ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

microcrack propagation. Therefore, it is important to balance spatial resolution of the
displacement and strain maps and their accuracy. Increasing the spatial resolution of the
deformable registration leads inevitably to a decrease in the accuracy of the computed
displacement and strain fields (3).
In order to optimize and validate the procedure for this problem, we defined benchmark
models, where the original tomographic image was synthetically deformed. Therefore,
the actual displacement and strains were known for every voxel of the image. The
models were either based on displacements and strains from finite element (FE)
simulations (Model I) or distinct patterns, such as constant displacement (Model II),
constant uniaxial strain (Model III) or shear motion (Model IV). We optimized the
parameters using the Model I based on deformations resulting from the FE simulation.
Model II was used to determine the accuracy of the displacement map and the accuracy
of the strain map in the regions with only rigid body motion. The accuracy of the strain
maps was measured using Model III. Finally, Model IV was used to determine the
spatial resolution of the displacement and strain maps in analogy to the slanted edge test
used for the imaging system to verify spatial resolution.
3. MATERIALS AND METHODS
3.1 Strain mapping
The procedure to calculate the final strain maps can be broken down into three parts
(Figure 1). Starting with two tomographic images: one of the sample prior to loading,
and one of the deformed sample, DVC is used to compute a displacement field with a
relatively low resolution. Subsequently, demons deformable image registration is used
to increase the spatial resolution of the displacement field and thus to improve the
localization of the deformations. Finally, the strain map is computed from the resulting
displacement field.
DVC measures the displacement at discrete locations by correlating patterns in the
surrounding region of the image, the so called sub-images, while the displacements for
the voxels in between these points are interpolated. Our implementation of DVC
differed from previous implementations in that it consisted of 3 iterations with a
decreasing size of the sub-images (100x100x100, 50x50x50 and 25x25x25 voxels),
while the number of sub-images was adapted to span the entire region without gaps. In
this way, the spatial resolution in the displacement field could be increased while
keeping the registration robust against the false registration of individual sub-images.
Mattes mutual information was used to measure the correlation of the image (5). Subimages,
where the threshold in mutual information was not achieved, were excluded
during the interpolation of the displacement field.
Demons deformable image registration (4) was used to improve the detection of small
local deformations. This diffusion-based registration method simulates an image-based
force aligning gradients in the grayscale values of the images. On the other hand,
stiffness is modeled as the restriction of neighboring points to move alongside each
other.
The displacement field from the demons registration is, by definition, smooth and thus