A Smooth Transition
Guillaume Gilet, Jean-Michel Dischler
Laboratoire des Sciences de l’Images, de l’Informatique et de la T
e Louis Pasteur, Bd Sebastien Brant, Illkirch, France
Luc Soler
Institut de Recherche contre le cancer de l’appareil digestif, 1 Place de l’hopital, Strasbourg, France
Volume Rendering, Point-Based Rendering, Raycasting.
Splatting-based methods are well suited to render large hierarchical structured or unstructured point-based
volumetric datasets. However, as for most object-order volume rendering methods, one major problem still
remains the processing of huge amounts of elements usually necessary to represent highly detailed densely
sampled datasets, which can lead to poor performances. Resampling into 3D textures to apply hardware-based
raycasting is a common way of improving framerate in such cases but often with a certain precision loss related
to limited texture memory. Switching between these two rendering techniques is interesting in order to keep
the advantages of both and has thus been proposed before, but not in a smooth and hierarchical manner. In this
paper, we show that for most point-based volumetric datasets, some parts of the model can be rendered more
efficiently with a texture-based method, whereas other parts can be rendered as usual using splatting. We ad-
dress the issue of providing a smooth hierarchical transition between the two methods using a data-dependent
approach based on a per-pixel ray-driven rendering scheme. In practice, our transition scheme allows users
a good control of the performance/quality trade-off. Through a comparison with standard hierarchical EWA
splatting, we show that our smooth transition can lead to an improvement of framerate without introducing
visual inconsistencies or artifacts.
Volume rendering is a useful technique for the effi-
cient visualization of volumetric datasets. Whether
these datasets result from simulations, from measure-
ments of some physical processes or from modern
3D scanning devices, they are very often expressed
as irregularly sampled point clouds. The most nat-
ural method to visualize these point-based datasets
is splatting, first introduced by Westover (Westover,
1989). The splatting process reconstructs a continu-
ous field from the sampled scalar field using 3D re-
construction kernels associated with each scalar value
and is therefore well suited for direct rendering of
large unstructured point-based datasets. However,
like all object order algorithms, such methods are
often bound by the inherent point complexity thus
showing poor performance for highly detailed and
very densely sampled datasets. Resampling such
datasets into 3D textures in order to use a hardware-
accelerated raycasting scheme is a common method
for real-time visualization. Whereas such a texture-
based scheme offers an efficient interactive visual-
ization tool, its usefulness can be hampered by sev-
eral constraints, such as GPU texture memory limita-
tion. It is therefore often impractical to use a texture-
based volume visualization tool for large point-based
Since each method has its strengths and draw-
backs, it seems to be an interesting idea to devise a
hybrid scheme using an appropriate combination of
these methods, in order to increase performance. Sev-
eral methods have been introduced to allow the vi-
sualization of large unstructured datasets using such
a hybrid scheme. However, whereas these methods
achieved efficient results, few relied on an effective
combination scheme of both rendering principles with
easy and efficient user control of visual results when
switching between both.
In this paper, we introduce a new method based
on an efficient combination of the EWA (Elliptical
Weighted Average) volume splatting framework and
hardware-accelerated raycasting. Basically, we pro-
pose a scheme aiming at a smooth transition be-
Gilet G., Dischler J. and Soler L. (2008).
In Proceedings of the Third International Conference on Computer Graphics Theory and Applications, pages 217-222
DOI: 10.5220/0001096002170222
tween a flexible point-based method and texture-
based hardware-accelerated methods. The main idea
is to render each part of a dataset using an efficient
combination of point/texture-based methods. Con-
trary to other transition methods, we do not propose
a binary choice between the two methods, but rather
an efficient combination of these methods, thus max-
imizing rendering performance. Our algorithm also
takes full advantage of the latest hardware accelera-
tions. In practice, our method improves the framer-
ate of splatting without introducing visual inconsis-
The remainder of this paper is structured as fol-
lows. Section 2 discusses some related works. Next,
we present our combination scheme and simplifica-
tion criteria. Finally, before concluding, results and
an analysis of our method are discussed in section 4.
Direct volume rendering methods have in common an
approximative evaluation of the volume rendering in-
tegral for each screen pixel, i.e. the integration of at-
tenuated colors and extinction coefficients along each
corresponding viewing ray. Color and extinction co-
efficients are computed by a classification step. Clas-
sification is achieved by means of a transfer function
which maps scalar values s = s(x) of the dataset to
colors c(s) and extinction coefficients τ(s). By as-
suming that the viewing ray x(λ) is parameterized by
λ the distance to the viewpoint, the classical volume
rendering integral can be written as:
I =
c(s(x (λ)))exp
with D being the maximum distance.
The continuous data field is usually represented by a
discrete function with values at vertices along with
an interpolation scheme, based on a reconstruction
kernel. This reconstruction kernel has a great impact
on image quality and signal reconstruction accuracy.
Two main approaches can be distinguished for direct
volume rendering : Forward projection methods and
backward projection methods. Whereas in forward
projection methods rays are cast from the image into
the volume ((Roettger et al., 2003)), backward projec-
tion methods map volume elements onto the screen
((Zwicker et al., 2001),(Cohen, 2006)). An overview
of recent volume rendering methods can be found in
(Kaufman and Mueller, 2005). Several of these algo-
rithms have now been successfully modified to take
benefits from latest graphics hardware ((Ma et al.,
2003) presents a brief overview of several hardware-
accelerated volume rendering methods).
Several volume splatting algorithms focus on im-
proving the image quality, such as (Mueller et al.,
1999), (Neophytou et al., 2006) and (Neophytou
and Mueller, 2003). Xue and Crawfis (Xue and
Crawfis, 2003) compared several hardware accelera-
tions for splatting algorithms, showing the efficiency
of shader-based methods for large datasets render-
ing. The popular EWA (Elliptical Weighted Average)
Splatting ((Zwicker et al., 2001), (Chen et al., 2004))
provides an efficient framework for interactive splat
based volume visualization. However, in order to ob-
tain correct and high quality images with splatting
methods, splats must often be depth-sorted, resulting
for most highly complex and densely sampled models
in a severe impact on performance. There are several
techniques to improve splatting performances by re-
ducing the number of splats to be projected ((Mueller
et al., 1999),(Laur and Hanrahan, 1991)), but with
some limitations.
To overcome issues of splatting methods when
dealing with densely sampled datasets and issues of
raycasting methods when rendering large unstruc-
tured datasets, hybrid methods are a natural solution
((Ma et al., 2002)). In a similar manner, Wilson et
al. introduced in (Wilson et al., 2002) a hardware-
assisted hybrid scheme using semi-opaque splatting
in conjunction with a texture-based method using a
uniformly subsampled version of the dataset. Re-
cently, Kaehler proposed in (Ralf Kaehler and Hege,
2007) an efficient hierarchical hybrid representation
for the storage and rendering of large unstructured
These methods basically propose a choice be-
tween using a point-based or a texture-based method
or both to render a subpart of a dataset. In contrast,
we propose in this paper a hybrid method based on an
effective combination of these techniques through the
use of a smooth transition between both.
This section describes our new hybrid rendering
scheme. The idea is to render the volumetric dataset
with a hybrid splatting/raycasting method.
As highlighted in (Meissner et al., 2000), we have
on the one hand a splatting method efficient to render
sparse structures and on the other hand a hardware-
based raycasting suited to render densely sampled
GRAPP 2008 - International Conference on Computer Graphics Theory and Applications
datasets. Therefore, the motivation of our method is
to obtain a framework allowing for the rendering of
a dataset using a combination of both methods, thus
attaining higher performance. In order to achieve an
Figure 1: Principle of the method. An element is projected
onto the screen plane, yielding a Gaussian 2D footprint. De-
tails are added to each pixel with ray marching inside the
corresponding 3D texture.
efficient combination of both object-order and image-
based methods, we need a uniform representation of
these techniques. To this end, we choose to define our
new hybrid technique as composed of two steps :
A splatting step, corresponding to the correct pro-
jection of 3D kernels into the screen, yielding 2D
A refinement step, i.e. the computation of a color
value for each pixel of the corresponding foot-
As one can see, both classical rendering schemes can
be straightforwardly mapped to this representation,
i.e. classical raycasting methods being the projection
of a single 3D kernel bounding the dataset and de-
tailed through a raycasting algorithm, classical splat-
ting methods being the projection of a collection of
3D kernels with a unique value for each kernel.
Figure 1 shows the principle of our method. The
key idea is to render the dataset as a collection of
overlapping 3D detailed kernels. These kernels can
be obtained by resampling the dataset at a given rate
and assigning a 3D texture and an interpolation kernel
to each sample point. The resampling rate of a dataset
and the resolution of the corresponding 3D texture are
key control-features of our hybrid scheme and must
be defined for each region (contiguous subpart) of the
dataset. To this end, we provide a hierarchical repre-
sentation of the input volumetric dataset, where each
node is a coarse representation of a region and is asso-
ciated with a 3D texture containing the necessary in-
formation for the rendering of the associated region.
As shown in figure 2, a subpart of this hierarchical
representation is selected at run time and rendered us-
ing a GPU-accelerated splatting scheme. Details are
then added to each footprint using raycasting princi-
ples with the 3D texture associated to the node. The
composition of each detailed footprint yields the final
We explain in the following subsection the actual
rendering method of a set of overlapping detailed 3D
kernels. Details concerning the hierarchical represen-
tation are given in subsection 3.2.
Figure 2: Hierarchical representation. Each node repre-
sents its child nodes and is associated with a 3D texture.
3.1 Hybrid Rendering
As described before, the integration of raycasting
principles into the splatting method must be carefully
analyzed in order to ensure consistent results with an
improvement of performance.
At each node of our hierarchical structure is
attached a truncated spherical interpolation function
(a radially symmetric Gaussian in our case). For each
fragment f
of a footprint F
at screen coordinates
x, y resulting from the projection of a Gaussian
kernel G
, a ray is cast through the fragment into the
volume. We focus on the intersection of this ray with
the kernel G
. Since G
is in our implementation a
truncated radially symmetric Gaussian, its bounding
box B
can be seen as a sphere centered at the original
sample point. The ray originating at fragment f
intersects the bounding sphere in two points p
(with p
= p
in extreme cases).
We then use a raycasting scheme into the adequate
3D texture stored in the graphics hardware to enhance
the appearance of f
by adding details along the
segment p
. Through a careful analysis of the
3D texture resolution and the extent of the truncated
kernel G
, we can derive an adequate sampling step
along the segment, and thus divide the segment p
into n equal sections of length l.
Each of these segments is associated with a
color and opacity value using a lookup into a 2D
table computed through a classical pre-integrated
classification scheme (Engel et al., 2001). Due
to the specificity of our scheme, segment lengths
may vary along with the size of the kernel. To be
able to rely on the 2D table lookup and still ensure
correct results, we use the approximation scheme
proposed by (Roettger et al., 2000) and weight the re-
sult of the 2D lookup with the length l of the segment.
3.2 Hierarchical Representation
Figure 3: Creation process of our hybrid representation.
Groups of points meeting the criterion are represented by
a single kernel. The information of the original region are
stored into the GPU texture memory.
We choose to simplify the volumetric dataset using
an octree as in (Laur and Hanrahan, 1991). The in-
put volumetric dataset is divided into a collection of
hierarchical nodes, each node representing a subpart
of the volumetric dataset. A feature-sensitive top-
down approach is applied during the construction of
the point hierarchy.
Our representation is based on a division crite-
rion E. This criterion represents relevant features
and properties of a subpart of the dataset. This cri-
terion is used to determine the parameters of our hy-
brid method, such as the sampling rate of the dataset,
the resolution of the 3D textures, thus orienting our
rendering scheme toward splatting or raycasting for
each subpart of a dataset. We propose in this paper
two different criteria described in sections 3.2.1 and
3.2.2. Each region approximated by a single node (i.e.
meeting the criterion requirement) is stored into a 3D
texture of equivalent resolution. This simplification
scheme yields a simplified representation of the vol-
ume coherent with our hybrid rendering solution.
3.2.1 Visual Variation Criterion
As highlighted in (Meissner et al., 2000), splatting
and raycasting methods produce slightly different vi-
sual results. This difference is the main cause of pop-
ping artifacts in most hybrid methods. The aim of our
method being a smooth artifact-less transition, these
visual differences should be minimized. Intuitively,
we want to resample and orient toward a raycasting
solution the regions which will induce low visual vari-
ations. In order to detect such regions, we need to
define a qualitative error metric measuring the visual
variation between the two schemes. This variation v
is expressed for a viewing ray r traversing the vol-
ume. We choose to define this variation as the dis-
tance in color space between two colors computed
along the viewing ray r by evaluating the volume ren-
dering integral (1) using the two different approxima-
tion schemes (splatting and raycasting):
= |C
| (2)
This visual variation reflects the visual differences be-
tween the splatting and raycasting solution for a sin-
gle viewing ray and can be considered as a measure-
ment of visual artifacts.
We choose to express the visual variation V over
a complete contiguous region as the average value of
the squared variation along all possible viewing rays
traversing this region :
V =
∂Ω (3)
with the sphere of all possible view directions.
We propose to approximate this integral by using a
discrete sum evaluated over a small subset N of view-
ing rays determined by using a stochastic distribution
of viewing rays across a region.
Although the precomputation of the transfer table
used by the ray casting scheme in section 3.1 can be
easily computed, thus allowing the transfer function
to be edited on the fly, our variation measurement
scheme is more complex. As of this moment, it is
not possible to modify the transfer function and keep
an interactive rendering, even for a small value of N.
For some applications however, it can be desirable to
edit the transfer function on the fly. To this end, we
provide another division criterion, thus allowing an
interactive simplification of the dataset.
3.2.2 Data Variance Criterion
The idea is to use data variance inside a region as a
decision criterion for our simplification. Intuitively,
regions of a dataset with high variance will introduce
more visual differences. It is then compared with a
user defined threshold, defined empirically as of now.
Whereas this criterion is plainly less efficient than the
visual variation measurement criterion, it allows for
an interactive simplification. It is to be noted that this
variance analysis can be performed with or without
taking the transfer function into account. Nonethe-
less, this criterion gives rather good and often suffi-
cient results for most datasets.
Figure 4: Tree Model. Left : Traditional splatting. 8M
splats - 2.2 fps. Middle : Our hybrid representation. Right :
Hybrid method with detailed textures. 46k splats - 8.3 fps.
GRAPP 2008 - International Conference on Computer Graphics Theory and Applications
This section deals with a study of visual quality and
performance of our method. We compare our hybrid
rendering obtained with different parameters with the
EWA splatting rendering of the same volumetric data.
We show results on both structured and unstructured
datasets. Timings were collected on an Intel Core 2
Duo Processor at 2.4Ghz and a GeForce 8800 graph-
ics card using a viewport resolution of 512 × 512. As
can be seen on figure 4 (right), our hybrid method al-
lows the rendering of datasets with a low splats count,
yet maintaining the same visual result as with tra-
ditional EWA splatting (left). This induces an in-
crease in performance over traditional splatting with-
out quality loss. Our visual variation criterion can
lead for most models to an efficient reduction (50-
80%) of the point count necessary to render a dataset
with almost the same visual quality. Figure 5 shows
the impact of different user-defined quality tresholds
on quality and framerate of our method. Naturally,
as the treshold grows higher, performance increases
while quality is degraded in some areas. On figure
6, we show the differences of the two criteria respec-
tively described in sections 3.2.1 and 3.2.2. While
most features are preserved, areas with low variation
(across the neck of the model) are degraded with the
variance data criterion but are accurately represented
using the visual difference criterion. Figure 7 shows
the same model rendered with and without texture de-
tails. Our method also induces an increase of framer-
ate for unstructured datasets, as shown in figure 8.
Figure 5: A 512
head dataset. Left : 2M splats - ε = 2%
- 2.9 fps; Middle : 386k splats - ε = 5% - 4.8 fps; Right :
250k splats - ε = 10% - 8.8 fps.
We presented in this paper a hardware-accelerated
hybrid volume rendering scheme. Our method pro-
vides a smooth transition between texture-based and
point-based techniques. Through an adequate divi-
sion of the dataset, each region of the dataset can be
rendered with an efficient combination of both meth-
ods. Furthermore, we provided efficient division cri-
teria for the analysis and simplification of a dataset
according to user-defined parameters controlling the
quality/speed trade-off. This technique leads to a
Figure 6: 512
Head Model rendered with 530k splats us-
ing the two criteria. Left : Visual Variation criterion. Right
: Variance data criterion.
smooth transition between two traditional principles
and an increase in performance over traditional splat-
ting methods for high quality rendering of point-based
volumetric datasets.
Several issues can be improved. In the future, we
want to increase the efficiency of our framework. First
of all, the use of a different hierarchical structure
(such as RBF-based representation) can allow for a
representation more fitting to data, thus allowing for
both performances and visual quality increase. An-
other improvement is to derive the idea of adaptive
hardware accelerated EWA splatting ((Chen et al.,
2004)) to further enhance framerate. However, such
an improvement is not trivially devised in our case.
An adaptive scheme can be used to affect, not only the
quality of the reconstruction kernel, but also the sam-
pling step of the raycasting scheme. Furthermore, an
adaptive criterion should be devised while taking into
account our visual variation metric and several impor-
tance factors, such as the size or visibility of a region
(as a measurement of visual importance of a region on
the screen), as to enhance the splats count reduction
without introducing visual artifacts. As it is, visual
variations over a region are bound by our metric, but
these variations are accumulated onto the screen by
different locally variation-bound regions. To this end,
a thorough analysis of our metric can be proposed to
lead to a better adjustment of parameters and provide
an approximation of the total visual variation on the
final resulting image.
Figure 7: A 512
medical dataset. Left :Our hybrid method.
2M splats at 2.1 fps. Right : Without texture details. 2M
splats at 12.3 fps.
Figure 8: An unstructured fluid dataset obtained through
simulation MAC. Left : splatting method - 1.5M splats - 11
fps. Right : our method - 250k splats - 16 fps.
The medical dataset was gratefully provided by IR-
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