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9.6.3 Example Applications
To demonstrate the soundness of the newly developed methodology, limestone and
sandstone aggregate particles passing a 25-millimeter sieve size but retained on a 9.5-
millimeter sieve have been studied by Wang et al. (2007). The particles were first
placed in a film cartridge and X-ray scanned. The image size is 512 512 pixels and
the in-plane resolution is 0.2 mm/pixel while the spacing between two adjacent sec-
tions is 0.4 mm. The gray images are then processed to obtain binary images. The
method (Wang et al., 2004) is applied to reconstruct and analyze each particle to ob-
tain the volume and mass momentums. The newly developed method is then used to
obtain the principal directions of the particles and their corresponding equivalent el-
lipsoids. Figure 9.24 presents all the particles of the two specimens and their corre-
sponding equivalent ellipsoids.

z z
y y

x x
(a) (b)

z z
y y

x x
(c) (d)
FIGURE 9.24 (a) Reconstructed sandstone specimen (b) Sandstone specimen of equivalent
ellipsoids (c) Reconstructed limestone specimen (d) Limestone specimen of equivalent ellipsoids.