**2.2.2 Edge blurring and imaging noise**

Especially in laboratory scale CXµT systems, like SkyScan and Xradia, the image quality of the material edges in the reconstructed geometry is limited by optical properties of the system. The edge spreading is caused by the non-zero aperture diameter of the x-ray source, the optics in between the source and detector, and scintillator, i.e. the component that converts the x-rays into visible light. Thus, instead of sharp transition between different material phases, there is a smooth curve called edge spread function (ESF). In Fig. 2, the edge smoothness can be seen in the intensity profile plot. The width of the ESF in this case is around 7 pixels.

The Effect of Tomography Imaging Artefacts on

**3. Fluid flow permeability analysis** 

porous medium by Darcys's law (Darcy, 1856; Bear, 1972)

is the superficial volume flux vector and

is defined by equation

*k*

permeability is a symmetric second-order tensor (Liakopoulos, 1965):

capillary model is the Kozeny-Carman relation

is the density of the fluid, and *g*

already burning.

The pietsometric head

Permeability

where *q* 

Structural Analysis and Numerical Permeability Simulations 473

We have developed a so-called forest fire algorithm to separate the material phases when their grey value distributions are overlapping too much for simpler methods. As an input, a user will give the limits for the overlapping area in the grey value histogram. The algorithm processes the grey values in between the given limits and decides whether it is solid or void by adding more voxels to each phase iteratively. In addition to grey value information, spatial information is incorporated. The voxels are added into the group if there are enough members of the same group around it. By adjusting the number of required neighbours, the sensitivity of the method can be adjusted individually for each phase. In practice, the method is closely related to region grow method, but it enhances the traditional region grow by adding a weak "surface tension" to it. The benefits of the method are smooth surfaces and possibility to alter the volume of selected phase by allowing either solid or void to conquer its area easier. The disadvantage of the method is that some of the smallest details can be lost. The name forest fire comes from simple forest fire simulations where forest is divided into cells which will catch fire if certain amounts of its neighbouring cells are

is a tensor valued measure of the ability of a porous material to transmit

*p*

(1)

is the acceleration due to a body force. In general,

(3)

*g*

is the dynamic viscosity of the fluid.

(2)

where *<sup>p</sup>* is the pressure and

fluids. It is defined for slow, steady-state, isothermal, Newtonian fluid flow through a

*, <sup>1</sup> q=- ×Ñ<sup>ψ</sup> <sup>μ</sup>* 

*kkk xx xy xz kkk yx yy yz kkk zx zy zz*

Several theoretical results for permeability coefficients have been reported in the literature. Perhaps the most common formula which can be derived analytically for simplified

> <sup>3</sup> <sup>1</sup> 2 2 <sup>2</sup> (1 ) <sup>0</sup>

*c S*

Fig. 2. An example of a noisy CXµT image (a) and the intensity profile plot for the area marked on the CXµT image (b).

In addition to ESF, the tomographic reconstructions are often contaminated by imaging noise. Collecting photons with Charge-Coupled Device (CCD) is a time-dependent discrete procedure that presents Poisson noise into the collected data. Utilisation of an analogue-todigital -converter such as in CCD causes Gaussian -type of noise into the images. In the final 3D representation of the tomographic sample, noise can be seen as random variation of grey values. This effect causes edge blurring. Furthermore, when binarised by thresholding procedure, falsely labelled voxels can appear.

Many algorithms have been developed to decrease the noise, e.g. anisotropic diffusion (Perona & Malik, 1987), bilateral filtering (Tomasi & Manduchi, 1998) and SUSAN filtering (Smith & Brady, 1997). However, none of the filtering methods is perfect and post processing is often necessary to reduce the artefacts from the binarised images.
