1. Evaluation of segmentation algorithms for x-ray-based microtomographic imaging of multi- phase flow in porous media Dorthe Wildenschild and Mark L. Porter School of Chemical, Biological, and Environmental Engineering Oregon State University

2. Motivation
Certain lack of verification of existing algorithms for calculating interfacial area (and other variables) from CMT data
Culligan et al. (WRR 2004, AWR 2006)
Generate Test Configurations
2-phase system (precision glass beads)
3-phase system (meniscus in capillary tube)
Schaap et al. (2007) and Porter et al. H43J-04

3. Advanced Photon Source Synchrotron x-ray microtomography facility (beam-line 13BMD)
“Equipment”
Experiment
Measurements
1104 m
~1 cm
New work at the Advanced Light Source
~5-15 mm

4. Image Processing/ Data Analysis Approach
Computed Microtomography (CMT) Data Collection
1. Preprocessing and Reconstruction
2. Segmentation/Classification
2-phase system (solid/nonwetting)
3-phase system (solid/nonwetting/wetting)
3. Isosurface generation and interfacial area calculation

5. Data Analysis – Step 1 Preprocessing Reconstruction
normalization using white (flat) and dark fields
Reconstruction
Correction of sinogram (centers rotation axis, normalizes to air on each side of the object)
Removes ring artifacts and filters the sinogram with a high-pass filter
Reconstructs the volume with a FFT-based algorithm, GRIDREC
(FFT faster than back-projection)

6. Data Analysis – Step 2 Segmentation
K-means cluster analysis on dry and wet images
cluster analysis takes into account correlation structure
median filter and image registration (dry and wet)
anisotropic diffusion filter (”intelligent” edge preserving filter)
histogram specification
edge enhancement using Canny operator
erosion and dilation operators
above and below edge imaging too time consuming
The Canny operator was designed to be an optimal edge detector (according to particular criteria --- there are other detectors around that also claim to be optimal with respect to slightly different criteria). It
takes as input a gray scale image, and produces as output an image showing the positions of tracked intensity discontinuities.
How It Works
The Canny operator works in a multi-stage process. First of all the image is smoothed by Gaussian convolution. Then a simple 2-D first derivative operator (somewhat like the Roberts Cross) is applied to the
smoothed image to highlight regions of the image with high first spatial derivatives. Edges give rise to ridges in the gradient magnitude image. The algorithm then tracks along the top of these ridges and sets to
zero all pixels that are not actually on the ridge top so as to give a thin line in the output, a process known as non-maximal suppression. The tracking process exhibits hysteresis controlled by two thresholds:
T1 and T2, with T1 > T2. Tracking can only begin at a point on a ridge higher than T1. Tracking then continues in both directions out from that point until the height of the ridge falls below T2. This hysteresis
helps to ensure that noisy edges are not broken up into multiple edge fragments.
Guidelines for Use
The effect of the Canny operator is determined by three parameters --- the width of the Gaussian kernel used in the smoothing phase, and the upper and lower thresholds used by the tracker. Increasing the
width of the Gaussian kernel reduces the detector's sensitivity to noise, at the expense of losing some of the finer detail in the image. The localization error in the detected edges also increases slightly as the
Gaussian width is increased.
Usually, the upper tracking threshold can be set quite high, and the lower threshold quite low for good results. Setting the lower threshold too high will cause noisy edges to break up. Setting the upper
threshold too low increases the number of spurious and undesirable edge fragments appearing in the output.
One problem with the basic Canny operator is to do with Y-junctions i.e. places where three ridges meet in the gradient magnitude image. Such junctions can occur where an edge is partially occluded by
another object. The tracker will treat two of the ridges as a single line segment, and the third one as a line that approaches, but doesn't quite connect to, that line segment.
We use the image
Grey-scale image of glass beads w. 3 identifiable phases
Cluster analysis segmented image - not perfect
Cluster analysis segmented image - after dry bead lay-over

7. Cluster Analysis = Classification
The process of identifying homogeneous subgroups of cases in a population (people, things, events, - voxels!)
Seeks to identify a set of groups or classes which both minimize within-group variation and maximize between-group variation
A K-means cluster algorithm assigns each point to the cluster whose center (also called centroid) is nearest. The center is the average of all the points in the cluster — that is, its coordinates are the arithmetic mean over all the points in the cluster... – requires iteration
My code is a modified version of the CCHIPS code: copyright -> The Imaging Research Center, Children's Hospital Medical Center, Cincinnati, OH  1 1 1 3 3 3 2

8. Data Analysis - Step 3 Area calculation
Isosurface generation using
marcing cubes algorithm
(AmiraTM)
2-phase area estimation
3-phase area estimation as an aw as

9. Pixel (voxel) counting vs. triangulated surfaces

10. Test Configurations Image well-defined geometries
Capillary tubes of different diameter
Precison-bead pack
Imaged at I edge (33.2 keV)

11. Segmentation of 2-phase system
No resample
High-precision soda lime beads (r=2.5 g/cm3)
0.8 mm diameter, tolerance 0.01 mm (~1.2%)
Known mass => area can be estimated
699.0 mm2 ± 8.6 mm2
5.9 um and 11.8 um pixel size
Segmentation
Cluster analysis, grey scale threshold, filters
Isosurface generation
Resample 3x3x3 or not
Isovalue (threshold) selection (0.5 or ~1300)
Area estimation
Resample 3x3x3 kernel
2000, 12000, 25000,28000, 29990

12. Error on 2-phase area estimate
Resample 3x3x3 kernel
No resample
Error on 2-phase area estimate
Grey scale
Cluster analysis
Cluster high-rez.
0.5 – 12 % error

13. 3-phase estimated vs. “actual” interfacial area
Test images
Cluster analysis
(Culligan et al.,
2004, 2006)
Modified cluster analysis
Modified cluster analysis (#ksegment only) + using
3 smoothed binary data sets
PMMC
(McClure et al., 2007)
Tube diameter
“actual” meniscus area
(mm2)
estimated meniscus area
Error
(%)
estimated meniscus area (mm2)
800 um
0.724±0.082
0.961
32.7
0.714
-1.50
0.709
-2.14
0.780
7.66
1340 um*
2.064
2.124
2.89
2.153
4.32
1.791#
-13.23
1500 um
2.85±0.15
2.768
-2.89
3.030
6.33
2.501
-12.24

14. Acknowledgments Image data sets available at:
Mark Rivers, GSECARS/Univ. of Chicago
James McClure and Bill Gray, Univ. of North Carolina
Marcel Schaap, Univ. of Arizona
Danielle Jansik, OSU
Kendra Brown, OSU
Katy Culligan, OSU
Funding from
NSF (EAR and EAR )
Danish Technical Research Council
Image data sets available at:

15. Measured vs. Actual Interfacial Area
Capillary tube diameter: 1.34 mm
IA for a zero contact angle = ½ x (area of the resulting sphere)
= ½ x 4p(1.34/2)2 = 2.82 mm2
Actual inscribed diameter: 1.46 mm
IA for scaled sphere (cap)
= 0.45 x 2p(1.46/2) = mm2
Segmented IA:
Based on CMT images
= 2.12 mm2
Error ~ 2.9 %
0.45 mm

16. NAPL-water interfacial areas
NAPL surface areas (green) and NAPL-water interfacial areas (red)
CMT image showing NAPL surface areas (green) and NAPL-water interfacial areas (red).
NAPL
water
solid
Films can be estimated from total and capillary-associated areas
IF assumption of films applies....