Image Processing

Two-dimensional slices extracted from the 3-D tomographic images are provided in the upper left portions of Figs. 1 and 2. From these images, it is clear that a predominant artifact is the circular ring pattern emanating from the central point. These artifacts result from dust on the monochromator surface. Attempts to remove these artifacts using median filtering [13] were only partially successful, resulting in images which could not be easily thresholded to obtain binary pore/solid representations. Thus, a more direct approach to removing this noise pattern was developed. Basically, our goal is to remove the variation in greylevel as we proceed from one radial distance to another, since it is this variation that is responsible for the observed ring pattern. Because of the concentric ring nature of this noise, a special filter function of the form:

$$g (x,y,z)=[g(x,y,z)-\bar{g_z(r)}] + 128 \hspace{0.5 cm} \vert _0^{255}$$ (1)

is applied in each z plane, where $\bar{g_z(r)}$ is the average greylevel computed at each radial distance r in plane z and the result is limited to the range [0,255]. Originally, this filter was applied to each 2-D slice of the image in its entirety, but this resulted in the emergence of a new artifact due to the subtle greylevel variation in various quadrants of the image. Thus, each image plane was subdivided into four subquadrants ( x<0, y<0; x<0, y>0; x>0, y<0; x>0, y>0) where (x=0,y=0) represents the central point of the image plane. The above function was then applied separately in each quadrant. Finally, a 3-D median filter of size 5 pixels x 5 pixels x 5 pixels was applied to remove any remaining X-ray imaging artifacts and randomly distributed noise. As will be presented in the results section, this produced images of greatly enhanced contrast, where the ring artifacts were basically removed and no longer influenced the segmentation process.

From the previous study [1], the porosities of the two bricks were known experimentally. For the clinker brick, the processed 256 x 256 x 256 3-D image was thresholded to obtain a porosity of 20 % and the central 100 x 100 x 100 and 200 x 200 x 200 portions were selected for further computations. For the lime silica brick, the threshold porosity was set at 16 %, as determined previously for this coarser scale [1], with the remainder of the overall porosity being distributed at a finer scale within the solids (16 % porosity also within the solids resulting in 0.16 + (1.-0.16)*0.16 = 0.294 total porosity). In this manner, the overall porosity is very close to the experimentally determined value of 30 %[1].