Visualization of 3D Cluster Results for Medical Tomographic Image Data

Sylvia Glaßer, Kai Lawonn and Bernhard Preim

Department of Simulation and Graphics, Otto-von-Guericke University, Magdeburg, Germany

Keywords:

Computer Graphics, I.3.5, Picture/Image Generation, Display algorithms.

Abstract:

We present an approach for the 3D visualization of clustered tomographic image data using the example of

breast perfusion image data. Our visualization provides fast visual access to the amount of clusters, cluster

size, presence and amount of outliers, and the spatial extent as well as the spatial orientation of the clusters.

The spatial perception of a cluster’s elements is improved with a connection via geometric primitives and

appropriate shading styles and color mapping. Our technique can be easily adapted to any cluster result

arising from medical tomographic image data.

1 INTRODUCTION

Medical image data sets become larger and more

complex, thus increasing the demand for computer

support during the evaluation by a biomedical expert.

Hence, clustering is important to group objects with

similar attributes, e.g., voxels representing certain tis-

sue types. The appropriateness of a cluster algorithm

depends on the medical problem and image parame-

ters. To improve the adoption of a clustering to a spe-

ciﬁc problem, the biomedical expert has to evaluate

the quality of the clustering result, like the topology

of the clusters and the spatial orientation of the struc-

ture that has been decomposed.

We present a new 3D clustering view to visualize

clustering results of medical image data, e.g., 4D tem-

poral perfusion data. For the evaluation of perfusion

data sets, clinical diagnosis aims at the identiﬁcation

of areas that exhibit similar characteristics. For exam-

ple, clustering of breast tumor perfusion data is em-

ployed to evaluate the tumor’s heterogeneity (Preim

et al., 2012). Beyond grouping of voxels with similar

perfusion characteristics, clustering is applied to var-

ious medical image data, such as fMRI data. Hence,

peaks in a histogram often represent overlaps of tis-

sue types that are not particularly interesting. To de-

tect the interesting data parts, clustering is often em-

ployed to analyze the gradient versus the intensity

histogram space (Maciejewski et al., 2009). Further-

more, cluster analysis is carried out to generate trans-

fer functions for this kind of data (Maciejewski et al.,

2013). In addition, cluster analysis is also applied to

identify regions with similar boundary characteristics,

which in turn are used for transfer function speciﬁca-

tion (Sereda et al., 2006). DTI data forms another im-

portant medical application area for clustering, where

ﬁber tracts are clustered (Moberts et al., 2005).

We illustrate our new 3D cluster view based on the

example of clustering of medical perfusion MRI data

for breast cancer diagnosis. Perfusion MRI exhibits

a higher sensitivity than conventional X-ray mam-

mography in younger women and is often consulted

to conﬁrm benignity (i.e., non-cancer) or malignancy

(i.e., cancer) of a tumor. Contrast-enhanced perfusion

MRI data is acquired to analyze the contrast agent ki-

netics of the tumor. A breast tumor is considered as

malignant as its most malignant tumor part.

Consequently, biomedical researchers try to detect

new correlations between heterogeneity and malig-

nancy based on the clustering result of breast tumors.

For the evaluation of a clustering’s quality, the cluster

shapes and spatial orientations as well as their average

enhancement are assessed. Also, the topology and the

connectivity of the clusters is evaluated such that con-

clusions are made about a necrosis in the tumor center

or varying enhancement kinetics at the tumor bound-

ary. Generally, a standard 2D slice view is analyzed

since this visualization does not suffer from any oc-

clusion. However, we aim at a 3D representation to

not only show the spatial orientation of the clusters,

but also how they penetrate each other.

When it comes to a 3D visualization of different

groups of data (i.e., different groups of voxels that

could be arbitrarily shaped and be nested into each

169

Glaßer S., Lawonn K. and Preim B..

Visualization of 3D Cluster Results for Medical Tomographic Image Data.

DOI: 10.5220/0004719901690176

In Proceedings of the 9th International Conference on Computer Graphics Theory and Applications (GRAPP-2014), pages 169-176

ISBN: 978-989-758-002-4

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

other), in general each group is visualized with its

boundary surface and one is directed to the embed-

ded surface problem. We avoid this by employing a

3D scatter plot-like view. The objects (in our case the

voxels) are mapped to small spheres in the 3D scat-

ter plot-like coordinate system. Thus, we can avoid

occlusion, since no surfaces or blocks of data are ren-

dered. To emphasize the connection of the data points

to the corresponding clusters, we employ tubes and

use color-coding. Additional information about the

clusters, like average relative enhancement curve, is

provided with a necklace map legend (Speckmann

and Verbeek, 2010). Our framework is developed

based on the clustering of medical perfusion data.

However, our method is feasible for each cluster 3D

visualization arising from other medical areas.

In summary, we present a visualization with the

following contributions. First, we describe a cen-

ter point-oriented projection of a tumor into a sphere

model, where different spheres represent different

neighbor layers. Now, each voxel can be rendered

as small object on such a sphere’s surface. Sec-

ond, we introduce a 3D scatter plot-like visualiza-

tion for breast clustering results employing the sphere

model and featuring well-ﬁtted tubes. The visual-

ization comprises selected shading styles to enhance

the different scatter plot parts and a perception-based

color mapping to enhance visual differentiation be-

tween clusters. Furthermore, it is adapted to the ex-

tent of the tumor. Third, a necklace map-based legend

provides different information about the clusters. We

evaluate our visualization in a quality user study.

2 RELATED WORK

To improve and support the radiologist’s work, ad-

vanced methods including visual analytic solutions

were developed. Lundstr

om and Persson charac-

terized the visual analytic tasks in diagnostic imag-

ing (Lundstr

om and Persson, 2011). Hence, the de-

termination of shape, size, and relative position of

different parts of the anatomy was identiﬁed as im-

portant component of a radiologist’s image review

work, albeit it was considered less important than

the diagnosis of primary and secondary ﬁndings in

the image data in an efﬁcient way. For the evalua-

tion, Glaßer et al. stated that density-based clustering

techniques are well suited for the underlying breast

perfusion image data due to the arbitrarily shaped

clusters as well as outlier detection (Glaßer et al.,

2013). The aim of the current work is not to iden-

tify the best clustering but to visualize an extracted

cluster result such that important information, e.g.,

number of clusters, number of outliers, can be ex-

tracted. A Multiﬁeld data visualization can be car-

ried out with geometric presentations like the scat-

ter plot (Wong and Bergeron, 1997) for 2D object

spaces or the parallel coordinates plot (Inselberg and

Dimsdale, 1990) for higher dimensional object spaces

without spatial information. To maintain spatial infor-

mation in high-dimensional cluster visualization, Lin-

sen et al. presented a surface extraction approach for

spatial visualization of multiﬁeld clustered data (Lin-

sen et al., 2008). Hence, boundary surfaces are ex-

tracted and semi-transparently visualized in a 3D star

coordinate layout to reveal nested clusters. Poco

and colleagues employed a least square projection to

map high-dimensional data to 3D visual spaces (Poco

et al., 2011). Their framework enables the map-

ping of multidimensional non-spatial data as well as

the feature space of multi-variate spatial data. Both

approaches employ surface representations for their

cluster results. Due to the limited number of voxels

in a medical data set, we do not want to visualize sur-

faces but rather present each object directly.

In (Zhang et al., 2006), a method to visualize

gene clusters in 3D is described. First, a spring

model is used to locate genes within a cluster into

InfoCubes. Afterwards, the same method is used

to allocate the InfoCubes into 3D space. The algo-

rithm avoids the space partition problem. Unfortu-

nately, clusters on our tumor data sets can be entwined

around each other such that we need a representation

of such cases. The approach by Quigley deals with

large data sets and generates hierarchical compound

graphs (Quigley, 2001). The clusters are represented

as a graph where the nodes act as the clusters. Yang

et al. presented a system for the processing of DNA

microarray data (Yang et al., 2003). They introduce

a space-undivided and a space-divided 3D gene plot.

In the ﬁrst plot, every gene is assigned to a sphere

and the cluster membership is color-coded. The sec-

ond plot splits the 3D space into cubes and puts the

clusters into these cubes. In the ﬁrst case, clusters

seem to be huge point clouds, and in the second case,

no spatial information about the clusters exists. Aono

and Kabayashi developed a visual interface for non-

technical users to understand the output from cluster-

ing algorithms (Aono and Kobayashi, 2011). Their al-

gorithm displays clusters which are projected on a 3D

subspace based on the user’s keyword input. Thus, the

computed recommendations for the 3D visualization

cannot present the spatial impression on the tumor.

In contrast, our approach aims at direct mapping

of each voxel to a data point in the 3D space, which is

possible due to our small data set extents. Similar to

our work, Kosara et al. presented the VoxelPlot, a 3D

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scatter plot that interactively links scientiﬁc and infor-

mation visualization (Kosara et al., 2004). A voxel-

based representation of clustered / grouped data for

perfusion MRI was presented in (Oeltze et al., 2007).

Sanftmann and Weiskopf introduced the illuminated

scatter plot, where shape perception is improved by

applying a dedicated illumination technique to the

3D scatter plot point cloud representation (Sanftmann

and Weiskopf, 2009). Piringer and colleagues map

the distance to color and the point size of the scat-

ter plots (Piringer et al., 2004). In contrast to these

approaches, we do not only employ color or shad-

ing to represent the type of cluster, but also add ge-

ometric objects into our 3D scatter plot to enhance

the connections of cluster voxels to cluster centers.

This is similar to the work presented in (Healey et al.,

2001), where contextual cues in the ﬁnal 3D scatter

plot-based visualizations for large, multidimensional

collections of data are included. Another example re-

lated to the aspect of connected cluster elements is

the butterﬂy plot (Schreck et al., 2008). Hence, multi-

dimensional point clouds are projected into 2D space

and clusters are visualized by compact shapes that en-

close all members of a given point cloud.

Our visualization method is extended by a legend

that is based on the necklace map (Speckmann and

Verbeek, 2010). This technique is related to boundary

maps, which map labels around the map in the center,

and is well suited for cluster visualization.

3 MATERIAL AND METHODS

In this section, we describe the steps to create the 3D

clustering view, see Figure 1. At step I, the neighbor-

hood model is extracted (described in Sec. 3.1). At

step II, the voxel size and tumor extent is determined

(see Sec. 3.2). At step III, we project the voxels onto

spheres (refer to Sec. 3.3), connect the cluster ele-

ments with their associated cluster center points via

tubes (presented in Sec. 3.4), and reshape the spheres

according to the tumor’s extent. A legend that is based

on the necklace map is added to the 3D visualization

to provide additional information about the clusters,

described in Section 3.5. The assignment of color and

shading styles is presented in the last part of this sec-

tion.

3.1 Neighborhood Model for Voxel

Ordering

Given a voxel in a 3D tomographic data set, the cor-

responding neighbors are deﬁned as adjacent voxels

that share

• a face (yielding 6 neighbors),

• an edge (yielding 18 neighbors),

• or a vertex (yielding 26 neighbors).

We choose the edge-based neighborhood relation-

ship. We build a neighborhood structure by an itera-

tive process. First, we start at an initial voxel v

init

that

is typically the centroid of the tumor T . If the cen-

troid is not part of the tumor due to an irregular tu-

mor shape, we choose its nearest neighbor contained

in the tumor. The ﬁrst layer L

of our neighborhood

structure contains only v

init

. The second layer L

in-

cludes the neighbors v

∈ T of v

init

that are also part

of the tumor. For simplicity, we denote Neigh(v) as

the neighbors of v in T . The i-th layer can be written

as:

[

v∈L

i−1

Neigh(v) \ L

i−1

. (1)

3.2 Integration of Voxel and Tumor

Extent

The voxel extent is determined by the image ma-

trix that deﬁnes the image plane resolution, i.e., the

voxel’s width and height. The voxel’s depth is set

down by the slice thickness, which usually differs

from the image plane resolution. We rescale the

voxel’s depth v

such that the voxel’s width and height

equals uniform length.

The tumor extent is characterized with a princi-

pal component analysis. The voxel’s x, y and z in-

dices serve as input, whereas z was rescaled with v

Hence, the principal components match the eigen-

vectors of the covariance matrix that was constructed

for the principal component analysis. With the three

eigenvalues corresponding to the three principal com-

ponents, we obtain the tumor’s three main extents.

3.3 Projection onto a Sphere

After we extracted the neighborhood structure, we

build up our cluster visualization. Each layer of

neighborhood information is projected onto a sphere.

Therefore, we translate a sphere of radius r = i

to the

initial voxel, i.e., the centroid. Afterwards, we deter-

mine the intersection point of the sphere with the line

constructed by the initial voxel and an element in the

i-th layer L

. In detail, we translate the voxel such

that the initial voxel is in the origin. Given the mid-

point q

of v

∈ L

, we obtain the intersection point

by calculating

= q

)

. (2)

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171

Origin

Step I Step II

Step III

Figure 1: Scheme of our cluster visualization pipeline. The example holds ﬁve voxels, each forming its own cluster. In step I,

we create a sphere model, holding all voxels of the tumor. In step II, the voxel dimensions are adapted to the image resolution.

A principal component analysis yields the main directions of the tumor. In step III, the 3D clustering visualization is generated

by positioning the voxels onto spheres. The sphere-shaped visualization is adapted to the main tumor extents, approximated

with the principal components.

(a)

(b)

(c)

Figure 2: We start with the initial voxel (cyan color-coded),

see (a). Next, we determine L

and calculate the intersec-

tion point of the line constructed by the initial voxel and an

element of L

with the circle, see (b). In (c), we obtain the

intersection points of the second layer L

See Figure 2 for an illustration in 2D.

3.4 Connection of Cluster Elements and

their Associated Midpoints

To support the perception of clustered elements, we

connect all elements and their associated midpoints.

The connections, shaped like tubes, are motivated

by the natural model of neurons and their dendrites

as well as blobby surfaces (Blinn, 1982). We em-

ploy a visualization which connects the start points,

i.e., the extracted positions for each voxel, with the

end point, i.e., the cluster center, by smooth organic

linkage. Hence, the algorithm comprises three steps.

First, we connect the start point and the end point

with a straight line. As an optional step, we add sev-

eral equidistant points on the line. Afterwards, we

use the normalized vector which points to the start

point. We scale this vector to one tenth of the length

from the end point to the start point and add it to the

added points on the line. The scaling linearly changes

to zero such that the ﬁrst points are more translated

than the last ones. This approach yields a bending

of the tubes and reduced visual clutter. The second

step is about generating a cubical spline to connect

the end point and the start point via the middle points.

The last step generates a Frenet frame around the

curve. Afterwards, we use this frame to generate a

tube around the curve. Inspired by the following for-

Figure 3: An example of a visually pleasing tube connecting

the start point to the end point.

mula:

thick(x) = radius



1 −







, (3)

we generate a function which determines the thick-

ness of the tube at every point. Let r

be the radius

of the sphere at the start position, r

the radius of the

sphere at the end point, and d denotes the distance be-

tween the start and the end position. Additionally, we

deﬁne r

= 0.25min(r

). Furthermore, r

= r

− r

and r

= r

− r

. Then, the thick(x) function with

x ∈ [0,d] can be written as:

thick(x) =













1 −







+ r

if x ≤



1 −



4(d−x)





+ r

if x ≥

otherwise.

(4)

The construction of thick(x) ensures a smooth change

from r

for x = 0 to r

for x = d. First, the value

thick(x) decreases smoothly from r

to r

for x ∈

[0,d /4] and keeps its value r

for x ∈ [d /4,3 d /4].

For x > 3d /4 the function is smoothly increased to

the value r

. See Figure 3 for an example.

3.5 Combination with a Necklace Map

To assess a clustering’s quality, additional informa-

tion to the cluster’s spatial orientation should be pro-

vided. These information may include the cluster’s

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average value of a parameter, its standard deviation,

or its size, etc.

For perfusion imaging, the average perfusion en-

hancement curve is of major interest from the radi-

ologist’s point of view. For each cluster, we provide

its average curve in a legend that is based on a neck-

lace map (Speckmann and Verbeek, 2010). The neck-

lace map was developed for 2D maps and is similar to

cartograms or choropleth maps. However, it arranges

symbols (e.g., circles) around the initial map in a lin-

ear ordering. Thus, the symbols can carry information

but no occlusion arises.

The necklace map is perfectly suited for our

method, since we want to display additional informa-

tion for a group of well-deﬁned objects – our clusters

– albeit we want to accomplish a 3D scene instead of

a 2D scene. The according symbol for each cluster

is a circle that is color-coded with the corresponding

cluster color. All circles are arranged on the necklace

ordered by cluster size, starting in the top right. The

necklace itself is an ellipse that is obtained by scaling

a circle with tumor extents extracted in Section 3.2.

The necklace legend is depicted in Figure 4. The size

of the necklace pearls is linearly decreased, and not

proportional to the cluster size due to strong varia-

tions of cluster sizes, e.g., a cluster may contain 3 or

500 voxels.

3.6 Representation of Clusters

The tubes are rendered with a Phong shading to im-

prove the shape perception. To support the visual-

ization of the start point, and thus a good differentia-

tion from the Phong-shaded connecting tube, we ap-

ply Fresnel shading to the start point.

We assign a speciﬁc color to each cluster and its

start points. For the color assignment, we employ

the CIELAB color space to establish high perceptual

color contrast. The ﬁrst cluster is always assigned to

orange, with the corresponding CIELAB components

L = 67, a = 43, and b = 74. For the n remaining clus-

ters, we extract n colors with the following routine.

We place a circle in the CIELAB space. The circle’s

center is set to (a = 0; b = 0). Given the a- and b-value

for orange, we deﬁne its radius r with r

= a

+ b

Then, we deﬁne the angle α B arcsin(b/r). Next, we

compute new values for a and b by increasing α with

β , where β ranges from 0 to 2π/n in n steps. We now

compute a = r · cos(α + β ) and b = r ·sin(α +β ), and

combine them with the starting value for L.

For the ﬁnal representation, we scale the spheres

holding the voxels according to the tumor extent to

highlight the tumor’s biological form. Thus, a tumor

with a biological ellipsoid form yields a scaling of

the spheres along the main tumor extents, whereas a

sphere-shaped tumor will only cause minimal scaling.

4 RESULTS

We present our approach adapted to a breast tumor in

Figure 4. There, an overview of our 3D scatter plot-

like clustering visualization is provided. The user can

examine the spatial extent of the single clusters and

their spatial position. The spheres, which hold the dif-

ferent neighbor layers, are visualized with a Fresnel

shading. We assign gray to these spheres. Outliers are

presented with white colored spheres. Furthermore, a

standard headlight is applied to the visualization.

The 3D view is accomplished with a necklace

map. Thus, the user has a fast overview of all exist-

ing clusters and additional information are mapped.

As demanded by our medical experts, we provide the

cluster’s average relative contrast agent enhancement

as time-intensity curve. Our framework also holds a

conventional slice view. To study a cluster’s spatial

orientation in more detail, the user can pick a cluster

by clicking via the necklace map or the 2D view and

study its extent in more detail. Now, Fresnel shad-

ing is interactively applied to the non-selected clus-

ters with a gray color. This emphasizes the selected

clusters and supports the individual examination, re-

call Figure 4.

In Figure 5, we loaded a brain tumor data set

comprising a masked perfusion MRI data set. For

brain perfusion, the parameter cerebral blood volume

(CBV) is analyzed to detect hot spots, i.e., regions

with elevated CBV values. The brain tumor was de-

composed into ﬁve clusters with k-means based on the

parameter CBV. Hence, no outliers are present. In-

stead of presenting the whole contrast agent enhance-

ment curve, the pearls of the necklace map provide

average CBV values and identify the pink cluster as

cluster with highest averaged CBV value.

5 EVALUATION

We performed a qualitative evaluation of our cluster

visualization method. Our goal was to assess the ca-

pability to express the topology of the clustering result

in the 3D visualization. Hence, we focussed on the

3D representation of the clusters in combination with

connecting tubes and presented a point-based scatter

plot view and transparent isosurfaces for comparison,

see Figure 6. The evaluation was conducted with one

medical researcher and physician, and ten researchers

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173

Figure 4: Example of a breast tumor clustering result of tomographic perfusion data. The 3D cluster visualization (left) and

the 2D slice (top right) are integrated in our framework and reveal three clusters arranged at three layers. The necklace map

(placed around the 3D visualization) and the slice view allow for a fast selection of clusters. Once the user selected a cluster,

only this cluster is color-coded, and the remaining clusters are visualized with a Fresnel shading (bottom right). Outliers are

highlighted with bright red after selection according to observations from our user study.

who are familiar with the visualization and evaluation

of medical tomographic image data.

In this study, we asked the participants to handle a

few minor tasks about

• the topology of the clustering result,

• the presence of outliers,

• and the impression about the tumor’s boundary

and shape.

Figure 5: Illustration of the clustering result of a brain tu-

mor. The tumor has an elongated shape and was clustered

into ﬁve clusters, no outliers exist. The necklace map pro-

vides additional cluster information, i.e., the cluster’s aver-

age parameter value of the cerebral blood volume (CBV).

The slice view was added for a 2D view.

The topology of the clustering result was covered

by the request to identify the largest cluster and to cat-

egorize the clustering result’s topology in pre-deﬁned

categories. It was questioned if the participants could

identify outliers and how many outliers there are with

respect to number and percentage to the whole tumor.

The last question concerned the tumor’s boundary

(from round to stellated boundary) and shape (from

spherical to ellipsoidal). For each answer, we pro-

vided well-deﬁned categories to make the answers of

different participants comparable.

First, the participants were introduced to the three

techniques by presenting a clustering result of a test

data set (recall Fig. 6). Next, the subjects solved the

tasks for nine examples, created by applying each vi-

sualization technique to three new data sets. The vi-

sualizations were presented such that no data set was

consecutively shown, but after each presentation an-

other data set with another 3D view was depicted. Af-

ter answering the questionnaire, we asked the partici-

pants to rate the techniques according to their appro-

priateness to evaluate the clusters’ topology, the re-

quired user interaction, as well as for additional feed-

back.

As a result, all volunteers correctly identiﬁed the

largest cluster for each example. However, when it

comes to the cluster number, our technique achieved

better results than the other two methods, see Fig-

ure 7. This is very relevant, since a wrong number of

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Figure 6: The three 3D views of a clustering result, including a point-based view (left), the isosurface view (center), and our

approach (right).

clusters implies that some clusters were not detected

at all or (very rare) that some single, spatially con-

nected, clusters were interpreted as different clusters.

The majority of the participants rated our method to

be the most appropriate for evaluating the clusters’

topology (8 out of 11).

Outliers were present in all examples, and with

two exceptions (arising from our visualization and an

isosurface-based view) for two single examples, all

participants detected the outliers for each view. When

it comes to tumor shape, the volunteers assign higher

ratings, i.e., more stellated boundaries based on our

visualization in comparison to the other two views.

This is due to the arrangement of the voxels onto

the spheres. Hence, our view suggests a more stel-

lated boundary, which is a limitation. However, there

was no trend with respect to the employed technique,

when the participants should evaluate the tumor size

via the number of voxels that were clustered. All

participants had no difﬁculty with the interaction or

with the visualization. But the majority (9 out of 11)

needed less interaction with the 3D scene, e.g., cam-

era rotation, with our method due to the good spatial

impression of the connected clusters.

However, the study does not allow for a deﬁni-

tive statement. A further evaluation is required with

more participants and data sets. In summary, the par-

ticipants were able to fulﬁll the assigned tasks with

our method very well. They rated it as best suited for

Figure 7: Bar diagrams illustrate the average squared error

of the approximated number of clusters (left) by all users for

the three techniques: point-based 3D view, isosurface view

and our 3D scatter plot-like view. On the right, the number

of users is presented that chose a technique as best suited

for evaluation of the clustering’s topology.

the evaluation of a clustering topology. Furthermore,

they preferred it due to the visual cluster connections

via tubes and due to the lesser scene interaction in

comparison to the other techniques. They asked for

a more prominent color-coding of outliers, like bright

red, which we included in the framework afterwards.

It must also be stated that our visualization indicates

a more stellated boundary due to the spatial represen-

tation of the voxels on the spheres. On the other hand,

these representations reduce the amount of occlusion

and thus the amount of required user interaction.

6 DISCUSSION AND FUTURE

WORK

In this paper, we presented a novel method for 3D

cluster visualization for analyzing medical tomo-

graphic image data. We applied our techniques to

clustering results of breast perfusion data. However,

our methods are feasible for each clustering arising

from other medical areas. Our 3D scatter plot-like

cluster visualization addresses the spatial information

as well as the size of each cluster. A fast overview

of how many clusters are present and how they are

spatially aligned is presented. Geometric modeling

enhances cluster connections. The 3D view is com-

pleted with a necklace map legend, maintaining that

each cluster can be adressed. Hence, the user can se-

lect a cluster of interest for further exploration in the

3D view. While the appearance of the selected cluster

does not change, color and shading of the remaining

clusters change from opaque visibility to Fresnel.

For future work, we like to address an improved

perception in case of a huge number of cluster el-

ements. We think about a view-dependent trans-

parency representation similar to the work by G

unther

and colleagues, who reduce the number of displayed

lines by smoothly fading them out (G

unther et al.,

2011). Connections very close to the camera are

opaque, whereas connections far away are rendered

Visualizationof3DClusterResultsforMedicalTomographicImageData

175

transparent. This is done to improve the visual ap-

pearance of the tubes and to concentrate on the focus

of the camera. Furthermore, we like to use the GPU to

get a real-time interaction while changing the param-

eters of the cluster algorithm yielding an immediate

result in the 3D cluster visualization after parameter

changes.

ACKNOWLEDGEMENTS

This work was supported by the DFG Priority Pro-

gram 1335: Scalable Visual Analytics.

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