IEEE Signal Processing - March 2018 - 130

(a)

(b)

Figure 11. Watershed segmented CT images of Bentheim sandstone acquired under (a) confining pressure of 1 MPa and (b) confining pressure of
20 MPa. Red circles show some of the differences in watershed lines caused that were caused by the increased pressure. (Figure used with permission
from [40].)

areas in the image correspond to watershed lines. Increasing pressure changes the structure and location of these watershed lines.
Next, a calibrating technique was developed to match experimental and laboratory-based measurements. The method assigns
varying elasticity moduli to rock grains in watershed lines. The
derived moduli obeys a linear relationship with the confining
pressure. The slope and the x-intercept of the line were determined using laboratory-based measurements. Elasticity moduli
for grains in other locations were also lowered to help match
numerical results with laboratory measurements. The derived
model was then used to estimate pressure vs. elasticity relationships and the results showed a good agreement.
Similarly, the effect of stress on the morphology of carbon
rock structure was investigated in [41]. Coal samples were imaged
under different stress levels. It is well known that permeability
of CBM decreases with depth. Numerical simulations revealed
that effective stress closes, narrows down, or disconnects cleats.
This was found to cause a sharp drop in permeability and a linear
decrease in porosity.
An alternative framework for DRP that avoids the use of standard segmentation algorithms was proposed in [11] and [42]. This
method exploits the proportional relationship between material
density and its attenuation coefficient (6). The gray-level distribution of various portions in the acquired data set is utilized to
obtain gray scale to density calibration. The components used in
the calibration are: air, aluminium alloy, the rock sample, and the
sample holder. The density of the rock sample was acquired from
laboratory measurements. After calibration, the following equation was found to convert gray-scale voxel values to density t L
3

t L (kg/m ) = 36.79 I

130

0.593

- 9405.3,

(15)

where I is the gray-scale intensity value of voxel L. Next, a
porosity value of z = 1 is assigned to air voxels, and a porosity
value of z = 0 is assigned to voxels with density values higher
than a threshold value t Th. In [11], t Th was set to the density of
quartz which is the most abundant mineral in the Berea sandstone sample used in this experiment. Next, remaining porosity
values were assigned using the equation
zL = 1 -

tL
.
t quartz

(16)

Estimated voxel-based porosity values, z L, can now be used in
segmentation and in various numerical simulations to compute
other physical properties. The preceding approach handles partial volume effects by assigning voxels in overlap regions with a
range of density and porosity values that were calibrated using
known material properties. Initial experimental results demonstrate that this density-based segmentation approach provides better estimation of elasticity parameters than conventional methods
[42]. Intensity values computed by (15) and (16) are pixel-based
estimates. Acquisition artifacts cause irregularities in pixel intensities. Enforcing smoothness constraints within each material is
likely to improve the results.

Conclusions
In this article, we provided an overview of recent development in DRP. We presented the major steps in DRP systems
from image data acquisition to the computation of physical
properties. We also presented some recently proposed novel
contributions that have the potential to influence future activities in this research area. Advances in DRP technology will
continue to bring substantial opportunities to the oil, gas,

IEEE Signal Processing Magazine

March 2018

Table of Contents for the Digital Edition of IEEE Signal Processing - March 2018