Eurographics/ IEEE-VGTC Symposium on Visualization 2009
H.-C. Hege, I. Hotz, and T. Munzner
(Guest Editors)
Volume 28 (2009), Number 3
Direct Visualization of Deformation in Volumes
Stef Busking, Charl P. Botha and Frits H. Post
Delft University of Technology, the Netherlands
Abstract
Deformation is a topic of interest in many disciplines. In particular in medical research, deformations of surfaces
and even entire volumetric structures are of interest. Clear visualization of such deformations can lead to important
insight into growth processes and progression of disease.
We present new techniques for direct focus+context visualization of deformation fields representing transforma-
tions between pairs of volumetric datasets. Typically, such fields are computed by performing a non-rigid regis-
tration between two data volumes. Our visualization is based on direct volume rendering and uses the GPU to
compute and interactively visualize features of these deformation fields in real-time. We integrate visualization
of the deformation field with visualization of the scalar volume affected by the deformations. Furthermore, we
present a novel use of texturing in volume rendered visualizations to show additional properties of the vector field
on surfaces in the volume.
Categories and Subject Descriptors (according to ACM CCS): I.3.7 [Computer Graphics]: Three-Dimensional
Graphics and Realism—Raytracing I.4.7 [Image Processing and Computer Vision]: Feature Measurement—
Feature Representation
1. Introduction
Comparisons play an important role in many scientific areas.
When comparing one object to another, differences between
the two can be interpreted as deformations which transform
one object to the other. In a medical context, such defor-
mations often correlate directly to growth processes or the
progression of diseases. For this reason, analysis of defor-
mations has become an important technique for medical re-
searchers to understand these processes.
The analysis of deformation-fields with the purpose
of studying morphological changes is called deformation-
based morphometry, or DBM [AHF∗98]. DBM is primarily
promoted in brain-imaging research, where it is especially
popular as it can be used to detect morphological differences
over an entire brain. This is used, for example, to analyze all
differences between subject brains and a standard brain in
order to determine image-based characteristics that are asso-
ciated with schizophrenia [GNB∗01].
Another example illustrating the importance of volumet-
ric changes in medical data is the study of rheumatoid arthri-
tis (RA) and ostheoarthritis (OA). These are joint diseases
that affect bone and cartilage in different ways. 3D MRI is
increasingly being used to study the progression of these
diseases over time. The diseases inflict progressively more
damage on the affected joints in the form of, for exam-
ple, bone erosions, bony outgrowths called osteophytes and
changes in the cartilage. These characteristics are measured
in MRI datasets [MSC∗99, KKS∗07] and are used to track
the progression of the disease.
In all cases where 3D deformation fields have been used to
study morphological changes (mostly brain imaging), only
rudimentary visualization techniques have been applied. In
general, aggregative metrics such as Jacobian-based volume
change are calculated and used to typify differences. With
suitable visualization techniques, differences can be stud-
ied in far more detail. In other areas where 3D image-based
changes are being studied but deformation-fields are not yet
being used, such as RA and OA progression, suitable visu-
alization techniques should stimulate their introduction and
hence facilitate these studies as well.
In this paper, we present new techniques for the direct fo-
cus+context visualization of 3D deformation fields, aimed
at facilitating the study of volumetric change in medical re-
c© 2009 The Author(s)
Journal compilation c© 2009 The Eurographics Association and Blackwell Publishing Ltd.
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S. Busking & C.P. Botha & F.H. Post / Direct Visualization of Deformation in Volumes
search. More specifically, they have been designed for use
during the early exploration and hypothesis-generation stage
of the medical research pipeline. Due to the nature of de-
formation fields, an ideal visualization of such data should
provide insight into three things:
• the local behavior of the deformation in specific areas,
• the context of the deformations, in the form of the scalar
volume that is being deformed,
• the effects of this deformation on this scalar volume
Our visualization approach fulfills these requirements: It
enables the researcher to explore the deformation field in
terms of areas with specific characteristics, such as growth or
loss of tissue. Our techniques place these features within the
context of the anatomical features present in the scalar vol-
ume, and also visualize how these features and the volume
itself are affected by the deformations. In the next sections,
we first discuss existing techniques for analyzing and visual-
izing deformation fields. In section 3 we present the details
of our visualization. Finally, we present and discuss results
obtained by applying our visualization to both synthetic and
clinical data, and give directions for future research.
2. Related work
2.1. Deformation analysis
The currently accepted standard for analyzing deformation
between 3D images (e.g., CT, MRI) uses non-rigid regis-
tration (e.g., [ABH∗06, RCA∗06]). Registration is the pro-
cess of deriving a transformation under certain constraints,
which aligns images to bring them into the same coordinate
frame. A rigid registration limits this transformation to, for
instance, an affine transformation, while non-rigid registra-
tion allows the registration to match free-form deformations.
The most commonly used class of non-rigid transformations
are B-splines [RSH∗99,KSP07].
After registration, the deformation field which represents
the transformation from one image’s coordinate frame to the
other holds important information about the differences be-
tween the two images. Traditionally, this deformation field
is analyzed using statistical methods (e.g., [PHS∗08]).
2.2. Vector field visualization
While direct visualization can provide valuable insight, e.g.
for selecting analysis methods and areas of interest, few pa-
pers have explored visualization of deformation fields. As
deformation fields are vector fields, they are often visual-
ized using techniques from flow visualization. For instance,
Tittgemeyer et al. [TWK02] proposed a visualization based
on an estimation of critical points within the vector field.
Color-mapped surfaces are used to show the local deforma-
tions relative to certain important features within the scalar
volume. Riddle et al. [RLF∗04] used 2D color-mapped Ja-
cobians to show changes in tissue volume on separate slices
of the dataset.
Our visualization of deformation fields is based on di-
rect volume rendering (DVR). DVR is commonly used to
visualize scalar volumes. Volume rendering has been used
in combination with methods such as LIC [HA04] in order
to visualize vector fields. However, such methods require
a pre-processing stage to generate the LIC volumes. Simi-
larly, Crawfis et al. [CMBC93] applied LIC, volumetric ex-
tensions of streamlines called flow volumes and other tech-
niques to create scalar “density” volumes based on the vector
fields. These were then rendered using traditional methods.
Direct rendering of the vector fields has not received much
attention. In earlier work, Crawfis and Max [CM92] pre-
sented an approach where the vector image is filtered with
an oriented kernel during rendering, thereby visualizing the
vector direction as an oriented line segment. Frühauf [Frü93]
visualized vector fields with DVR by mapping vector direc-
tion and magnitude directly to colors and opacities. Both
approaches suffer from problems due to occlusion. In fact,
dense 3D vector field visualization is considered an unsolved
problem. Additionally, traditional flow and vector field visu-
alization techniques are often not suitable for deformation
visualization, as they do not provide enough context infor-
mation to understand the deformations.
Compared to general vector fields, deformation fields
such as those encountered in medical research have several
properties which could be taken advantage of to improve
their visualization. Depending on the nature of the data and
problem under consideration, certain types of deformation
may be considered more important than others. For example,
changes in the amount of tissue are likely to be of greater in-
terest to a researcher than movement of the patient between
scans. Additionally, such features are likely to be local (e.g.,
growth of tumors or development of lesions). Because of
this, visualizations of these features are less likely to suffer
from occlusion problems.
Other techniques for analysis and visualization of defor-
mation have been presented based on mechanical model-
ing and stress/strain tensor fields [HFH∗04]. Computation
of such fields operates under certain assumptions and im-
plies an extra level of abstraction. Our visualization does
not require pre-processing beyond the initial computation of
the deformation field. Furthermore, we use techniques from
importance-based visualization and non-photorealistic ren-
dering to create a sparse but meaningful visualization of the
field and its context.
3. Visualizing deformation
In this section, we present a focus+context visualization of
deformation fields. While the process of obtaining the defor-
mation field is outside the scope of this paper, this usually
involves applying registration twice. Here, the first registra-
tion is used to remove differences from the data which are
not considered relevant to the problem being studied. For ex-
c© 2009 The Author(s)
Journal compilation c© 2009 The Eurographics Association and Blackwell Publishing Ltd.

S. Busking & C.P. Botha & F.H. Post / Direct Visualization of Deformation in Volumes
Figure 1: Visualizing deformation fields
ample, an affine registration can remove a difference in ori-
entation of the patient between two scans. The second, non-
rigid registration captures the remaining differences between
the images in a deformation field. We share the assumption
made in DBM that the deformation field for a large part re-
flects the actual physiological changes in the patient.
Figure 1 shows the components making up our visualiza-
tion. The focus of the visualization consists of a direct ren-
dering of features derived from the deformation field. We
define measures that allow the user to highlight areas of the
volume where the deformation has certain characteristics,
e.g., growth or loss of tissue. Context is provided by simul-
taneous sparse volume rendering of the scalar volume. We
distinguish between static and dynamic context in order to
show both the surrounding anatomical features as well as the
effects of the deformation. We present both interactive and
static enhancements to the context visualization that show
these effects.
The focus and context visualizations are integrated into
a single visualization, such that the resulting combination
presents relevant deformation features in an easily identi-
fyable way within the context of the deforming volume. For
this purpose, we define interest functions, which assign im-
portance to features in each part of the visualization. Finally,
we discuss the use of texture in direct volume rendering as
a channel to provide additional information about the defor-
mation vector field.
3.1. Deformation measures
The deformation fields our visualization deals with are given
as vector-valued volumes. Traditional volume rendering uses
a transfer function to map values in a volume to colors and
opacities. Independently, however, the components of the
vector field mean little. Furthermore, the design of transfer
functions (let alone general three-dimensional transfer func-
tions) is highly non-trivial. When examining deformations,
(a) Magnitude (b) Growth
Figure 2: Visualizations of a synthetic 643 vector field. The
left figure only shows vector magnitude (in orange), while
the right figure shows our growth measure (yellow for nega-
tive values, blue for positive), giving a more detailed repre-
sentation of deformation.
a researcher is often interested in areas where the deforma-
tion has certain characteristics. Therefore, we define scalar
valued measures that capture these characteristics. By visu-
alizing these measures using volume rendering, we are able
to highlight areas of the volume corresponding to the char-
acteristics that are of interest to the user, without requiring
explicit segmentation.
The most straightforward example of this is areas where
the magnitude of the deformation exceeds a certain thresh-
old. A direct volume rendering of vector magnitude in a syn-
thetic deformation field is shown in figure 2(a). While this
clearly shows areas of significant deformation, the nature of
the deformation is not visible.
In analyzing vector fields, the Jacobian matrix J of the
field is often used to gain insight into the local behavior of
the field. The Jacobian is a matrix consisting of the three
first-order partial derivatives of the field. The absolute value
of its determinant, ‖J‖, indicates the local volume change,
and is therefore especially useful for analyzing deformations
in medical data, as this directly corresponds to growth or loss
of tissue. Based on the Jacobian determinant, we define the
growth measure g:
g =
{
‖J‖−1 for ‖J‖ < 1
1− 1‖J‖ otherwise
(1)
Negative growth indicates loss of tissue. The measure is
symmetric, and in the range [−1,1], with g = 0 meaning no
change in volume, g = −1 meaning total loss of volume,
and g = 1 meaning infinite growth. Its absolute value repre-
sents local tissue change. We therefore visualize the growth
measure by using this absolute value to determine opacity.
Features are color coded to indicate whether they represent
growth or shrinkage. Figure 2(b) shows a direct volume ren-
dering of growth features in a synthetic dataset.
Because the Jacobian is a derivative of the field, we can
c© 2009 The Author(s)
Journal compilation c© 2009 The Eurographics Association and Blackwell Publishing Ltd.

S. Busking & C.P. Botha & F.H. Post / Direct Visualization of Deformation in Volumes
introduce the concept of scale [Wit83]. Approximation of
derivatives is usually sensitive to noise in the data. By com-
puting the Jacobian (and the measures derived from it) at
a higher scale, the impact of such noise can be removed.
Moreover, manipulation of this scale allows the user to eas-
ily filter the features in the dataset based on their scale.
For this reason, computation of the Jacobian is done on the
GPU, allowing for near-interactive manipulation of the scale
parameter. We implemented derivative approximation using
central differencing, where scale determines the spacing be-
tween samples. We also implemented derivative approxima-
tion based on convolution with a Gaussian derivative kernel.
This yields higher quality approximations of the derivative
with a smoothly adjustable scale, at the cost of performance.
While the growth measure is effective in showing areas
where change in volume occurs, it fails to highlight ar-
eas of possibly significant deformation where the volume
remains the same (e.g. translations). The simpler magni-
tude visualization shown in figure 2(a) does show these ar-
eas. However, these often occlude areas where the growth
measure is significantly large, as well as potentially useful
context structures (see section 3.2). To solve this problem,
we use our importance-based filtering techniques presented
in section 3.3 to combine the two visualizations, assigning
higher importance to the growth features. This essentially
highlights areas where deformation occurs without volume
change. To avoid occluding growth features, these areas are
not visualized directly. Instead, the magnitude measure is
used in section 3.3 to determine areas where dynamic con-
text information should be shown, which is sparse enough
not to cause occlusion problems.
It should be noted that most non-rigid registration tech-
niques result in a deformation field with vectors which for
each point in a so-called fixed image point to the correspond-
ing point in the moving image. Applying the growth measure
to such a field assumes the semantics of going from the fixed
image to the moving image. That is, interpreted directly, the
field describes a transformation which “deforms” the fixed
image. Determining the inverse transformation is often im-
possible, however, due to the symmetry of the growth mea-
sure, its sign can simply be reversed to reverse these seman-
tics.
3.2. Providing context
Deformation features such as those visualized in the previ-
ous section are meaningless to a medical researcher unless
they can be related to anatomical features. In our visualiza-
tion, such context information is provided by a scalar vol-
ume. Often, this will be one of the volumes used to compute
the deformation field. Assuming the registration is perfect,
the second volume can be derived from the first by applying
the deformation. Therefore, we only need a single volume to
provide context information.
In visualizing the context volume, we distinguish between
two kinds of structures. Static context consists of structures
not significantly affected by the deformation. Dynamic con-
text consists of those structures wich are deformed signifi-
cantly, as well as the effects of the deformation on the vol-
ume itself. We use separate modes to visualize both types of
context.
In order to minimize occlusion issues, we propose a sparse
visualization of the context volume. As our visualization
is aimed at medical researchers, we can assume advanced
knowledge about the anatomical structures present in the
volume. Therefore, it is not as important to show all in-
formation present in the scalar volume; such information
can be better obtained using traditional volume visualization
techniques. Because the deformations affect the shape of
(anatomical) features within the volume, we focus on show-
ing just these shapes.
Because values in CT or MRI scans are relatively uni-
form within separate tissues, high gradients often indicate
boundaries between different types of tissue. Furthermore,
the gradient can be used as an estimation of the normal of
the boundary surface. To provide static context information,
we only show parts of the boundary surface where this gra-
dient is near-perpendicular to the viewing direction. This
is achieved by volume rendering a contourness measure c,
which is defined as follows:
c = s |~n|
(
1−max
(
1,α
∥
∥
∥
∥
~n
|~n| ·~e
∥
∥
∥
∥
))
(2)
where s is the scalar value at the current position, ~n is the
scalar volume gradient,~e is the unit vector pointing towards
the camera and α ≥ 1 is a parameter controlling the sharp-
ness of the contours. This results in a silhouette representa-
tion of the surfaces within the volume, shown in figure 3(b).
Visualizing dynamic context consists of two parts. First,
we show the effects of the deformation on the structures
shown in the static context mode. To achieve this, we can
simply use the deformation field multiplied with a user-
controllable value to offset sampling positions. This allows
the user to interactively morph between the volume before
and after deformation. We exaggerate deformations by al-
lowing values outside of the range [0,1]. The resulting cari-
caturistic visualization [RVG06] can make small changes in
the volume more apparent. For example, the silhouette con-
tours in figure 3(b) can be smoothly morphed between the
two datasets visualized, or even show exaggerated deforma-
tions, thus emphasizing their effects.
While morphing works well in an interactive setting, it re-
quires the use of animation, which is not always available
when communicating results. For this reason, we also ex-
plored static methods for visualizing the effects of the defor-
mation. As a static alternative to morphing we overlay the
contours from the deformed volume on those from the origi-
c© 2009 The Author(s)
Journal compilation c© 2009 The Eurographics Association and Blackwell Publishing Ltd.

S. Busking & C.P. Botha & F.H. Post / Direct Visualization of Deformation in Volumes
(a) focus (b) static context (c) dynamic context
Figure 3: Deformation visualization elements
nal volume. We use different colors for both sets of contours,
so they can easily be distinguished.
The second part of our dynamic context visualization is a
visualization of the effects of the deformation on the volume
itself. For this, we use a dense vector field visualization tech-
nique similar to spot noise. For each position p we sample
a precomputed volume containing uniform noise at multiple
positions p+ δ~v, where~v is the deformation vector at p and
δ ranges from 0 to a user-configurable maximum. This es-
sentially smears out the noise volume along the vectors in
the deformation field (see figure 3(c)).
3.3. Integrated visualization
The visualization described so far has threemodes, examples
of which are shown in figure 3:
Focus: visualization of features in the deformation field.
Static context: visualization of parts of the scalar volume
unaffected by the deformation.
Dynamic context: visualization of the effects of the defor-
mation on the volume.
These three modes could be used separately to visualize
a given dataset. However, in that case relations between fea-
tures seen in the different modes are not always apparent.
We therefore integrate the modes into a single visualization.
Our approach is to render all three modes simultaneously
and combine results for each step through the volumes.
For each position in the volume, we select the mode that
is most relevant for showing that particular point. We do this
by defining interest functions, which assign importance to
each point in the volume. The domain of these functions can
be any value computed for this point in any of the modes.
However, here we define interest functions which create a
meaningful visualization, in which it is easy to distinguish
areas with specific flow characteristics.
For the focus mode, the objects of interest are the areas
where growth or shrinkage is high. We therefore use the ab-
solute value of growth (equation 1) as the domain of the in-
terest function. Defining the interest function similar to the
opacity transfer function for this mode leads to good visibil-
ity of the features in the visualization. The interest function
could be extended slightly outside the range of opacities to
create an empty shell around growth features. This makes
them stand out more in the resulting image.
As our static context consists of thin and very sparse con-
tours, we can afford to assign these high importance. This
way, they will always be visible, even if other features oc-
cupy the same space. Importance is again assigned similar
to opacity, based on the measure defined in equation 2. A
distinction between dynamic and static context can easily
be made based on the local magnitude of the deformation
field. We therefore use magnitude as the domain for the dy-
namic context interest function. We assign dynamic context
features lower importance than focus features. This way, we
highlight areas where deformation occurs without a change
in the amount of volume / tissue.
During rendering we compute the values of these three in-
terest functions for each step through the volume. The mode
with the highest importance is selected and applied, result-
ing in a color and opacity. Finally, these colors and opaci-
ties are composited as in traditional direct volume render-
ing. In our prototype implementation, the interest functions
consist of simple linear interpolations from 0 to 1 between
double thresholds on the function’s domain. These thresh-
olds can be manipulated interactively by the user (as well as
the normal transfer functions for each mode), allowing for
easy manipulation of the relative importance of features in
the visualization (see figure 4)
One important issue to consider when combining multiple
modes in a single visualization is that it may not be clear to
which mode a given feature belongs. To solve this issue, we
use color only to distinguish between features with different
semantics. Furthermore, the different modes each have their
own visual style, to make them easily distinguishable.
3.4. GPU-based raycasting of scalar and vector fields
We base our techniques on our GPU-accelerated multi-
volume raycaster. This raycaster uses a similar technique to
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Journal compilation c© 2009 The Eurographics Association and Blackwell Publishing Ltd.

S. Busking & C.P. Botha & F.H. Post / Direct Visualization of Deformation in Volumes
Figure 4: Combined visualization of focus and context fea-
tures in a 512×512×80 knee dataset. Jacobians were com-
puted with a kernel radius of 4×4×0.6 voxels. Growth fea-
tures are shown for |g| > 0.14.
that presented by Krüger and Westermann [KW03]. In short,
we use a depth peeling approach to render proxy geometry
for each volume one layer of geometry at a time. A frag-
ment shader is used to perform raycasting between the lay-
ers. We keep track of active volumes for each layer, thereby
enabling simultaneous multi-volume raycasting. The com-
plete rendering process for two volumes is shown in figure 5.
Rays are cast for each layer from the positions on the pre-
vious layer to those on the current one, using a fixed step
size (see figure 5). Active volumes are determined, loaded
as textures, and sampled for each position along the ray by
transforming the current position into their local coordinate
frame. Both the measures described in section 3.1 and the
visualizations described in section 3.2 are computed in real-
time from the vector and scalar volumes on the GPU. The
resulting colors and opacities are combined using the impor-
tance filtering techniques described in section 3.3, and then
composited to form the resulting color and opacity for the
layer. To reduce the visual impact of artifacts caused by the
fixed step size, we offset the sampling positions of the rays
in neighboring pixels by fractions of the step size. While the
result has a dithered appearance, it leads to better visibility
of structures within the volume, even for larger step sizes,
which in turn lead to better performance.
Optionally, gradients can be computed in real-time using
central differencing. These can then be used for lighting, al-
lowing for better perception of shapes in the resulting vi-
sualization. Due to the computational complexity, however,
computing gradients of growth features may be too expen-
sive for real-time rendering. A simple alternative, used in the
figures in this paper, is to use a limb darkening effect similar
to that used in [HA04]. Limb darkening can be achieved by
using a softer transfer function to create a darker halo around
surfaces, providing the effect of shading without needing to
compute surface normals.
Figure 5: Using a layered approach for GPU-based multi-
volume raycasting
A different technique we explored is using streamline
shading [Frü93] to visualize deformation direction. How-
ever, this technique only works well on thin, line-like ob-
jects oriented in the direction of the deformation. As the fea-
tures in our focus mode generally form blob-like surfaces,
streamline lighting creates a confusing appearance and does
not provide intuitive insight into the deformation direction.
For this reason, we apply this form of lighting only to the
smears in our dynamic context visualization, which do have
a clear linear structure.
3.5. Using texture
While texture hardware is often used for volume rendering,
actual texturing is not commonly used in volume visualiza-
tion due to the complexities of mapping two-dimensional
images on arbitrary surfaces. However, due to the simplistic
and (at least at larger scales) relatively smooth nature of the
surfaces in our visualization, and due to our choice of sin-
gle colors for different features, texture forms an available
channel for presenting additional information to the user.
We use texture to indicate the local direction of the de-
formation vector field. Because this direction is obviously
three-dimensional in nature, we split the vector in a surface-
tangential and a perpendicular component. The tangential di-
rection is visualized using an oriented stripe texture. The an-
gle between the vector and the surface is visualized in the
color of the stripes. Similarly, color can be used to visual-
ize vector magnitude. Figure 6 shows the same feature both
without and with several variations of our texturing tech-
nique.
Because the surfaces of features might be noisy at lower
scales, computing the texture directly on the tangent plane
results in a noisy image where the direction may not be
clearly visible. Instead, we project the deformation vector
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Journal compilation c© 2009 The Eurographics Association and Blackwell Publishing Ltd.

S. Busking & C.P. Botha & F.H. Post / Direct Visualization of Deformation in Volumes
(a) No texture (b) Direction (c) Perpendicularity (d) Magnitude
Figure 6: Enhancing the visualization with texture reveals various properties of the deformation field, such as a rotational
component in this synthetic saddle point deformation (1283). Colors in the last two figures go from blue (low) to orange (high).
to the axis-aligned plane most similar to the tangent plane,
and compute the texture based on this vector. Next, a strip-
ing pattern is applied along the vector perpendicular to the
projected deformation vector in the plane. The width of the
stripes can be changed by the user to adapt the texture to
vector fields with different smoothness.
4. Results
The algorithms described in this paper were implemented
in C++ using OpenGL and the GLSL shading language
for GPU programming. The visualization runs with inter-
active performance on Nvidia GeForce GTX 280 hardware,
achieving an average framerate of 10 fps on the visualization
shown in figure 7. Applying texture or lighting to the focus
features is more computationally intensive, as this requires
estimation of the surface normal for these features. Given
current trends in GPU capabilities, however, performance of
these techniques is likely to improve significantly with next
generation hardware. The current implementation is limited
to volumes and deformation fields that fit in GPU memory.
Out-of-core techniques could be used to remove this limita-
tion.
Results from applying our visualizations to artificially
generated deformation fields are shown throughout sec-
tion 3. These vector fields were generated by additive combi-
nation of simple vector fields representing rotations, saddles,
translations, sources and/or sinks [WH91]. While we applied
our visualization to datasets from an OA study (shown in
figure 3 and figure 4), these images are intended only to
illustrate our techniques as we have yet to work with do-
main experts to validate these results. In addition to these
datasets, we used a pair of MRI images, taken 4 months
apart, of the brain of a patient suffering from Multiple Scle-
rosis. MS leads to the appearance of lesions in the white
matter of the brain. The data shows a high number of such
lesions, some of which grow, shrink, appear or disappear be-
tween the two scans. The images had previously been nor-
malized. As is common in deformation analysis research, we
used elastix [KSP07] to apply a standard B-spline non-rigid
registration between the two images in order to obtain a de-
formation field. We then applied our techniques to visualize
this field together with one of the original MRI images.
Our visualization, shown in figure 7, shows that changes
in the brain clearly appear as growth and shrinkage features.
Most of these features are yellow, which corresponds to con-
traction or loss of tissue. Experts hypothesize that the in-
creasing number of lesions leads to a reduction in the volume
of the brain ventricles. The yellow features in the center of
the brain seem to be in line with this hypothesis, although
further analysis is required to confirm this. The visualiza-
tion also shows a large deformation outside the brain in the
lower left corner, which is probably due to misalignment.
The yellow feature on the far left is an artifact, resulting from
padding the dataset.
5. Conclusions and future work
We presented new techniques for the focus+context visual-
ization of deformation in volumes, useful in studying devel-
opment and disease progression in medicine. Our techniques
directly visualize deformation fields in terms of the nature
and effects of the deformations. In summary, we identify the
following contributions:
• direct visualization of features derived from deformation
fields, allowing exploration of the fields on a higher se-
mantic level than traditional vector visualizations,
• direct volume rendering of the underlying scalar volume,
to show both context and effect of the deformations,
• importance-based integration of both visualization tech-
niques into a single image,
• the use of texture to present additional information about
the deformation field in relation to the features shown in
the visualization.
While our focus in this research was on medical datasets,
the techniques presented in this paper can be applied in other
areas as well. In future work, we intend to refine these tech-
niques and work with domain experts, most notably in OA
research, to apply our approach to real data. For this, new
types of measures may need to be developed to capture char-
acteristics of interest to these experts. Additionally, we aim
c© 2009 The Author(s)
Journal compilation c© 2009 The Eurographics Association and Blackwell Publishing Ltd.

S. Busking & C.P. Botha & F.H. Post / Direct Visualization of Deformation in Volumes
Figure 7: Visualization of deformation due to changing
white matter lesions in a brain MRI dataset of 181× 217×
179 voxels. Jacobians were computed with a kernel radius
of 2 voxels. Growth features are shown for |g| > 0.09.
to extend our filtering techniques to allow a user to select
features based on various criteria other than scale. Finally,
we intend to extend our techniques to allow comparison of
two or more deformation fields.
Acknowledgements
We are grateful to Dr. G. Kloppenburg and Dr. I. Watt of
respectively the Reumatology and Radiology departments
of the Leiden University Medical Center for their valu-
able input and OA research datasets. This research is sup-
ported by the Netherlands Organisation for Scientific Re-
search (NWO), project number 643.100.503 “Multi-Field
Medical Visualisation”.
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