IMPORTANCE-DRIVEN VOLUME RENDERING
AND GRADIENT PEELING
Shengzhou Luo, Xiao Li, Jianhuang Wu and Xin Ma
Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China
The Chinese University of Hong Kong, Hong Kong SAR, China
Keywords: Importance-driven, Volume rendering, Gradient peeling.
Abstract: Volume rendering is widely used in visualizing and exploring volume datasets. In volume visualization, it is
challenging to obtain desired results, because different tissue types are represented in overlapping ranges of
scalar values and interesting structures will be partly or completely occluded by surrounding tissue of less
importance. This paper introduces importance-driven volume rendering and gradient peeling techniques to
reveal inner structures of interest. The importance of clusters is specified interactively and composited into
the opacity of voxels. Then gradient peeling is performed on the clusters whose importance is greater than
the user-defined threshold. This semi-automatic approach provides users with the freedom to visualize
clusters of interest and the ability to peel off surface layers of the material. Experiment results show that our
approach has superior capability in revealing inner structures and removing surrounding tissue which
occludes the tissue of interest.
1 INTRODUCTION
Volume rendering has become an important
technique for various visualization applications such
as medical imaging and scientific visualization. In
volume rendering, there are two key factors that
prevent us from obtaining desired results, especially
for interior tissues. Firstly, different tissues are
represented in similar or even overlapping ranges of
scalar values in MRI and CT datasets. Secondly,
interesting structures may be partly or completely
occluded by surrounding tissue, which is common in
visualizing inner structures.
In traditional volume rendering, these two
problems are handled by transfer function
specification. However, traditional transfer function
approach, which assigns optical properties only
based on scalar values, is inadequate to extract inner
structures of interest from the volume data. For
instance, there are skin and fat tissue around the
brain, and their intensities lie in the same range as
the brain. If we want to visualize the brain by setting
the scalar value range of the brain to opaque, the
surrounding skin and fat tissue will also be set to
opaque. Then the brain will be occluded by these
surrounding soft tissues. Common approaches to this
problem are to introduce explicit segmentation of
structures of interest before the volume rendering
process (Rezk-Salama & Kolb, 2006).
The work in this paper focuses on visualizing
inner structures in volume datasets. In traditional
transfer function approaches, regions of interest are
usually areas of relatively homogeneous material. If
an organ is opaque in rendering, inner structures of
the organ will be invisible from outside. To solve the
occlusion problem, the volume dataset is classified
into clusters, and weights of the clusters are
specified interactively, and then rendering and
peeling are performed on the clusters of interest.
2 RELATED WORKS
It is difficult to visualize complicated information of
volume datasets, because the outer opaque layers
always occlude the internal information. Rezk-
Salama and Lolb (Rezk-Salama & Kolb, 2006)
introduced opacity peeling, inspired by depth-
peeling for volume rendering (Nagy & Klein, 2003),
for the extraction of feature layers that allows the
extraction of structures which are difficult to classify
with conventional transfer functions.
211
Li X., Luo S., Wu J. and Ma X..
IMPORTANCE-DRIVEN VOLUME RENDERING AND GRADIENT PEELING.
DOI: 10.5220/0003368002110214
In Proceedings of the International Conference on Computer Graphics Theory and Applications (GRAPP-2011), pages 211-214
ISBN: 978-989-8425-45-4
Copyright
c
2011 SCITEPRESS (Science and Technology Publications, Lda.)
Boundaries often cannot be distinguished by
transfer functions based only on scalar values
(Sereda et al., 2006). However, higher dimensional
transfer function shows superior capability in
distinguishing between different boundaries
(Kindlmann & Durkin, 1998). For example,
Figure 1
shows a nucleon dataset, and
Figure 2
shows that
boundaries in the nucleon dataset appear as arches in
2D histograms of the scalar value and the gradient
magnitude. Kniss et al. introduced interactive
widgets to manually select boundaries in these 2D
histograms of arches (Kniss et al., 2001). Huang and
Ma (Huang & Ma, 2003) used these histograms for
partial region growing to select features in the
volume. These semi-automatic approaches turned
out to be effective on a small number of boundaries.
However, it is inadequate to deal with an increasing
number of boundaries since their separation
becomes more difficult due to intersections and
overlaps.
Figure 1: A nucleon
dataset (The Voreen
Team, n.d.).
Figure 2: Boundaries in the
nucleon appear as arches.
3 OUR APPROACH
There are three steps in our approach. First, voxels
are classified into clusters automatically based on
their scalar values (), gradient magnitudes (′) and
second derivative magnitudes ( "). Second, each
cluster is assigned an importance I (∈
0,1
)
interactively. Voxels are considered to have the
importance of the cluster that they belong to. Then
the importance of a voxel is composited into its
opacity during the volume ray-casting process.
Third, gradient peeling is performed on clusters
whose importance is greater than the user-defined
threshold.
3.1 Clustering Voxels in
Multidimensional Space
We adopt clustering techniques to automatically
classify voxels into clusters based on the scalar
value, gradient magnitude and second derivative
magnitude. The voxels are projected into a 3D space
which is made up of the scalar value, gradient
magnitude and second derivative magnitude. To
measure the difference D between two voxels (voxel
A and voxel B) in this space, we apply the following
formula which is similar to the Euclidean distance:
(1)
′
′
(2)
"
"
(3)
(4)
where
,
′, and
" denote the scalar value, the
gradient magnitude and the second derivative
magnitude of voxel A respectively. Similarly,
,
′, and
" denote those of voxel B. w
0
, w
1
, and w
2
are scale factors depending on the ranges of the
scalar, the gradient magnitude, and the second
derivative magnitude.
3.2 Rendering with Importance
After clustering, clusters are rendered in different
colors, then the user can interactively select each
cluster and assign an importance I to it. The
importance I of a cluster will be composited into
opacity of voxels belong to that cluster during the
volume ray-casting process.
In volume ray-casting, there are two methods to
calculate this rendering equation by iteration along
the ray, the back-to-front compositing and the front-
to-back compositing. The front-to-back compositing
is used in our implementation. It starts with zero
radiance at the eye position and proceeds in the
direction away from the eye. The radiance and the
opacity are composited with the following equations:
1
(5)
1
(6)
where L
i
is the radiance and A
i
is the opacity
accumulated along the ray so far, and q
i
and
is the
source term and the opacity of the i-th ray segment.
In our approach, the importance of clusters I are
incorporated into the opacity equation:
1
(7)
3.3 Gradient Peeling with Importance
The initial idea behind the peeling techniques for
direct volume rendering is quite simple. That is to
peel off parts of the volume when certain criterions
are met. The aim of boundary peeling is to reveal
boundaries of inner structures in volume data sets
GRAPP 2011 - International Conference on Computer Graphics Theory and Applications
212
which are not easy to visualize without explicit
segmentation of structures of interest.
The importance of clusters is utilized in gradient
peeling with importance. In other words, gradient
peeling with importance will only be triggered on
clusters with importance factors greater than the
user-defined threshold.
Instead of peeling off opaque material, gradient
peeling is design to peel off translucent material and
boundary regions. This is based on an observation
that the boundaries in a volume data set contribute
most to the accumulated value of gradients. Hence
gradient peeling which accumulates and measures
the gradients will has better performance on peeling
off boundary regions than opacity peeling which
accumulates and measures opacity values.
The mechanism of gradient peeling is very
similar to that of opacity peeling. That is to peel off
layers of material with certain accumulated gradient
magnitude and only to start new layers in blank
regions. Two thresholds are used for peeling, the
accumulated threshold and the current sampled
threshold. When the accumulated value reaches the
accumulated threshold and the sampled value of
current voxel is less than the sample threshold, a
layer will be peeled off.
4 RESULTS AND DISCUSSION
For the convenience of comparison, we implemented
our importance-driven techniques with a simple
scalar value (1D) transfer function, and put the
rendering results with and without the importance-
driven techniques in this section.
The importance-driven techniques allow users to
visualize the clusters of their interests.
Figure 3
and
Figure 4
are rendered from the same nucleon dataset
in
Figure 1
. In
Figure 3
, the exterior of the nucleon is
removed, because the importance of the exterior of
the nucleon is set to zero. On the contrary, in
Figure 4
,
the importance of interior of the nucleon is set to
zero, so that it is invisible in the image. These two
images show the ability of the importance-driven
techniques to rendered specific parts of the dataset
by assigning importance to clusters.
The importance-driven techniques are capable to
reveal inner structures.
Figure 5
is a foot dataset
rendered with the 1D transfer function, and
Figure 6
is the same dataset rendered with the 1D transfer
function and the importance-driven techniques. In
Figure 6
, the exterior of the foot (skin and muscles)
are completely removed, and the articulations and
the phalanges are exposed entirely. Similarly, in the
result of the VisMale dataset (Roettger, 2006)
rendered with the 1D transfer function (
Figure 7
), the
outside clusters are nearly opaque so that the
visibility of the skull inside is very limited. By
contrast, in the result with importance-driven
techniques (
Figure 8
), the outside clusters, i.e. skin
and muscles, are transparent, and the inside clusters,
i.e. the skull, is clearly visible.
Gradient peeling is better at peeling translucent
material and thin structures than the opacity.
Compare to the results of opacity peeling (
Figure 9
and
Figure 10
), the results of gradient peeling (
Figure
11
and
Figure 12
) have more details of the surface of
the skull. It is more obvious in the second layer than
in the first layer. In
Figure 10
, parts of the surface of
the skull are peeled away entirely, and the skull can
be seen through. This difference is derived from the
thresholds setting in opacity peeling and gradient
peeling. When peeling translucent boundaries of soft
tissues or thin structures, it is difficult to set an
appropriate threshold in opacity peeling, and a slight
adjustment to the thresholds will reflect in a rapid
change in the resulting image. Since the thresholds
in opacity peeling are set on accumulated opacity, it
is more capable in peeling opaque materials than
translucent boundaries, which are of little opacity.
On the other hand, since the thresholds in gradient
peeling are set on accumulated gradients, gradient
peeling is sensitive to the changes of opacity even if
that is translucent, which is usually happen in the
boundaries of soft tissues and thin structures.
Figure 3: The exterior of
the nucleon is removed.
Figure 4: The interior of
the nucleon is removed.
Figure 5: 1D transfer
function.
Figure 6: 1D transfer
function with
importance.
IMPORTANCE-DRIVEN VOLUME RENDERING AND GRADIENT PEELING
213
Figure 7: 1D transfer
function.
Figure 8: 1D transfer
function with
importance.
Figure 9: The first layer by
opacity peeling with
importance.
Figure 10: The second
layer by opacity peeling
with importance.
Figure 11: The first layer
by gradient peeling with
importance.
Figure 12: The second
layer by gradient peeling
with importance.
5 CONCLUSIONS
In this paper, we presented the importance-driven
techniques and its application in volume rendering.
We also proposed the gradient peeling with
importance. The importance-driven volume
rendering and gradient peeling techniques provide
useful tools to reveal inner structures and peel off
translucent material and thin structures. The
importance of clusters is assigned interactively and
composited into the opacity of voxels in the GPU
volume ray-casting process. With this semi-
automatic approach, users can choose the clusters of
interest to visualize and peel off surface layers of the
material.
The work presented in this paper exploits the
clustering technique for volume classification in
multidimensional space. Statistic properties can be
taken into account to improve the understanding of
volume datasets. The gradient peeling technique in
this paper focuses only on heterogeneous regions.
This method is flexible and can be extended to other
properties of volume datasets.
ACKNOWLEDGEMENTS
The work presented in this paper was supported by
National Natural Science Foundation of China
(Grant No.60803108, No.30700165).
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