**4.1.2 Effect of edge blurring**

Grey scale profiles on solid-void boundaries of a material in tomographic images are often blurred due to ESF. Imaging noise combined with blurred boundaries can cause the thresholded solid-void boundary of the final reconstruction to look rough, see visualisation in Fig. 8b. Without noise, the pure edge spreading causes changes mainly in the porosity value of the sample geometry and thus changes in the permeability value, see e.g. the results published by Koivu et al. (2010). When noise is incorporated, the surface roughness will have an effect to the fluid flow close to the surfaces.

Artificial edge roughness was generated into the geometries of the hexagonal arrays of cylinders, see visualisations of the rough edges in Fig. 8a. To generate the simulation geometries the original geometry was blurred using standard 3D Gaussian blur. Gaussian distributed noise with known standard deviation was added to the blurred image. The image was then thresholded using 128 as the threshold value (in the original image void is 0 and solid is 256). Finally, all the particles not touching the solid phase were removed. The number of the edge roughness level corresponds to the standard deviation of the Gaussian distributed noise.

The effect of noise on pore size distribution was evaluated as a function of noise level, see Fig. 7. The pore size distributions were determined with the so-called sphere fitting algorithm. In the sphere fitting method, the pore space is filled by non-overlapping spheres. The distribution of the radii gives estimation for the pore size distribution (Wu et al., 2007). The pore size distribution was found to change dramatically as a function of noise level. The mode value of the distribution of the geometry with the noise level of 0.01 % was

Fig. 7. Normalized pore size distribution for the hexagonal array of cylinders as a function

Grey scale profiles on solid-void boundaries of a material in tomographic images are often blurred due to ESF. Imaging noise combined with blurred boundaries can cause the thresholded solid-void boundary of the final reconstruction to look rough, see visualisation in Fig. 8b. Without noise, the pure edge spreading causes changes mainly in the porosity value of the sample geometry and thus changes in the permeability value, see e.g. the results published by Koivu et al. (2010). When noise is incorporated, the surface roughness will

Artificial edge roughness was generated into the geometries of the hexagonal arrays of cylinders, see visualisations of the rough edges in Fig. 8a. To generate the simulation geometries the original geometry was blurred using standard 3D Gaussian blur. Gaussian distributed noise with known standard deviation was added to the blurred image. The image was then thresholded using 128 as the threshold value (in the original image void is 0 and solid is 256). Finally, all the particles not touching the solid phase were removed. The number of the edge roughness level corresponds to the standard deviation of the Gaussian

of pore size in pixels with different noise levels.

have an effect to the fluid flow close to the surfaces.

**4.1.2 Effect of edge blurring** 

distributed noise.

approximately one third of the mode value for the noise free geometry.

Fig. 8. Visualisations of artificially generated edge roughness on the hexagonal array of cylinders (a) and edge roughness on reconstruction of wool fibre web caused by CXµT and image processing methods (b).

Edge roughness on solid-void boundary increases the specific surface area of the sample and therefore decreases the permeability value, see Figs 9 and 10. Edge roughness has only small effect on the pore size distribution, see Fig. 11.

Fig. 9. Numerically solved permeability values for the hexagonal array of cylinders as a function of edge roughness level. Analytical value for noise free geometry is also given (Drummont & Tahir, 1984).

The Effect of Tomography Imaging Artefacts on

images, 20 µm.

**4.2.1 Effect of artefacts on fluid flow permeability** 

Structural Analysis and Numerical Permeability Simulations 481

Visualisations of wool fibre web sample with different threshold values are shown in Fig. 12. The sample geometries in (a) – (c) were denoised and then binarised using grey value based threshold (Gonzales & Woods, 2002). At the lowest threshold levels (a) and (b), the noise is clearly visible in the void space. While threshold value was gradually increased, the noise became less evident and the thickness of the fibres (or size of the solid particles) diminished. The sample geometry in Fig. 12d was segmented utilising the forest fire method. The forest fire method was found to give noise free pore space and a fibre radius that corresponded well with the mean value obtained from scanning electron microscope

Fig. 12. Visualisation of segmented wool fibre web sample at different threshold values: (a)

20, (b) 30 and (c) 40, and with the forest fire method (d).

Fig. 10. Dimensionless specific surface area as a function of edge roughness level for the hexagonal array of cylinders.

Fig. 11. Normalized pore size distribution as a function of pore size in pixels for the hexagonal array of cylinders with different edge roughness levels.
