The 3DMA software package is designed to provide a convenient tool for
analyzing the geometry of a randomly shaped object in 2- and 3-dimensional
images.
Specific examples include the pore and grain phases in rocks such as
Fontainebleau and Berea sandstone,
vesiculated basalt, and carbonates,
neurons, fiber networks, two-fluid mixtures, and
rock fractures.
The input to the package is a 2 or 3D digitized, grey-scale, image of the
object.
Specifically it is assumed that the image consists of two populations of
voxels comprising an object and its background.
A wide variety of input formats for the image are currently supported,
either in volume or slice-wise form.
Typically the images are produced either by synchrotron computed
microtomography, laser scanning confocal microscopy or visual
microscopy.
Geometric analysis of the object in such a grey-scale image typically
requires three major steps:
Segmentation
Segmentation is the process of converting the grey-scale image
into a `black and white' image by determining the population assignment
(object or background) for each voxel in the image.
Typically the object/background boundary in the image is fuzzy due
to finite voxel resolution and possible collection noise (e.g. tomographic
reconstruction artifacts).
3DMA provides four segmentation algorithms:
Dimensional Reduction
Analysis of the geometry of a three dimensional object, especially one of random
shape is very difficult.
More extensive analysis of the object's geometry is based upon determining and
characterizing its one dimensional skeleton (medial axis).
The skeleton of a digitized object is efficiently obtained by erosion-based
algorithms; the 3DMA code uses the algorithm of Lee-Kashyap and Chu,
| T.-C. Lee, R.L. Kashyap and C.-N. Chu |
| Building skeleton models via 3-D medial surface/axis thinning algorithms |
| CVGIP: Graph. Models Image Process., 56 (1994) pp. 462-478 |
3DMA provides the following analyses of the three dimensional object:
During the erosion process, the distance from each voxel in the object to the closest object surface voxel is computed and stored. This provides another characteristic distribution of the three dimensional object:
The following analyses of the skeleton are provided:
Currently, for rock images, 3DMA uses the skeleton to determine the following:
Currently, for neuron images, 3DMA uses the skeleton to determine the following:
Currently, for fiber network images, 3DMA uses the skeleton to determine the following:
Note: As this is a research code undergoing extension of its capabilities, recently developed/developing capabilities may not be included in the latest released verion of 3DMA
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| 256 x 256 x 256 voxel segmented image of Fontainbleau sandstone, 12% porosity, 6 micron resolution | Medial axis of the pore space for this sample. Colors represent relative distance (red - close, blue - far) to the nearest grain surface. For visual clarity, the grains are not shown in the figure. |
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| 319 x 319 x 68 voxel segmented image of a vesiculated basalt, 46% porosity, 20 micron resolution | The contact surfaces between vescicles that touch are shown in grey. The medial axis of the vesicle space is shown in black. |
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| Segmented images of pyramidal hippocampus neuron, 1 micron resolution. These neurons have two dendritic fans, apical and basal. | The medial axis for the hippocampal neuron. |
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| Segmented image of lateral geniculate neuron, 1 micron resolution. | The medial axis for the lateral geniculate neuron. |
The 3DMA code is designed to provide statistical analysis of the
geometrical distribution of the phases in a two or three dimensional
image of a bi-phase material.
The code has been applied to the analysis of void and grain phases of
rock, cellulose fiber networks, fish movement, and the structure
of neurons.
For literature studies based upon the 3DMA code
see the following references: Lindquist et al., J. Geophys. Res. 101B, 1996;
Lindquist and Venkatarangan, Phys. Chem. Earth A25, 1999;
Lindquist et al., Report No. SUSB-AMS-99-13, submitted to J. Geophys. Res.
This guide provides general installation and execution instructions for
the 3DMA code, version Dec. 1999.
In addition to general algorithms employed in all four applications,
algorithms to support specialized computation for each of these applications
are also contained in the Dec. 99 version.
This manual describes only the general algorithms and those designed
for applications analogous to that for rock microstructure.
Available in
compressed PostScript
The three-dimensional geometry and connectivity of pore space controls the
hydraulic transport behavior of crustal rocks.
We report on direct measurement
of flow-relevant geometrical properties of the void space in a suite of 4
samples of Fontainebleau sandstone ranging from 7.5\% to 22\% porosity.
The measurements are obtained from computer analysis of three dimensional,
synchrotron X-ray computed microtomographic images.
We present measured distributions of coordination number, channel length,
throat size and pore volume, and of correlations between
throat-size/pore-volume and nearest neighbor pore-volume/pore volume
determined for these samples.
We also present quantitative characterization of the distributions measured.
The effects of finite sample volume are investigated.
The accuracy of the numerical algorithms employed is investigated using
a simulated image of hexagonal closed packed spheres.
Available in
compressed PostScript
We consider the problem of segmenting a digitized image consisting of two
univariate populations.
Assume a priori knowledge allows incomplete assignment of voxels in the image,
in the sense that a fraction of the voxels can be identified as belonging
to population $\Pi_0$, a second fraction to $\Pi_1$, and the remaining
fraction have no a priori identification.
Based upon estimates of the short length scale spatial covariance of the image,
we develop a method utilizing indicator kriging to complete the image
segmentation.
Available in
compressed PostScript
We present spatial distributions for pore path length and coordination number, pore throat size and nodal pore volume obtained for a $1.5^3$ mm${}^3$
volume of 12.1\% porosity Fontainebleau sandstone. The sandstone was imaged using Synchrotron X-Ray computed microtomography at 6 micron
resolution. The spatial distributions were computed based upon three dimensional medial axis analysis of the void space in the image. We also present
vesicle size and vesicle-vesicle contact surface area distributions for a 1.36 mm length of a 6.36 mm diameter core of basalt from a vesiculated lava flow
imaged at 20 micron resolution.
Available in
compressed PostScript
Preliminary results of a study combining three-dimensional imaging, extraction
of statistical microgeometric descriptions from volumetric image data, and
experimental measurement of transport properties of porous geomaterials are
presented. High-resolution (< 1 micron) three-dimensional image data are obtained
using laser scanning confocal microscopy. Image processing techniques are first
applied to segment the raw image data into solid versus void space. The resulting
binary data are then further processed to extract quantitative statistical
descriptions of first-order properties of porous media such as porosity and
specific surface area whereas more complex aspects of the three-dimensional
microgeometry are characterized using the media axis analysis. The derived
microgeometric descriptions are briefly considered in light of laboratory
measurements of fluid transport properties such as permeability.
We introduce the medial axis as a tool in the analysis of geometric
structure of void space in porous media.
The medial axis traces the fundamental geometry of the void pathways.
We describe an algorithm for generating the medial axis of the void
structure from digitized three dimensional images of porous media
obtained from X ray CAT scans.
The medial axis is constructed during an iterative erosion procedure
which, at each step, replaces the image of the void structure
with a smaller version obtained by eroding its surface layer of voxels.
The algorithm is applied to high (5 $\mu$m) resolution microtomographic
images of two rock chips (Berea sandstone and Danish chalk) and a
sample of uniform (100 $\mu$m) diameter, packed glass beads.
We statistically investigate several geometrical
properties of the structure of the medial axes obtained.
The first is the distribution of relative volumes in each erosion layer of
the void space. We find the distributions to be exponential for the
two real rock samples and normal for the packed glass beads.
The second property investigated is the distribution of volumes of disconnected
segments of the medial axis which are in one-to-one correspondence with
disconnected void segments of the sample.
We find indications for a universal power law behavior governing the
distribution of volumes of the smallest disconnected pieces.
The final behavior studied is a geometric tortuosity as measured by shortest
paths through the medial axis.
This tortuosity distribution appears well described by a gamma distribution.
Available in
compressed PostScript
Papers
Support Acknowledgements
This work has been supported by