Versatile and efficient pore network extraction method using marker-based watershed segmentation

Obtaining structural information from tomographic images of porous materials is a critical component of porous media research. Extracting pore networks is particularly valuable since it enables pore network modeling simulations which can be useful for a host of tasks from predicting transport properties to simulating performance of entire devices. This work reports an efficient algorithm for extracting networks using only standard image analysis techniques. The algorithm was applied to several standard porous materials ranging from sandstone to fibrous mats, and in all cases agreed very well with established or known values for pore and throat sizes, capillary pressure curves, and permeability. In the case of sandstone, the present algorithm was compared to the network obtained using the current state-of-the-art algorithm, and very good agreement was achieved. Most importantly, the network extracted from an image of fibrous media correctly predicted the anisotropic permeability tensor, demonstrating the critical ability to detect key structural features. The highly efficient algorithm allows extraction on fairly large images of ${500}^3$ voxels in just over 200 s. The ability for one algorithm to match materials as varied as sandstone with 20% porosity and fibrous media with 75% porosity is a significant advancement. The source code for this algorithm is provided.

Figure 1

Illustration of marker-based watershed segmentation procedure on simple images of cubic packings of spheres. (a),(c) Distance transform of void space. (b),(d) Segmented pore space resulting from the marker-based watershed segmentation. (e) Segmentation results on 3D body-centered-cubic packing showing a slice of the sphere locations.

Figure 2

Illustration of marker-based watershed segmentation procedure on a simple 2D image of overlapping disks. Peaks in the distance transform are identified as locations where a maximum filter with a structuring element of radius $R>1$ is equal to the distance transform. Without intervention it is clear that the image is oversegmented due to the identification of many spurious peaks that are not true local maxima resulting in many incorrect basins.

Figure 3

Illustration of the SNOW algorithm to remove spurious peaks. The top row shows the peaks of the distance transform at each step, and the bottom row shows the resulting segmentation of the pore space. The progressive elimination of spurious peaks can be seen from left to right. The Gaussian blur of the distance transform produces the most striking improvement [column 2 (c),(d)]. The elimination of saddle points removes thin regions between pores [column 3 (e),(f)]. Merging peaks that are near each other prevent the bisection of large continuous regions [column 4 (g),(h)].

Figure 4

(Left) Impact of Gaussian filter parameter sigma on the number of local maxima in the image. (Right) Impact of structuring element size on number of final peaks found after applying a maximum filter.

Figure 5

Schematic diagram showing saddle finding method. (a) Shows a 3D view of the saddle contour, (b) shows a distance map, and (c-i)–(c-iii) show the progression of steps that determine if the peak lies on a saddle.

Figure 6

Illustration of connectivity and size determination for a pore in 2D. (a) The labeled pore regions with pore 6 as the pore of interest, and neighboring pores 14, 28, and 66. The throat regions are found by dilating region 6 and identifying overlapping regions, shown by pale-colored pixels. (b) The distance transform of the image is used to determine the pore and throat size information from the peak values indicated by black boxes. (c) Using the global distance map results in the pore diameter extending into the neighboring pore. (d) Using the distance map obtained within the pore only results in the inscribed pore diameter and a more geometrically consistent pore centroid.

Figure 7

Performance of the key image analysis routines used in the SNOW algorithm as a function of image size. Tests were performed on a Dell Precision 7550 Workstation with a Xeon E2660 Processor (12 cores) and 72 GB of RAM. The largest size corresponds to an ${800}^3$ image.

Figure 8

Generated Voronoi graph to represent fibers (blue voxels) with the extracted network overlaid. The pores are represented by spheres that are smaller than actual size to improve visualization.

Figure 9

Comparison of generated Voronoi pore network (blue) with the network extracted from a voxel image of its vertices (red). Mercury intrusion was simulated in both networks as well as using morphological image opening of the Voronoi image (green), yielding very consistent results. Inset: Various size distributions of the generated and extracted networks.

Figure 10

Views of the Berea sandstone sample. (a) The voxel image showing the solid in gold and the SNOW extracted network overlaid; (b) same as (a) but with some of the solid cut away. (c) The stick and ball representation of the maximal ball extraction, and (d) the stick and ball representation of the SNOW extraction.

Figure 11

Comparison of Berea network extracted by the SNOW algorithm (blue) to the maximal ball extraction (red). Mercury intrusion was simulated in both networks as well as using morphological image opening of the Berea image (green), yielding very consistent results. Inset: Various size distributions of the extracted networks.

Figure 12

Views of the fibrous sample Toray 120A (no PTFE) trimmed to $600\times 600\times 221$ for easier visualization. (a) SNOW extracted network overlaid with the fiber image (dark gray); (b),(c) are top and side views of the SNOW extracted network, showing the notable amount of in-plane throat alignment.

Figure 13

Capillary pressure curves for Toray 120A (no PTFE) produced by image analysis (green), mercury porosimetry (black), and the SNOW network using either inscribed or equivalent throat diameter. Inset: Various size distributions of the extracted network.