77544585 31.77544585 31.77544585 31.77544585
31.77544585 31.77544585 31.77544585 31.77544585 31.77544585 31.77544585
31.77544585 31.77544585 31.77544585 31.77544585 31.77544585 31.77544585
31.77544585 31.77544585 31.77544585 26.26967516 45.40236583 38.76109729
26.70232471 52.50298672 59.30166627 45.47242044 25.10485162 34.74235295
29.16374489 21.79262146 17.98340469 29.51094456 41.24376355 22.90359562
19.47884453 36.94472617 17.66192765 38.84313145 28.90060798 45.82108695
51.30093702 26.41467907 26.31809857 22.62393195 41.39783119 23.85661494
33.01352829 18.6438836 27.10459772 35.87819923 35.05247724 31.04581027
45.3743137 19.67396304 20.49802551 19.44613444 23.39856842 32.52786593
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14.56021976 12. 2. 19.69771576 13.41640759 8.24621105
12. 12. 6. 22.80350876 6. 16.
4. 6. 10. 5.65685415 7.21110249 12.
6.3245554 6.3245554 10. 2. 6. 4.47213602
4.47213602 19.79899025 24. 25.61249733 6.3245554 5.65685415
8. 16. 8.94427204 22.36067963 8.24621105 5.65685415
5.65685415 14. 10. 23.32380676 14.42220497 11.31370831
10. 4. 6. 28.28427124 8.24621105 12.64911079
10. 21.54065895 8.94427204 10. 32. 10.
18. 17.88854408 12. 4.47213602 10.19803905 29.73213768
28.28427124 28. 10. 2. 5.65685415 24.
32. 50. 46. 10. 4. 8. ]
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35.21363372 43.17406629 34.51086785 23.17326045 22.4053565 43.32435804
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36.52396474 34.0147027 38.44476557 29.69848481 36.81032464 43.63484846
70.09992867 46.9041576 37.88139385 47.66550115 44.98888752 34.88552709
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float64
throat.perimeter
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24. 24. 23. 28. 25. 16. 28. 23. 18. 23. 28. 23. 17. 24. 33. 20. 16. 23.
28. 18. 14. 17. 15. 38. 9. 19. 26. 18. 15. 22. 20. 17. 19. 22. 33. 18.
24. 24. 19. 25. 20. 14. 22. 21. 15. 17. 27. 13. 24. 11. 16. 30. 23. 23.
26. 24. 17. 25. 34. 20. 20. 18. 26. 17. 19. 15. 15. 25. 13. 19. 35. 23.
10. 20. 23. 16. 21. 8. 22. 17. 24. 20. 16. 21. 21. 14. 22. 16. 19. 19.
16. 37. 19. 23. 13. 26. 23. 19. 24. 27. 22. 20. 23. 29. 12. 24. 27. 13.
11. 22. 18. 23. 5. 24. 23. 30. 15. 19. 10. 23. 40. 26. 15. 30. 21. 25.
11. 23. 18. 15. 20. 12. 23. 23. 14. 22. 34. 23. 13. 34. 14. 24. 20. 35.
18. 39. 15. 20. 21. 21. 15. 23. 33. 20. 16. 27. 19. 25. 21. 23. 21. 16.
32. 27. 17. 17. 11. 20. 29. 10. 19. 22. 12. 37. 21. 17. 17. 13. 12. 24.
18. 25. 23. 34. 24. 11. 27. 13. 32. 20. 38. 29. 14. 11. 22. 11. 19. 26.
14. 23. 15. 18. 24. 12. 31. 33. 28. 19. 14. 18. 11. 18. 12. 33. 13. 26.
20. 25. 21. 19. 27. 19. 11. 17. 16. 29. 23. 15. 19. 14. 21. 29. 23. 14.
7. 19. 23. 14. 30. 25. 12. 18. 26. 36. 22. 24. 19. 27. 24. 14. 31. 23.
28. 14. 20. 30. 19. 26. 17. 7. 20. 3. 31. 37. 24. 12. 14. 21. 22. 23.
31. 26. 18. 17. 24. 21. 24. 23. 20. 9. 23. 21. 19. 26. 28. 21. 17. 11.
23. 21. 23. 14. 26. 31. 35. 28. 24. 26. 14. 15. 22. 18. 37. 20. 11. 18.
24. 19. 33. 23. 36. 26. 8. 32. 26. 24. 13. 32. 23. 18. 18. 33. 23. 17.
9. 10. 32. 24. 1. 1. 1. 3. 2. 1. 2. 2. 1. 2. 1. 2. 3. 2.
1. 2. 2. 2. 1. 2. 1. 2. 2. 3. 2. 2. 2. 2. 1. 2. 2. 1.
3. 2. 2. 2. 3. 2. 2. 3. 2. 2. 2. 2. 2. 3. 2. 2. 2. 2.
1. 2. 1. 2. 2. 2. 2. 3. 2. 3. 2. 3. 2. 2. 2. 2. 1. 2.
2. 3. 3. 2. 2. 2. 2. 2. 1. 2. 2. 2. 2. 3. 3. 2. 2. 2.
3. 2. 2. 2. 2. 2. 2. 2. 2. 2. 3. 2. 1. 2. 2. 2. 1. 2.
2. 3. 2. 2. 2. 2. 2. 3. 3. 2. 3. 2. 3. 2. 1. 2. 3. 2.
2. 2. 2. 2. 2. 2. 1. 2. 2. 2. 2. 2. 2. 3. 2. 1. 2. 3.
3. 2. 2. 2. 3. 3. 2. 2. 3. 3. 2. 2. 3. 1. 2. 2. 3. 3.
2. 1. 2. 2. 3. 2. 2. 3. 2. 2. 2. 3. 1. 3. 2. 2. 2. 3.
2. 2. 2. 1. 2. 2. 1. 1. 1. 1. 1. 1.]
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793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793.
793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793.
793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793.
793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793. 793.
793. 793. 793. 793. 793. 793. 793. 793. 793. 542. 1619. 1180.
560. 2165. 2762. 1624. 495. 948. 668. 373. 254. 684. 1336. 412.
298. 1072. 245. 1185. 656. 1649. 2067. 548. 544. 402. 1346. 447.
856. 273. 577. 1011. 965. 757. 1617. 304. 330. 297. 430. 831.
1010. 1016. 486. 463. 294. 2124. 2968. 1700. 1130. 457. 316. 984.
716. 473. 294. 489. 729. 2570. 1027. 355. 2316. 1285. 406. 354.
488. 384. 617. 2158. 449. 387. 788. 350. 260. 272. 374. 269.
1447. 373. 589. 258. 1479. 595. 2225. 261. 366. 935. 573. 362.
304. 1968. 1536. 466. 1374. 568. 599. 520. 1770. 796. 731. 285.
232. 707. 2512. 1817. 1290. 1614. 1371. 142. 615.]
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pore.surface_area
[ -4. -4. -4. -4. -4. -4. -4. -4. -4. -4. -4. -4. -4. -4.
-4. -4. -4. -4. -4. -4. -4. -4. -4. -4. -4. -4. -4. -4.
-4. -4. -4. -4. -4. -4. -4. -4. -4. -4. -4. -4. -4. -4.
-4. -4. -4. -4. -4. -4. -4. -4. -4. -4. -4. -4. -4. -4.
-4. -4. -4. -4. -4. -4. -4. -4. -4. -4. -4. -4. -4. -4.
-4. -4. -4. -4. -4. -4. -4. -4. -4. -4. -4. 75. 164. 144.
90. 202. 195. 119. 90. 94. 101. 71. 57. 87. 127. 80. 57. 100.
47. 98. 102. 113. 177. 77. 69. 86. 109. 79. 111. 54. 79. 113.
104. 91. 176. 56. 52. 56. 62. 89. 101. 107. 68. 69. 60. 154.
211. 121. 92. 82. 60. 96. 103. 79. 62. 86. 80. 210. 100. 59.
158. 105. 63. 80. 50. 66. 87. 158. 80. 84. 104. 67. 57. 46.
67. 74. 150. 57. 46. 56. 141. 81. 168. 52. 87. 95. 66. 62.
87. 149. 147. 54. 99. 98. 66. 89. 127. 83. 71. 79. 54. 71.
183. 175. 179. 162. 157. 57. 124.]
<class 'numpy.ndarray'>
float64
throat.cross_sectional_area
[36. 33. 23. 37. 37. 18. 29. 24. 24. 15. 24. 38. 30. 23. 23. 29. 17. 44.
24. 24. 23. 28. 25. 16. 28. 23. 18. 23. 28. 23. 17. 24. 33. 20. 16. 23.
28. 18. 14. 17. 15. 38. 9. 19. 26. 18. 15. 22. 20. 17. 19. 22. 33. 18.
24. 24. 19. 25. 20. 14. 22. 21. 15. 17. 27. 13. 24. 11. 16. 30. 23. 23.
26. 24. 17. 25. 34. 20. 20. 18. 26. 17. 19. 15. 15. 25. 13. 19. 35. 23.
10. 20. 23. 16. 21. 8. 22. 17. 24. 20. 16. 21. 21. 14. 22. 16. 19. 19.
16. 37. 19. 23. 13. 26. 23. 19. 24. 27. 22. 20. 23. 29. 12. 24. 27. 13.
11. 22. 18. 23. 5. 24. 23. 30. 15. 19. 10. 23. 40. 26. 15. 30. 21. 25.
11. 23. 18. 15. 20. 12. 23. 23. 14. 22. 34. 23. 13. 34. 14. 24. 20. 35.
18. 39. 15. 20. 21. 21. 15. 23. 33. 20. 16. 27. 19. 25. 21. 23. 21. 16.
32. 27. 17. 17. 11. 20. 29. 10. 19. 22. 12. 37. 21. 17. 17. 13. 12. 24.
18. 25. 23. 34. 24. 11. 27. 13. 32. 20. 38. 29. 14. 11. 22. 11. 19. 26.
14. 23. 15. 18. 24. 12. 31. 33. 28. 19. 14. 18. 11. 18. 12. 33. 13. 26.
20. 25. 21. 19. 27. 19. 11. 17. 16. 29. 23. 15. 19. 14. 21. 29. 23. 14.
7. 19. 23. 14. 30. 25. 12. 18. 26. 36. 22. 24. 19. 27. 24. 14. 31. 23.
28. 14. 20. 30. 19. 26. 17. 7. 20. 3. 31. 37. 24. 12. 14. 21. 22. 23.
31. 26. 18. 17. 24. 21. 24. 23. 20. 9. 23. 21. 19. 26. 28. 21. 17. 11.
23. 21. 23. 14. 26. 31. 35. 28. 24. 26. 14. 15. 22. 18. 37. 20. 11. 18.
24. 19. 33. 23. 36. 26. 8. 32. 26. 24. 13. 32. 23. 18. 18. 33. 23. 17.
9. 10. 32. 24. 22. 4. 1. 8. 8. 10. 4. 6. 10. 6. 1. 5. 9. 6.
19. 19. 6. 13. 18. 28. 5. 8. 27. 7. 3. 7. 5. 10. 17. 20. 6. 9.
11. 25. 16. 5. 7. 35. 12. 5. 7. 28. 12. 7. 6. 7. 7. 13. 17. 6.
3. 20. 20. 7. 7. 7. 10. 9. 4. 10. 17. 6. 6. 15. 6. 11. 1. 14.
9. 11. 11. 15. 16. 8. 7. 13. 14. 4. 18. 15. 15. 7. 26. 7. 9. 11.
15. 8. 12. 29. 22. 6. 18. 3. 7. 24. 14. 15. 3. 6. 6. 22. 1. 23.
5. 10. 4. 13. 7. 9. 12. 23. 8. 17. 23. 16. 16. 12. 1. 21. 15. 8.
11. 11. 6. 24. 5. 15. 2. 6. 9. 5. 7. 11. 6. 6. 9. 1. 6. 5.
5. 15. 24. 23. 6. 6. 7. 15. 9. 25. 8. 6. 6. 7. 10. 27. 15. 12.
10. 2. 5. 23. 9. 14. 10. 25. 9. 10. 32. 10. 9. 20. 11. 4. 10. 32.
21. 27. 9. 1. 5. 23. 16. 25. 23. 5. 2. 4.]
<class 'numpy.ndarray'>
float64
throat.equivalent_diameter
[6.770275 6.48204481 5.41151638 6.86366252 6.86366252 4.78730736
6.07650778 5.52790639 5.52790639 4.37019372 5.52790639 6.95579634
6.18038723 5.41151638 5.41151638 6.07650778 4.65242649 7.48482064
5.52790639 5.52790639 5.41151638 5.97082132 5.64189584 4.51351667
5.97082132 5.41151638 4.78730736 5.41151638 5.97082132 5.41151638
4.65242649 5.52790639 6.48204481 5.04626504 4.51351667 5.41151638
5.97082132 4.78730736 4.22200825 4.65242649 4.37019372 6.95579634
3.3851375 4.91849076 5.75362739 4.78730736 4.37019372 5.29256743
5.04626504 4.65242649 4.91849076 5.29256743 6.48204481 4.78730736
5.52790639 5.52790639 4.91849076 5.64189584 5.04626504 4.22200825
5.29256743 5.17088295 4.37019372 4.65242649 5.86323014 4.06842895
5.52790639 3.74241032 4.51351667 6.18038723 5.41151638 5.41151638
5.75362739 5.52790639 4.65242649 5.64189584 6.57952464 5.04626504
5.04626504 4.78730736 5.75362739 4.65242649 4.91849076 4.37019372
4.37019372 5.64189584 4.06842895 4.91849076 6.67558118 5.41151638
3.56824823 5.04626504 5.41151638 4.51351667 5.17088295 3.19153824
5.29256743 4.65242649 5.52790639 5.04626504 4.51351667 5.17088295
5.17088295 4.22200825 5.29256743 4.51351667 4.91849076 4.91849076
4.51351667 6.86366252 4.91849076 5.41151638 4.06842895 5.75362739
5.41151638 4.91849076 5.52790639 5.86323014 5.29256743 5.04626504
5.41151638 6.07650778 3.9088201 5.52790639 5.86323014 4.06842895
3.74241032 5.29256743 4.78730736 5.41151638 2.52313252 5.52790639
5.41151638 6.18038723 4.37019372 4.91849076 3.56824823 5.41151638
7.13649646 5.75362739 4.37019372 6.18038723 5.17088295 5.64189584
3.74241032 5.41151638 4.78730736 4.37019372 5.04626504 3.9088201
5.41151638 5.41151638 4.22200825 5.29256743 6.57952464 5.41151638
4.06842895 6.57952464 4.22200825 5.52790639 5.04626504 6.67558118
4.78730736 7.04672564 4.37019372 5.04626504 5.17088295 5.17088295
4.37019372 5.41151638 6.48204481 5.04626504 4.51351667 5.86323014
4.91849076 5.64189584 5.17088295 5.41151638 5.17088295 4.51351667
6.38307649 5.86323014 4.65242649 4.65242649 3.74241032 5.04626504
6.07650778 3.56824823 4.91849076 5.29256743 3.9088201 6.86366252
5.17088295 4.65242649 4.65242649 4.06842895 3.9088201 5.52790639
4.78730736 5.64189584 5.41151638 6.57952464 5.52790639 3.74241032
5.86323014 4.06842895 6.38307649 5.04626504 6.95579634 6.07650778
4.22200825 3.74241032 5.29256743 3.74241032 4.91849076 5.75362739
4.22200825 5.41151638 4.37019372 4.78730736 5.52790639 3.9088201
6.28254931 6.48204481 5.97082132 4.91849076 4.22200825 4.78730736
3.74241032 4.78730736 3.9088201 6.48204481 4.06842895 5.75362739
5.04626504 5.64189584 5.17088295 4.91849076 5.86323014 4.91849076
3.74241032 4.65242649 4.51351667 6.07650778 5.41151638 4.37019372
4.91849076 4.22200825 5.17088295 6.07650778 5.41151638 4.22200825
2.98541066 4.91849076 5.41151638 4.22200825 6.18038723 5.64189584
3.9088201 4.78730736 5.75362739 6.770275 5.29256743 5.52790639
4.91849076 5.86323014 5.52790639 4.22200825 6.28254931 5.41151638
5.97082132 4.22200825 5.04626504 6.18038723 4.91849076 5.75362739
4.65242649 2.98541066 5.04626504 1.95441005 6.28254931 6.86366252
5.52790639 3.9088201 4.22200825 5.17088295 5.29256743 5.41151638
6.28254931 5.75362739 4.78730736 4.65242649 5.52790639 5.17088295
5.52790639 5.41151638 5.04626504 3.3851375 5.41151638 5.17088295
4.91849076 5.75362739 5.97082132 5.17088295 4.65242649 3.74241032
5.41151638 5.17088295 5.41151638 4.22200825 5.75362739 6.28254931
6.67558118 5.97082132 5.52790639 5.75362739 4.22200825 4.37019372
5.29256743 4.78730736 6.86366252 5.04626504 3.74241032 4.78730736
5.52790639 4.91849076 6.48204481 5.41151638 6.770275 5.75362739
3.19153824 6.38307649 5.75362739 5.52790639 4.06842895 6.38307649
5.41151638 4.78730736 4.78730736 6.48204481 5.41151638 4.65242649
3.3851375 3.56824823 6.38307649 5.52790639 5.29256743 2.25675833
1.12837917 3.19153824 3.19153824 3.56824823 2.25675833 2.7639532
3.56824823 2.7639532 1.12837917 2.52313252 3.3851375 2.7639532
4.91849076 4.91849076 2.7639532 4.06842895 4.78730736 5.97082132
2.52313252 3.19153824 5.86323014 2.98541066 1.95441005 2.98541066
2.52313252 3.56824823 4.65242649 5.04626504 2.7639532 3.3851375
3.74241032 5.64189584 4.51351667 2.52313252 2.98541066 6.67558118
3.9088201 2.52313252 2.98541066 5.97082132 3.9088201 2.98541066
2.7639532 2.98541066 2.98541066 4.06842895 4.65242649 2.7639532
1.95441005 5.04626504 5.04626504 2.98541066 2.98541066 2.98541066
3.56824823 3.3851375 2.25675833 3.56824823 4.65242649 2.7639532
2.7639532 4.37019372 2.7639532 3.74241032 1.12837917 4.22200825
3.3851375 3.74241032 3.74241032 4.37019372 4.51351667 3.19153824
2.98541066 4.06842895 4.22200825 2.25675833 4.78730736 4.37019372
4.37019372 2.98541066 5.75362739 2.98541066 3.3851375 3.74241032
4.37019372 3.19153824 3.9088201 6.07650778 5.29256743 2.7639532
4.78730736 1.95441005 2.98541066 5.52790639 4.22200825 4.37019372
1.95441005 2.7639532 2.7639532 5.29256743 1.12837917 5.41151638
2.52313252 3.56824823 2.25675833 4.06842895 2.98541066 3.3851375
3.9088201 5.41151638 3.19153824 4.65242649 5.41151638 4.51351667
4.51351667 3.9088201 1.12837917 5.17088295 4.37019372 3.19153824
3.74241032 3.74241032 2.7639532 5.52790639 2.52313252 4.37019372
1.59576912 2.7639532 3.3851375 2.52313252 2.98541066 3.74241032
2.7639532 2.7639532 3.3851375 1.12837917 2.7639532 2.52313252
2.52313252 4.37019372 5.52790639 5.41151638 2.7639532 2.7639532
2.98541066 4.37019372 3.3851375 5.64189584 3.19153824 2.7639532
2.7639532 2.98541066 3.56824823 5.86323014 4.37019372 3.9088201
3.56824823 1.59576912 2.52313252 5.41151638 3.3851375 4.22200825
3.56824823 5.64189584 3.3851375 3.56824823 6.38307649 3.56824823
3.3851375 5.04626504 3.74241032 2.25675833 3.56824823 6.38307649
5.17088295 5.86323014 3.3851375 1.12837917 2.52313252 5.41151638
4.51351667 5.64189584 5.41151638 2.52313252 1.59576912 2.25675833]
<class 'numpy.ndarray'>
float64
══════════════════════════════════════════════════════════════════════════════
net : <openpnm.network.Network at 0x18f49bbb070>
――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――
# Properties Valid Values
――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――
2 throat.conns 534 / 534
3 pore.coords 189 / 189
4 pore.region_label 189 / 189
5 pore.phase 189 / 189
6 throat.phases 534 / 534
7 pore.region_volume 189 / 189
8 pore.equivalent_diameter 189 / 189
9 pore.local_peak 189 / 189
10 pore.global_peak 189 / 189
11 pore.geometric_centroid 189 / 189
12 throat.global_peak 534 / 534
13 pore.inscribed_diameter 189 / 189
14 pore.extended_diameter 189 / 189
15 throat.inscribed_diameter 534 / 534
16 throat.total_length 534 / 534
17 throat.direct_length 534 / 534
18 throat.perimeter 534 / 534
19 pore.volume 189 / 189
20 pore.surface_area 189 / 189
21 throat.cross_sectional_area 534 / 534
22 throat.equivalent_diameter 534 / 534
――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――
# Labels Assigned Locations
――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――
2 pore.all 189
3 throat.all 534
4 pore.solid 81
5 throat.solid_void 346
6 pore.void 108
7 throat.void_solid 346
8 throat.void_void 188
――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――
Now we can see that the phases are named using our preferred nomenclature of “solid” and “void”. This is helpful if you have several phases like “electrolyte”, “binder”, “particles” for instance.
boundary_width#
Adding pores (or more generally nodes) on the boundaries of images is helpful when conducting transport simulations. Without boundary pores then boundary condtions must be applied to internal pores which are (a) hard to identify clearly and (b) make it impossible to know the exact length of the domain.
Note that boundary nodes are not physical and thus their sizes are ficticious. This can cause problems when computing the transport conductance for these nodes, so care must be taken.
The boundary_width argument was designed to work analogously to the numpy.pad function. You can specify different paddings along each axis and also along each face. For instance, here are some options (for a 2D image):
[0, 3]: 3 voxels only applied to the y-axis.[0, [0, 3]]: 3 voxels only applied to the end of y-axis.[0, [3, 0]]: 3 voxels only applied to the beginning of y-axis.
im = ps.generators.blobs([400, 400], porosity=0.6)
a = ps.networks.snow2(im, boundary_width=[[5, 0], 10])
fig, ax = plt.subplots(figsize=[6, 6])
ax.imshow(a.regions, origin='lower', interpolation='none')
ax.axis(False);
A few things to note:
The image contains regions on the left, right and bottom faces, which are added by padding the image after the segmentation was applied, then incrementing labels the padded regions so their labels are greater than any inside the original image.
These new regions are then treated like a normal region when the network topology and geometry is extracted.
The width of each boundary region is nearly the same as the corresponding internal regions, but they are only a few voxels thick (in this case because we specified 5 or 10). This means that the value of ‘pore.inscribed’ sphere for this regions will almost all be 5 or 10 voxels.
The solid touching the boundaries creates gaps in the boundary regions.
Two boundary regions neighboring each other are separated by 2 voxels. This prevents them from being considered as connected during the topology extraction stage.
The top and bottom of the image do not have any boundaries because we set the widths to 0 on this axis.
It is instructive to visualize the network over the image to see how the boundary pores work:
pn = op.io.network_from_porespy(a.network)
ax = op.visualization.plot_connections(pn, c='k')
ax = op.visualization.plot_coordinates(pn, markersize=50, ax=ax)
fig, ax = plt.gcf(), plt.gca()
ax.imshow(a.regions.T)
ax.axis(False);
accuracy#
This argument can either take the value of 'high' or 'standard', with standard being the default. It is not recommended to use 'high' since this uses some rather slow functions to measure the surface areas and perimeters. The increase in accuracy is basically futile since (a) the image has already been reduced to a coarse voxelization and (b) the pore network abstraction discards information about the actual microstructure in exchange for speed, so spending ages on the extraction step would undermine this purpose.
voxel_size#
This is the voxel size of the image, as in the length of one side of a voxel. Typical microtomography images are in the range of 1-5 um per voxel. NanoCT can be as low as 16 nm per voxel. FIB-SEM might be 4 nm per voxel. Note that all properties returned from the snow2 function, like ‘pore.volume’ will be in the same units are this value. It is strongly recommended to use SI, which is assumed in OpenPNM for most of the fluid property calculations.
sigma and r_max#
These values are passed on to the gaussian_blur and find_peaks functions.
The gaussian_blur is applied to the distance transfrom, which as discussed in the original snow paper is a very effective way to reduce the number of incorrect peaks that are found in the subsequent steps. A value of sigma=0.4 is the default.
The find_peaks function applies a maximum filter to the distance transform, which replaces each voxel with the maximum it finds with the specified neighborhood. It then looks for voxels that are the same between the filtered image and the original distance transform. Only voxels that are local maximas will be the same between the images.
The following code block illustrates the impact of applying the gaussian_blur filter on finding peaks.
np.random.seed(13)
im = ps.generators.overlapping_spheres([100, 100], r=7, porosity=0.7)
dt = edt(im)
mx1 = spim.maximum_filter(dt, footprint=ps.tools.ps_disk(r=4, smooth=False))
pk1 = dt == mx1
dt_blur = spim.gaussian_filter(dt, sigma=0.4)
mx2 = spim.maximum_filter(dt_blur, footprint=ps.tools.ps_disk(r=4, smooth=False))
pk2 = dt_blur == mx2
fig, ax = plt.subplots(3, 2, figsize=[8, 12])
ax[0][0].imshow(dt, origin='lower', interpolation='none')
ax[1][0].imshow(mx1, origin='lower', interpolation='none')
ax[2][0].imshow(pk1/im, origin='lower', interpolation='none')
ax[0][1].imshow(dt_blur, origin='lower', interpolation='none')
ax[1][1].imshow(mx2, origin='lower', interpolation='none')
ax[2][1].imshow(pk2/im, origin='lower', interpolation='none');
peaks#
Because finding correct peaks is such an important part marker-based watershed segmentationa, and therefore of snow2, it is possible to supply custom peaks found using any desired process. Obviously, if this is provided then sigma and r_max are ignored.
Let’s use the two sets of peaks found above:
net1 = ps.networks.snow2(phases=im, boundary_width=0, peaks=pk1)
net2 = ps.networks.snow2(phases=im, boundary_width=0, peaks=pk2)
fig, ax = plt.subplots(1, 2, figsize=[8, 4])
ax[0].imshow(net1.regions, origin='lower', interpolation='none')
ax[1].imshow(net2.regions, origin='lower', interpolation='none')
ax[0].axis(False)
ax[1].axis(False);
Clearly the image on the left is ‘over segmented’ while the image on the right seems to have identified the pores nearly perfectly, even without subsequent processing of the peaks that normally occur in snow2 like trim_saddle_points and trim_nearby_peaks.
parallelization#
The watershed function was identified as the bottleneck of the entire process, especially as images grew in size. Parallelization of the watershed function had not be throughly investigated in the literature, so Khan et al developed a basic protocol for dividing the image into chunks and processing each in parallel. The main challenge with this approach was ensuring sufficient overlap was allowed to prevent any artifacts, while not being overly conservative since large overlaps undermine the speedup obtained by parallelization. The parallelization if accomplished by dask which makes it trivial to dispatch duplicate jobs to different cores.
The snow2 function can optionally parallelize the watershed step. It calls porespy.filters.snow_partitioning_parallel behind the scenes, but this function requires several arguments. Instead of complicating the snow2 function signature, we instead chose to accept a dict of arguments and values which are then passed on. These are:
divs: The number of chunks to divide the image into. A value of 2 means the image is divided in hald along each axis, for a total of 8 chunks in a 3D image. It’s possible to specify a different number of divisions in each direction, likedivs=[2, 2, 1]. This could be useful if the image to be processed is very narrow in one direction, such as a piece of fibrous electrode.overlap: This controls the amount of overlap between each chunk in voxels. SpecifyingNone(the default) means that the algorithm finds the overlap automatically. Khan el al found that using the maximum of the distance tranform was suitable.cores: This controls the number of cores to use when processing the chunks. If not provided then all cores will be used. This may be problematic on computers without a large amount of RAM since each process will consume some RAM. In these cases in may be beneficial to set cores to a small number and simply wait longer for the result.
If parallel_kw=None then no parallelization is applied, while if parallel_kw={} then the default arguments of the snow_partitioning_parallel function are used.
In the following code block, the parallelization option is demonstrated with an overlap that is too small, resulting in a noticable artifacts in the center sectionof the watershed segmentation, where the divsions were located. For comparison, the same image is processed with the default overlap.
np.random.seed(0)
im = ps.generators.overlapping_spheres([400, 400], r=20, porosity=0.8)
parallel_kw = {'cores': 1, 'divs': [2, 2], 'overlap': 1}
net1 = ps.networks.snow2(phases=im, parallel_kw=parallel_kw)
parallel_kw = {'cores': 1, 'divs': [2, 2], 'overlap': None}
net2 = ps.networks.snow2(phases=im, parallel_kw=parallel_kw)
[10:50:17] WARNING Disabling paralelization as overlap exceeds than chunk size. _snow2.py:222
WARNING Disabling paralelization as overlap exceeds than chunk size. _snow2.py:222
fig, ax = plt.subplots(1, 2, figsize=[8, 4])
temp = ps.tools.randomize_colors(net1.regions)
ax[0].imshow(temp, origin='lower', interpolation='none')
ax[0].axis(False)
temp = ps.tools.randomize_colors(net2.regions)
ax[1].imshow(temp, origin='lower', interpolation='none')
ax[1].axis(False);
