Vis Comput
DOI 10.1007/s00371-010-0541-z
O R I G I NA L A RT I C L E
Image-based rendering of intersecting surfaces for dynamic
comparative visualization
Stef Busking · Charl P. Botha · Luca Ferrarini ·
Julien Milles · Frits H. Post
© Springer-Verlag 2010
Abstract Nested or intersecting surfaces are proven tech-
niques for visualizing shape differences between static 3D
objects (Weigle and Taylor II, IEEE Visualization, Proceed-
ings, pp. 503–510, 2005). In this paper we present an image-
based formulation for these techniques that extends their use
to dynamic scenarios, in which surfaces can be manipulated
or even deformed interactively. The formulation is based on
our new layered rendering pipeline, a generic image-based
approach for rendering nested surfaces based on depth peel-
ing and deferred shading.
We use layered rendering to enhance the intersecting sur-
faces visualization. In addition to enabling interactive per-
formance, our enhancements address several limitations of
the original technique. Contours remove ambiguity regard-
Electronic supplementary material The online version of this article
(doi:10.1007/s00371-010-0541-z) contains supplementary material,
which is available to authorized users.
S. Busking (

) · C.P. Botha · F.H. Post
Data Visualization Group, Delft University of Technology, Delft,
the Netherlands
e-mail: s.busking@tudelft.nl
C.P. Botha
e-mail: c.p.botha@tudelft.nl
F.H. Post
e-mail: f.h.post@tudelft.nl
C.P. Botha · L. Ferrarini · J. Milles
Division of Image Processing (LKEB), Department of Radiology,
Leiden University Medical Center, Leiden, the Netherlands
C.P. Botha
e-mail: c.p.botha@lumc.nl
L. Ferrarini
e-mail: l.ferrarini@lumc.nl
J. Milles
e-mail: j.r.milles@lumc.nl
ing the shape of intersections. Local distances between the
surfaces can be visualized at any point using either depth
fogging or distance fields: Depth fogging is used as a cue
for the distance between two surfaces in the viewing direc-
tion, whereas closest-point distance measures are visualized
interactively by evaluating one surface’s distance field on the
other surface. Furthermore, we use these measures to define
a three-way surface segmentation, which visualizes regions
of growth, shrinkage, and no change of a test surface com-
pared with a reference surface.
Finally, we demonstrate an application of our technique
in the visualization of statistical shape models. We evaluate
our technique based on feedback provided by medical image
analysis researchers, who are experts in working with such
models.
Keywords Comparative visualization · Image-based
rendering · Surface comparison · Nested surfaces
1 Introduction
In this paper, we examine one class of solutions to the prob-
lem of comparing the shapes of 3D surfaces. Comparison
of data plays an important role in many areas of scientific
research. Visualization can be useful to support compara-
tive data analysis. The most common approach to compar-
ative visualization of surfaces is a simple side-by-side dis-
play (with similar viewing conditions) of the two surfaces
under consideration. Such an approach relies on memory to
compare details of the surfaces, and local distances between
surfaces are hard to estimate. We identify the following re-
quirements for an effective comparative visualization:
– Differences should be made explicit, alerting the user to
the presence and nature of all differences present.

S. Busking et al.
– Visualization of differences should be local, showing not
only the presence but also the precise location and ex-
tent of all differences. In medical applications, for in-
stance, local information is required for understanding
differences between patients or studying changes in spe-
cific biological structures over time.
– The visualization should be able to show relevant differ-
ences and hide irrelevant ones.
As an example of what is meant by relevance, consider
the alignment of surfaces prior to comparison. Inaccuracies
in the registration process can result in misalignment of the
resulting surfaces. This misalignment, however, is usually
not relevant to the researcher’s problem. An ideal visualiza-
tion could automatically distinguish between relevant and ir-
relevant differences, and show only the former. However, the
notion of relevance is a highly application-dependent prop-
erty, which can generally only be decided by the researcher.
The use of user-feedback and interactivity is therefore essen-
tial to deal with this issue. Various applications can benefit
from interactive visualization:
– User interaction or guidance in the registration process.
– Local registration for exploring differences between spe-
cific parts of the objects under consideration, ignoring
more global differences.
– Analysis and comparison of dynamic or deformable sur-
faces.
In this paper we present a visualization for the com-
parison of 3D surfaces. Our visualization is based on the
proven intersecting surfaces technique, first introduced and
evaluated by Weigle et al. [1]. Our contribution consists of
three aspects: We present an alternative, image-based im-
plementation of this technique, which enables interactive
performance even when manipulating alignment or dealing
with dynamic objects. Furthermore, we present enhance-
ments designed to address specific limitations of the ex-
isting technique. Finally, we present a case study, evalu-
ating the suitability of intersecting surfaces and our en-
hancements for the visualization of statistical shape mod-
els [2].
Figure 1 shows the comparison of two segmentations of
the same brain ventricle MRI scan using our technique. Such
a visualization may give important information on the char-
acteristics of a new segmentation algorithm. The yellow sur-
face represents the baseline segmentation, while the blue
surface shows a different segmentation. This means blue ar-
eas and yellow glyphs represent areas not covered by the
new segmentation, while yellow areas and blue glyphs rep-
resent areas covered by this segmentation which are not in
the baseline segmentation. Differences are remarkably sym-
metric in overall shape, but the lack of coloring due to fog
indicates distances are small and contain little local varia-
tion. This may indicate these could be due to variations in
Fig. 1 Comparative visualizations of two partial brain ventricle sur-
faces segmented from MRI data. The top figures show the separate
surfaces, illustrating the difficulty to locate differences without an in-
tersecting surfaces approach. The basic intersecting surfaces visualiza-
tion [1] (bottom left) clearly shows some symmetry in the differences.
Our visualization adds intersection contours and thresholding to sup-
press smaller differences. The resulting 3-way visualization (bottom
right) reveals an area of considerable change
the segmentation process. In Fig. 1(d) we applied a thresh-
old at a distance of 1 mm, which reveals an area of con-
siderable difference in the shape of the segmented ventri-
cles.
Our implementation of the techniques described in this
paper is available as part of the open-source NQVTK library
(http://nqvtk.googlecode.com/).
2 Related work
In this section we first define the position of our technique
in the comparative visualization process. We use this as a
framework to present and discuss work related to our tech-
nique, including the intersecting surfaces visualizations by
Weigle et al., on which our approach is based. As a mean-
ingful discussion of work related to our implementation of
these techniques depends on the details thereof, such work
is discussed in Sect. 4.1.

Image-based rendering of intersecting surfaces for dynamic comparative visualization
2.1 Domain matching and comparison
Comparison can occur at any stage of the standard visual-
ization pipeline [3]. However, the process always requires
data sets to be aligned before differences can be determined
and/or visualized. Many solutions exist for this domain
matching step, the details of which are mostly application-
dependent. In part this is because the processes of align-
ing data and extracting differences cannot always be cleanly
separated. For instance, a body of work exists which applies
non-rigid registration to volume data [4, 5] or to features
extracted from it [6]. The deformation field resulting from
this process is then analyzed to determine differences. This
deformation field will typically also contain irrelevant dif-
ferences due to imperfect alignment, such as tissue defor-
mations caused by patient movement rather than by patho-
logical processes.
Our technique can be applied after domain matching in
order to directly visualize the remaining differences between
two surfaces. This enables such differences to be studied in
detail, but also gives insight into the quality of the matching
itself. We aim to be independent of the choice of domain-
matching technique. We only assume that a good (possibly
application-specific) solution for this stage is available: i.e.,
one that does not remove any of the relevant differences and
preferably leaves a minimum of irrelevant differences. As
perfect matching (i.e., separation of relevant and irrelevant
differences) is often impossible, our technique should pro-
vide enough information to assess the relevance of the dif-
ferences.
As stated in Sect. 1, our visualization of such differences
should be explicit and local. This means a suitable technique
should determine and extract localized differences after the
matching step rather than simply visualizing the aligned data
sets. These differences should then be mapped to clear ele-
ments in the resulting visualization. Many existing compar-
ison techniques are implicit in that they skip this extraction
step, which means the act of comparison is left to the user.
2.2 Comparative visualization of 3D surfaces
Numerous measures have been proposed that can be used to
express the difference (or similarity) in shape between two
surfaces; most notably in the area of image retrieval [7–9]
and shape retrieval [10, 11]. However, most of these mea-
sures, such as the commonly used Hausdorff distance, only
express similarity at a global level.
The local visualization of differences can yield important
insights which might not be obvious from global measure-
ments. However, only a few techniques have been presented
for comparing shape locally [12, 13]. Local distance mea-
sures often require establishing some form of correspon-
dence between the surfaces (i.e., domain matching). A com-
monly used method for visualizing local distance measures
is to display these on one of the two surfaces using an appro-
priate color map [12, 14, 15]. This has the disadvantage that
only one of the surfaces is shown; the shape of the second
surface is not obvious.
A way to overcome this is to make one or both surfaces
transparent and overlay them in the visualization. Such a
nested surfaces approach (used by, e.g., Tory et al. [16])
shows all context information. Similar approaches have been
proposed in uncertainty visualization (see, e.g., Johnson and
Sanderson [17]). However, in these visualizations the iden-
tification of differences is left to the user. This is compli-
cated by the fact that overlaying multiple transparent and
potentially intersecting surfaces results in an image which is
not always clear to a user. In particular, understanding the
shapes of transparent surfaces and classifying surfaces as
being either in front or behind other surfaces can be diffi-
cult perceptual tasks.
Attempts have been made to resolve these issues. Tex-
tures are commonly applied to improve shape perception of
transparent surfaces [18]. Interrante et al. [19] proposed us-
ing stroke textures based on the directions of principal cur-
vatures. Bair and House [20] investigated the use of several
types of grid textures, and performed user studies on their
effects on perception of surface shape. Bruckner et al. [21,
22] approached similar problems in volume rendering us-
ing illustrative techniques. They proposed using interactive
control over a special opacity function that allows a user to
focus on specific objects within a volume while also keeping
contextual surfaces in view.
Weigle et al. [1, 23] proposed the use of constructive
solid geometry (CSG) operations to solve the perceptual
problem of inside/outside classification. Their intersecting
surfaces technique, described in detail in the next section,
forms the basis for the visualization presented in this paper.
User studies performed by Weigle et al. have shown these
visualizations to be effective for the comparison and under-
standing of surface shapes.
2.3 Base visualization
Because of its proven effectiveness, we use the intersecting
surfaces technique by Weigle et al. as the basis for our vi-
sualization. The technique uses CSG operations to extract
differences between two surfaces: The intersection of the
closed objects formed by the surfaces represents the vol-
ume in common between both objects, and is rendered as
an opaque object. The remaining parts of the two surfaces
represent differences, and are rendered transparently in or-
der to show the intersection behind them. This solves the
inside/outside classification problem, as parts of each sur-
face inside the other are always opaque and outside parts are
always transparent.
As suggested by Interrante [19], Weigle’s visualization
includes curvature-aligned glyphs on the transparent parts

S. Busking et al.
of the surfaces to better illustrate surface shape. In order to
visualize local distances between the two surfaces, Weigle’s
method relies on shadows cast by these glyphs. As an al-
ternative to shadows, point-correspondence glyphs can be
used [23]. These are line segments which connect corre-
sponding points on the two objects that are being compared.
In their extensive user studies, Weigle et al. compared
their visualization to a number of previously existing tech-
niques [1, 23]. The studies show that the intersecting sur-
face visualizations, both with shadows and with point-
correspondence glyphs, are more effective than the exist-
ing techniques. The contribution of this paper includes im-
provements which address specific limitations of Weigle’s
technique.
3 Enhanced intersecting surfaces
In this section we present our enhanced visualization for
the comparison of 3D surfaces. We first identify and dis-
cuss limitations of the existing technique, and use these to
introduce and motivate our enhancements: an image-based
implementation for increased flexibility and interactive per-
formance, dynamic intersection contours, integration of dis-
tance cues and suppression of irrelevant differences.
3.1 Limitations of the original visualization
In their work, Weigle et al. identified a number of shortcom-
ings of their intersecting surfaces implementation. We sum-
marize these issues below, and add two more issues (5 and 6)
found when applying our requirements, described in Sect. 1:
1. Folded surfaces and other forms of self-occlusion can
hide differences. Weigle proposed interactive control of
the camera as a possible solution, which is also possi-
ble in our technique. However, similar issues occur when
glyphs are placed near intersections, which may cause
confusion regarding the shape of those intersections (see
Fig. 2).
2. Due to their fixed spacing, surface glyphs can only illus-
trate shape at a fixed scale. Because of this, small-scale
details can be missed. Weigle proposed making glyph
spacing adaptive to local shape characteristics. How-
ever, we found that the sparse nature of the glyphs also
means that the distance between surfaces can only be
estimated around glyph/shadow pairs, or around point-
correspondence glyphs.
3. The visualizations are not useful when objects are too dif-
ferent, or are not aligned properly during domain match-
ing. In this case, Weigle recommends that explicit corre-
spondence information be included in the visualization.
4. The approach is not easily extended to more than two
surfaces.
Fig. 2 Without contours, intersections between the blue surface and
the yellow surface are not always obvious. Marking all intersections
differentiates them from occlusions and highlights smaller features,
which might otherwise be hidden. The small triangular artifacts are
side-effects of our shadow mapping implementation and not a result of
our technique
5. In the base visualization, differences are shown regard-
less of their relevance, with no way to distinguish be-
tween relevant and irrelevant differences.
6. Importantly, Weigle et al. did not apply their techniques
to the comparison of dynamic surfaces and the origi-
nal implementation therefore does not support scenarios
where the objects are not static in shape or in their rela-
tive positions and orientations.
3.2 Enhancements
While simultaneous comparison of more than two surfaces
is considered outside the scope of this paper, we present en-
hancements to the base visualization that address each of
the remaining issues in the list above. The following sec-
tions discuss the motivation for and design of these enhance-
ments. The details of their implementation can be found in
Sect. 4.
3.2.1 Image-based implementation
In this paper, we present an image-based implementation of
the intersecting surfaces visualization. Our implementation
provides interactive control of the viewpoint, suggested by
Weigle as a possible solution to the first issue. It also enables
the visualization to be applied to dynamically deforming

Image-based rendering of intersecting surfaces for dynamic comparative visualization
objects with interactive performance (issue 6), as the inter-
section is not computed geometrically. This in turn enables
new applications for the visualizations. For instance, occlu-
sion issues could also be solved by a dynamic peel-away
approach. Additionally, our technique could enable interac-
tive domain-matching tools, or interactive local alignment
of corresponding features. Such tools could help in deal-
ing with objects with significant global differences but local
similarities, such as described in issue 3. While we consider
such solutions in future work and do not discuss them further
in this paper, we do present an example of dynamic objects
in our case study (Sect. 5).
In Sect. 4.1 we present a generic rendering pipeline
on which we base our image-based implementation. This
pipeline enables combinations of CSG rendering and trans-
parent surfaces in a straightforward and extensible way,
which can also be useful in other visualization scenarios.
3.2.2 Intersection contours
As described in issue 1 and shown in Fig. 2, the complex ap-
pearance of the intersecting surfaces can sometimes cause
confusion. Specifically, occlusions might be interpreted as
intersections and vice versa (Fig. 2(a)). Glyph placement
can also cause confusion when this occurs on the intersec-
tion curve, potentially distorting the shape of intersections or
hiding them completely (Fig. 2(b)). If the intersections be-
tween the surfaces are complex, the visualization becomes
more cluttered. In this case, such issues are likely to become
problematic, as small but possibly relevant differences may
be missed.
Explicitly marking the intersection curves in the visual-
ization removes any ambiguity in these cases. Contouring is
a commonly used technique in illustrative rendering. Lines
can be drawn to emphasize important boundaries in a visu-
alization. While it may seem more natural to enhance oc-
clusions rather than intersections, such contours are view-
dependent and can therefore make the visualizations harder
to perceive. Furthermore, in our case the intersections be-
tween objects are actual features of interest, and contour-
ing them serves the dual purpose of highlighting these fea-
tures. Similarly, changing the color of the outer surface (and
glyphs) would solve problems as shown in Fig. 2(b). How-
ever, as color is used to identify surfaces, such a change
would complicate the visualization. Contours provide a so-
lution that works independently of the choice of surface col-
oring and texturing. The intersection curves of the surfaces
provide clear contours for the “difference” areas in the visu-
alization. They also enable clear distinction between inter-
section and occlusion.
3.2.3 Local distance cues
In addition to the well-known difficulties of illustrating the
shape of transparent surfaces, the second issue is caused by
Fig. 3 The choice of viewing direction and placement of glyphs may
hide important information about the size and shape of differences.
By including local distance feedback in the visualization (here using
red fog added between the surfaces), larger differences are made more
obvious. The bottom figure shows a simplified schematic cross section,
where adding fog would highlight the larger distance on the left
local distance information being visualized only sparsely in
the original intersecting surfaces technique. Such informa-
tion is important for understanding the shape and size of
differences, and can also help in understanding the shape
of the objects themselves.
In Weigle’s technique, the user has to rely on shadows
cast by glyphs in order to judge local distances between
the surfaces. However, on many complex surfaces it may
not be straightforward to match up glyphs with their shad-
ows. It may also be the case that there simply is no glyph
present in an area of interest. One example of problem-
atic shape is shown in Fig. 3. In this case, areas with in-
creased depth (a simplified example is shown in the cross
section, Fig. 3(c)) are not immediately obvious in the visu-
alization (Fig. 3(a)). When using glyphs, a smart placement
of these glyphs (and their shadows) might solve such prob-
lems. However, this could lead to an uneven distribution of
glyphs over the surface, which causes other perceptual is-
sues.
We integrate two forms of local distance cues to alert
the user to these areas in an intuitive way. Specifically, we
simulate fogging between the inner and outer surfaces as
a viewpoint-dependent distance cue and integrate closest-
point distance for viewpoint-independent feedback. These
enhancements also provide a way to visualize the shape of
the surfaces at any scale, albeit relative to each other.
In fogging, we add a third color between surfaces, the
amount of which is computed in terms of the distance be-

S. Busking et al.
Fig. 4 Distance fields can be used to color each surface by its distance
to the other, even when surfaces are moved relative to each other
tween these objects along the viewing direction and a user-
controllable density parameter. The effect is that the areas
of difference between the objects are highlighted more for
larger distances. As can be seen in Fig. 3(b), differences
in depth between surfaces can be seen clearly after fog is
added. Interactive manipulation of fog density can help a
user compare relative depths of these differences. This in-
teractivity also eliminates the problem that fog obscures the
shape of the inner surface, as the fog can simply be removed
or made less dense in order to examine surface shape after
differences have been identified.
As fogging is view-dependent, results may change when
the viewpoint is moved. We integrate closest-point distance
as a view-independent alternative (Fig. 4), and enable color-
ing of either surface based on this distance. Our implemen-
tation, described in Sect. 4.3.2, achieves interactive perfor-
mance even when objects are moved relative to each other,
meaning that this technique could also be used in an interac-
tive domain-matching solution such as described earlier.
3.2.4 Relevance filtering
Issue 5 originates directly from our requirements. If objects
differ in some areas and are identical in others, the intersect-
ing surfaces visualization clearly shows such differences. In
real-world data, however, noise and other inaccuracies are
often a concern, which can cause many small differences be-
tween objects. In intersecting surfaces, each of these will be
shown with similar visual impact as other differences, clut-
tering the resulting images and distracting users from those
other, possibly more interesting differences.
We use the distance measures introduced in the previous
section in order to allow users to suppress smaller differ-
ences in the visualization. We selected to filter based on size,
as this is a common criterion for considering the relevance
Fig. 5 Mapping distance to saturation of the surface colors reduces
the prominence of small differences, but causes perceptual issues due
to the blurry appearance
of differences. We experimented with mapping distance to
the saturation of the surface color (Fig. 5). This has the ef-
fect of both surfaces fading to gray as the distance between
them gets smaller. Small differences such as those caused
by noise will therefore also appear gray, rather than the sud-
den change of object color they cause in the original visual-
ization. Unfortunately, changing saturation over the surface
negatively affects the ability to perceive object shapes.
A simpler solution is thresholding the local distance mea-
sure. This way, we allow users to suppress differences that
are considered too small to be relevant. Essentially, this has
the effect of widening the intersection contours into areas of
insignificant differences. We render such areas in an opaque
neutral white color. The result, shown in Fig. 6 and Fig. 1, is
a less cluttered visualization where the user is less distracted
by small fluctuations between the surfaces. The threshold
value can be controlled interactively by the user, to con-
trol the distance from which differences are considered large
enough. This way, we allow different thresholds to be used
when examining different parts of an object, and also en-
able exploring distances interactively by moving the thresh-
old value.
One limitation of the current solution is that while in
white areas the objects are considered similar, the two ob-
jects are still rendered as separate surfaces. This effect can
be seen in the two bottom images in Fig. 6, where thresholds
on the inner surface show up through the holes representing
significant differences. Especially for higher threshold val-
ues, this can cause the already complex visualizations to be
harder to interpret. In future work we aim to address this
limitation by using techniques from illustrative rendering in
order to reduce the visual complexity of the thresholded ar-
eas.

Image-based rendering of intersecting surfaces for dynamic comparative visualization
Fig. 6 Using increasing thresholds to hide small differences
4 Implementation
In this section we discuss our image-based implementation
of the intersecting surfaces visualizations and of the en-
hancements described in the previous section.
While not the focus of this work, we implemented both
opacity-modulating glyph textures (as used by Weigle et
al. [1, 23]) and grid textures (see Bair et al. [20]) to help
illustrate the shape of transparent surfaces. The integration
of such techniques in the layered rendering pipeline (de-
scribed next) is considered straightforward. Similarly, our
implementation uses standard shadow mapping [24] to make
the opacity-modulating textures cast shadows on the inner
surface, as recommended by Weigle et al. [1, 23].
4.1 The layered rendering pipeline
We introduce the layered rendering pipeline (Fig. 7) as a
generic basis on which we build our image-based implemen-
tation of the intersecting surfaces technique. Layered ren-
dering combines depth peeling, deferred shading and CSG
in order to create an approach for surface rendering simi-
lar to ray casting, but at interactive rates. In the intersecting
surfaces visualization, this pipeline enables interactive per-
formance even when objects are deformed. It also facilitates
the addition of further enhancements which address limita-
tions of the original visualization.
As stated in our requirements, we would like to be able
to deal with objects of arbitrary complexity, and support ob-
jects which are dynamic or interactively positioned relative
to each other. This requirement means that a geometric ap-
proach to computing the CSG intersection, as used by Wei-
gle et al. [1], is infeasible due to the complexity of such a
computation. We therefore investigated possibilities for an
image-based approach.
While image-based CSG solutions exist [25, 26], the
layered rendering pipeline is an extension of depth peel-
ing [27–29]: All image-based CSG approaches require mul-
tiple passes over the geometry, each extracting separate lay-
ers of geometry distinguished by the number of surfaces
occluding them. Depth peeling, however, also ensures that
the surfaces are extracted (and rendered) in strict front-to-
back order, which is required in order to properly render any
transparent surfaces. We extend the pipeline with a stage in
which deferred shading [30, 31] is applied to each layer ex-
tracted from the geometry. Furthermore, we extend deferred
shading to allow propagation of information between layers.
Weigle [23] described an image-based inside/outside
classification approach based on depth peeling. Weigle’s al-
gorithm, however, is limited to two surfaces and is not a
full CSG algorithm; any fragment appearing deeper than
a fragment already labeled interior is also labeled interior.
This makes, for example, clipping the geometry resulting
from the CSG operation or rendering the intersection with
transparency difficult to achieve. Other combinations of
depth peeling and image-based CSG have been presented
by Guennebaud et al. [32], used to handle transparent ob-
jects in point-based rendering, and Nienhaus et al. [33], who
presented a method for illustrative rendering of CSG mod-
els. These combinations were designed specifically for their
applications, however, and are not easily extended.
The layered rendering pipeline takes inspiration from ray
casting. The ray-casting algorithm takes an image-order ap-
proach, where rays are cast from each image pixel. These
rays traverse the scene and intersect any objects within. Due
to this image-order approach, achieving a correct ordering
for compositing transparent surfaces is inherent in the algo-
rithm. Similarly, CSG operations are implemented easily by
simply keeping track of object intersections along a ray.
The design of the layered rendering pipeline is based
on several observations. Firstly, rendering an object using
traditional rasterization essentially provides the intersection
points of all rays cast from the image simultaneously for a
single layer of geometry. Secondly, the depth peeling algo-
rithm can be used “as is” to process all intersections in the
scene in front-to-back order.
The layered rendering pipeline, therefore (see Fig. 7),
consists of repeated execution of two stages in order to
process the layers in the scene. The scribe stage performs
depth peeling using a dual-depth buffer approach [28] and
stores information about the current layer which is required
for shading in an info-buffer. The information in this buffer
is created by updating the info-buffer from the previous
layer with information from the geometry of the current
layer. This way such information can be propagated through
the scene in a way similar to ray casting. The painter stage
then compares this information with that of the previous
layer(s) in order to create the image for this layer. Similarly

S. Busking et al.
Fig. 7 The layered rendering pipeline. The scribe stage uses depth
peeling to process the scene one depth layer at a time in front-to-back
order. It propagates information between layers and also outputs in-
formation about each layer to the painter stage, which creates the im-
age for that layer using a deferred shading approach. These images are
composited to form the final visualization
to deferred shading, the painter stage does not require the
scene geometry to be drawn, as all information required for
shading is present in the info-buffers. The resulting images
are composited using front-to-back blending to create the fi-
nal image.
The total number of layers could be very large, depending
on the depth complexity of the scene being rendered. How-
ever, because each subsequent layer affects at most the same
pixels as the previous layer, and because of the front-to-back
blending used, later layers may not noticeably influence the
final image. Therefore rendering can be terminated after ei-
ther a set number of layers is reached, or when the number
of pixels in a layer is below some (small) fraction of the total
image size. This number is determined using occlusion tests
available in modern hardware.
In the following, we refer to the info-buffer for layer li
as Bi . The data in Bi describes (for each pixel) properties
either of the corresponding layer li , or of the depth slab si ,
which is the volume between li and li+1. An important part
of Bi is the in/out mask, a bit mask which indicates for
each pixel and for each of the objects in the scene whether
si is inside or outside of the object. We assume all objects
are closed, non-self-intersecting surfaces, although our ap-
proach still works with objects that extend into infinity in the
viewing direction (e.g., landscape surfaces such as Fig. 6,
viewed from above). In the scribe stage, the bit correspond-
ing to the visible surface for each pixel is set to 1 if that sur-
face is front-facing, and to 0 if it is back-facing. Other bits
are left unchanged and are copied from Bi−1. The mask for
B0 needs to be initialized according to the camera’s position
w.r.t. the objects in the scene. However, it can generally be
assumed in our visualizations that the camera is positioned
outside of all objects.
The in/out mask provides a simple way to perform arbi-
trary CSG operations on the objects in the scene, as well
as clipping objects to arbitrary geometry. Additionally, it
solves a common problem in depth peeling regarding copla-
nar surfaces. In our implementation, the mask is stored in
one of the 8-bit RGBA channels of the info-buffer texture.
This means we can track up to 8 objects at a time, which
is more than sufficient for the purposes of the intersecting
surfaces visualization.
4.1.1 CSG rendering
The base visualization uses only the CSG intersection of ob-
jects. In future extensions, however, other CSG operations
could be useful as well. For example, such operations could
be used as part of area-of-interest selection in a focus + con-
text visualization.
CSG rendering is as simple as applying the Boolean-
valued CSG expression to the in/out masks for both Bi
and Bi−1 during the painter stage. Surfaces of the result of
the CSG operation are characterized by a change in the value
of this expression. Therefore, if the resulting value for some
pixels on a layer is different from the value on the previous
layer, that part of li is a surface of the object resulting from
the CSG operation, and can be rendered as such (see Fig. 8).
4.1.2 Clipping
One advantage of this approach is that it results in the CSG
surfaces on all depth layers rather than only a single layer.
For instance, the Goldfeather algorithm [25] only provides
the first depth layer of the CSG object. Similarly, Weigle’s
image-based classification technique only locates the first

Image-based rendering of intersecting surfaces for dynamic comparative visualization
Fig. 8 Layered rendering for the CSG intersection of two spheres.
In/out masks are shown for each depth slab for positions along the
arrow. Changes in CSG(Bi) correspond to surfaces of the CSG result
intersection surface along the viewing direction. Having cor-
rect CSG surfaces on all layers means it is easy to imple-
ment clipping techniques in the painter stage. These can be
used, for instance, to enable viewing of interior structures of
the CSG model. Furthermore, because we maintain an in/out
mask between layers, the objects in the scene can be clipped
against arbitrary geometry. Clipping against arbitrary closed
objects is done trivially during the painter stage by discard-
ing all fragments for which the bit corresponding to the clip-
ping object is set in the in/out mask (indicating they are part
of surfaces located inside this object).
4.1.3 Coplanarity
One important limitation of the depth-peeling algorithm is
that it does not deal well with coplanar, overlapping sur-
faces. As only depth information is used to distinguish be-
tween surfaces in peeling, in the case of coplanar overlap-
ping surfaces only one of the surfaces will be detected. In
addition to causing visual artifacts when surfaces are not
rendered, this will cause problems for a CSG implementa-
tion such as the one described above.
Our layered rendering approach offers an elegant solution
to the problem. The problem stems from the fact that nor-
mal depth peeling only allows fragments with a depth value
larger than the previous layer. In our coplanarity peeling al-
gorithm, identical depth values are also allowed, as long as
the in/out mask resulting from the previous layer indicates
we have not rendered these before. Our assumption that sur-
faces are not self-intersecting enables us to perform only
a single “greater or equal” test against the previous layer,
rather than testing for equality separately, thereby simplify-
ing the implementation.
Fig. 9 Using depth comparison to filter the contours: silhouettes are
removed while intersection contours remain
4.2 Intersection contours
Like the intersection objects themselves, intersection curves
can be computed geometrically. Such computations, how-
ever, are complicated, hard to generalize and unsuited to
interactive visualization. We use our layered rendering
pipeline to create an image-based derivation for these con-
tours.
In illustrative rendering, a common technique is to de-
rive object silhouettes and feature contours from discontinu-
ities in images containing depth values or surface normals
respectively [31]. Similarly, we use the info-buffer to record,
for each pixel, the identity of the object which contributed
that pixel for the current layer. During the painter stage, we
perform simple edge detection on this buffer by compar-
ing pixels to their immediate 4-connected neighbors. This
approach, however, leads to more than just the intersection
contours (see Fig. 9(a)).
In order to filter this set of contours, we also store the
depth values for each pixel in the layer. Our reasoning is as
follows: if two neighboring pixels are on opposite sides of
a true intersection contour, their depth values will be simi-
lar as well. While this assumption does not hold in general,
we benefit from the fact that in most comparison scenarios
objects are similar. If depth values on opposite sides of a de-
tected edge fall within an epsilon range of each other, the
edge is rendered in the image (Fig. 9(b)). The value of this
epsilon depends on the scale of objects in the scene and is
currently determined empirically on a per-application basis.
4.3 Integrating local distance information
As stated in Sect. 3.2.3, we integrated two types of local
distance cues. Their implementations again take advantage
of the layered rendering pipeline, and are described in the
next sections.
4.3.1 Fogging
When using ray casting to render fog, colors and opacities
are accumulated along the rays while they travel through

S. Busking et al.
fog volumes. Similarly, we determine the amount of fog be-
tween two surfaces as a function of the distance between
those surfaces. In our layered rendering pipeline, this means
we can simply compare the depth values for the current
layer li to those of the previous layer li−1 in the painter
stage, in order to determine the distance for each pixel.
Based on this distance, we compute the accumulated fog
opacity for the depth slab si−1 and then blend the fog over
the current layer. Distance can be mapped into opacity lin-
early; however, as multiple slabs may contribute to an area
of fog, an exponential mapping yields better results.
As in CSG rendering, a Boolean expression can be ap-
plied to the in/out mask (in Bi−1) in order to specify the
(combinations of) objects in which fogging should be ap-
plied. An alternative to fogging is distortion (e.g., defo-
cussing, blurring) of the layer image due to refraction or
translucent materials. To implement this, the layer should
be rendered normally, after which the resulting image can
be distorted in accordance with previous layers in order to
produce the desired effect.
4.3.2 Distance fields
As discussed in Sect. 2, many shape (dis)similarity measures
have been proposed in the literature. The values resulting
from these measures change whenever either object is ma-
nipulated by the user. Recomputing the measure for each
point on both surfaces may not be feasible in an interactive
system. We therefore propose a solution based on distance
fields.
A distance field is a sampling of a distance function,
which maps positions in 3D space into the distance of that
position to the surface. The simplest such function uses the
Euclidean distance metric between the position in space and
the position of the closest point on the surface. In the case of
a closed surface, such a distance function could be signed,
i.e., the sign of the distance could indicate whether a point
is inside or outside of the object. Although creating such
fields is computationally expensive, they only need to be
computed once per object.
We use the Closest Point Transform algorithm by Mauch
[34] to precompute (signed) distance fields for our surfaces.
These distance fields are made available during rendering
as 3D textures. When objects are rendered during the scribe
stage of the pipeline, we sample the distance fields in order
to obtain distances between the objects. To accomplish this,
3D locations corresponding to each surface pixel need to be
transformed to the local coordinate frame of the other object,
after which the corresponding 3D texture can be sampled.
This effectively results in the distances of each point to the
closest point on the other object. Additionally, objects can
easily be manipulated in this approach; the corresponding
transformations simply need to be taken into account when
determining lookup locations in the distance fields.
Although this technique technically does not require the
use of the info-buffer, we still benefit from the basic depth
peeling and deferred shading options inherent in the lay-
ered rendering formulation, as well as allowing the visual-
ization of the distances to be handled separately from their
measurement. In our current implementation, the distance
fields only work for static surfaces. In the case where one of
the surfaces is dynamic, the distance field of the static sur-
face can still be used to display the distance on the dynamic
surface. In recent literature, GPU-accelerated methods have
been presented [35] which could enable interactive perfor-
mance in the fully dynamic case. Fogging works for static
and dynamic surfaces, and combinations thereof.
4.4 Relevance
Implementing the relevance-thresholding technique in our
framework is as simple as adding a threshold test after sam-
pling the distance field in the scribe-stage. We replace our
object identification in the layer information buffer by a clas-
sification. This classification can take one of three values. If
for some fragment the distance is smaller than the thresh-
old, the fragment is classified as being “equal.” Otherwise,
the fragment is classified as significantly belonging to one
of the objects.
During the painter stage, we render “equal” fragments as
opaque in a neutral color. Our contour detection approach
can be performed on the new classification buffer (rather
than on the object identification buffer) in order to empha-
size the areas of large difference.
4.5 Performance
We created a prototype implementation of the techniques
presented in this paper in C++, using VTK for data process-
ing and OpenGL for rendering. The OpenGL shading lan-
guage (GLSL) was used to implement all GPU-based algo-
rithms, which require at least NVIDIA GeForce 7 graphics
hardware (or equivalent). The resulting system allows for in-
teractive rendering of the visualization, as well as interactive
manipulation of the surfaces involved in the comparison, the
viewpoint and the parameters of the various techniques.
Our layered rendering implementation makes full use of
deferred shading. For this, our layer information buffer con-
sists of three 32-bit render targets. The first two contain color
and surface normals for use in deferred shading. The third
is used to store surface classifications, the in/out-mask and
surface depth values. As only this third buffer needs to be
propagated between layers, the memory costs of the algo-
rithm are those of five 32-bit images at the display resolution
(see Sect. 4.1). The use of distance fields adds to this re-
quirement; we used two 2563-byte distance volumes, which
provide sufficient accuracy for the purposes of our visual-
izations.

Image-based rendering of intersecting surfaces for dynamic comparative visualization
Tests were performed on a single core of an AMD Athlon
2.6 GHz dual core machine with 3 GB RAM and NVIDIA
GeForce 8800 graphics. Images were rendered with shadow
mapping enabled at 1000 × 700 resolution, resulting in
frame rates between 10 and 50 frames per second for four
depth layers (depending on surface complexity), which is
sufficient for most intersecting surfaces visualizations. As
noted, the use of shadow mapping requires scenes to be ren-
dered twice per frame: once from the light’s viewpoint and
once from the camera. This means a doubling of frame rates
can be achieved when shadow mapping is not required.
We used the brain ventricle segmentations (Fig. 1, 79 668
triangles), an artificial height field data set (Fig. 6, 1 044 484
triangles) and the ventricle shape models (Fig. 12, 3788 tri-
angles) for our measurements. Both the number of triangles
and the number of depth layers linearly influence the render-
ing performance. This is expected, as geometry is rendered
once for each layer. Decreasing the maximum number of
layers increases performance, but at the cost of image qual-
ity. A lower number of layers may cause display artifacts
when large numbers of transparent surfaces overlap each
other. In the case of the intersecting surfaces visualization,
depth complexity of the scene rarely exceeds 4, due to the
fact that the inner object is rendered opaque. However, the
use of clipping techniques (as described in Sect. 4.1.2) may
cause an increase of the number of layers required. This is
because clipping is performed in the painter stages, mean-
ing the hidden geometry and the clipping object itself both
contribute to the depth complexity of the scene in the scribe
stages.
The k-buffer architecture proposed by Bavoil et al. [36]
could be used to greatly reduce the number of passes re-
quired to perform depth peeling. However, currently no
hardware implementations of this architecture exist.
Depth peeling based algorithms are usually criticized for
their high memory requirements. We note, however, that in
our technique only information from the current and pre-
vious layer is required in order to render any given layer.
Therefore, we require only two buffers in memory at all
times. Furthermore, rather than storing each layer, we up-
date the final image on the fly. This brings the total memory
requirements of the layered rendering algorithm down to the
memory required for two info-buffers and one final image.
As only a subset of information needs to be propagated be-
tween layers, memory requirements can be further reduced.
The interactive performance achieved by our image-
based implementation of the intersecting surfaces visualiza-
tion enables new uses of such visualizations. As the inter-
section does not have to be computed explicitly, the objects
involved in the comparison do not need to be static. The next
section illustrates an application of the comparison of dy-
namic surfaces.
5 Case study
We performed an expert evaluation study of the techniques
presented in this paper. This section describes our collabora-
tion with two researchers in medical image analysis, who are
experts in creating and analyzing statistical shape models. In
this study, we applied our technique to visualize real-world
statistical shape model data provided by the researchers.
The researchers are also the third and fourth authors of
this paper. They contributed to this work by providing in-
formation on the problem domain and by giving feedback
on our prototypes, but did not work on the implementation
itself. In this context, their role as test users and evaluation
subjects was not compromised.
5.1 Statistical shape models
In medical research, statistical shape modeling [2] is an im-
portant tool for understanding both differences in and vari-
ability of shapes of anatomical features. A shape model is
created by first identifying corresponding points on all indi-
viduals in a population. Principal component analysis is then
applied to determine the average shape of the population, as
well as the principal modes of variation, ranked from most
to least significant.
For this case study, the researchers provided us with
a pair of statistical shape models used in research of
Alzheimer disease (AD). The shape models represent the
variation of the shape of the brain ventricles within two
populations: a group of AD patients and a control group
of healthy patients. It has been shown [37] that brain ven-
tricles enlarge significantly due to the loss of brain tissue
caused by AD. Figure 10 shows a visualization using our
technique of the mean shapes of both groups, in which this
shape difference is clearly visible.
Fig. 10 Comparative visualization using our technique of the mean
ventricle shape of the healthy group (yellow) versus the mean ventricle
shape of the AD group (blue). The visualization clearly shows the latter
shape to be larger, and therefore almost completely shown as transpar-
ent

S. Busking et al.
Shape models are a special case of comparison, for which
a known correspondence between points on both meshes
is not only available but in some cases highly relevant to
the comparison. Currently, such correspondence is visual-
ized by the researchers by showing a single surface com-
bined with point-correspondence glyphs (i.e., lines or ar-
rows) pointing from this surface to where the other surface
would be. Additionally, the researchers frequently use color
mapping to visualize measures on a single surface.
5.2 Evaluation method
The evaluation consisted of two meetings, during which we
discussed our visualizations with the researchers. The first
meeting was an informal introduction of our visualization,
consisting of a demonstration of our technique and a dis-
cussion of shape model visualization in general. We used
the information gathered at this meeting to improve our pro-
totype implementation, which was used to formally evalu-
ate our technique in the second meeting. Also, we gathered
information on currently used visualization techniques, and
used the feedback to formulate a set of three shape research
scenarios in which our visualizations could be applied.
1. Exploring shape differences between two static 3D sur-
faces. This scenario has been studied in detail by Weigle
et al. [1].
2. Exploring variation of a single shape model. This in-
cludes both comparing new individuals to an existing
model and examining variation within the model with re-
spect to the mean shape. For this scenario as well as the
next, the user can interactively control the shape model
parameters to explore different shapes.
3. Validation (error-checking) of a shape model. A shape
model is created by moving the vertices of a mesh to
match different individuals in a population. If these ver-
tices move along the surface of the model to match two
individuals, the model may indicate a difference where in
fact there is none. The models are validated by checking
for such errors.
The comparison of two different shape models is another
important topic for shape model visualization. However, this
requires statistical information to be included in the visual-
ization and is therefore considered future work.
We defined eight visualizations (Fig. 11) for exploring
shape differences. The combinations were selected to al-
low for the evaluation of the strengths of each technique
separately while still creating meaningful visualizations. To
achieve this, we included both single surface and inter-
secting surfaces visualizations, intersecting surfaces with
fogging or with shadow-casting glyphs, and combinations
with or without relevance thresholding. To compare the
proposed enhancements to currently accepted visualization
techniques, we also included basic color mapping, point-
correspondence glyphs and Weigle’s original intersecting
surfaces visualization (without our enhancements) in the
evaluation. During the second meeting, the researchers were
asked to grade these visualizations for each scenario.
We used a Likert scale [38] to grade agreement with the
statement “Visualization X is suitable for use in scenario
Y ,” where X and Y formed all combinations of the visual-
izations in Fig. 11 and the three scenarios mentioned above.
Secondly, the researchers were asked to rank the visualiza-
tions in order of preference for each scenario. As a final
Fig. 11 The eight visualizations used in our evaluation

Image-based rendering of intersecting surfaces for dynamic comparative visualization
question, we asked the researchers to create their preferred
visualization from the techniques in the prototype applica-
tion.
In order to avoid distortion of the results, the researchers
were explicitly warned about possible biases in using a Lik-
ert scale and told to evaluate each visualization indepen-
dently of the others for the first question, leaving compar-
ison for the ranking question. We limited the evaluation to
the interactive use of each visualization, as such use is the
primary aim of our contribution.
5.3 Software setup
We performed the case study using a specially prepared ver-
sion of our software, which could be toggled between each
of the predefined combinations of techniques. For the pur-
poses of this study, we added an implementation of point-
correspondence glyphs, similar to the glyphs currently in
use by the researchers (shown in Fig. 12) and those used
by Weigle [23].
In analyzing shape models, the researchers are most fre-
quently interested in the statistical properties of the model.
However, there are use cases in which direct shape compar-
isons can be useful. The interactivity provided by our tech-
nique enables the intersecting surfaces technique to be used
on dynamically deforming surfaces. We adapted our soft-
ware to allow for interactive deformation of the shape model
mean surfaces along each of the modes of variation, in or-
der to explore the variability of the statistical model. The
researchers were allowed free use of this functionality for
the evaluation of each technique in the latter two scenarios.
Based on feedback received from the researchers at the
initial meeting, we enhanced the user interface of the proto-
Fig. 12 Point-correspondence glyphs connect corresponding points
on the mean and deformed shape model surfaces. Here they are used to
show the third principal mode of variation in the control group shape
model
type application for the formal evaluation by adding quan-
titative feedback about visualization parameters. We also
added linked views showing the separate shapes involved
in the comparison, with linked cursors between all views.
While the researchers were asked to only use the intersect-
ing surfaces visualization for comparison, they indicated the
simple views were helpful in learning how to interpret the
intersecting surfaces visualizations.
5.4 Evaluation results
After evaluating each visualization, the experts were asked
to explain their grades. The Likert scale grades and rankings
served to provide important structure to this discussion. This
section summarizes the feedback gathered from this process.
In all scenarios, the researchers preferred the intersect-
ing surfaces visualizations over the single-surface visualiza-
tions. In a single-surface visualization, it is hard to deter-
mine the shape of the second surface. The researchers did
note that for certain specific questions, such as examining
statistical relevance of deformations, a color-mapped sur-
face provides enough information.
Fogging and shadow-casting surface glyphs Both fogging
and glyphs are preferred over plain intersecting surfaces, as
without them it is very hard to see the 3D structure of and
separation between both surfaces. However, the researchers
had some concerns regarding the fog, causing them to pre-
fer the glyphs. First, fogging adds visual complexity; opac-
ity is not commonly used in current visualization techniques
to indicate distance, and the fog color adds a third color to
the visualization. Secondly, glyphs also served to emphasize
the shape of the outer surface. Their removal, coupled with
the fact that the fog obscures the inner surface, makes the
shape of both surfaces harder to perceive. The fog color can
be useful, however, to quickly direct attention to areas with
large difference. Other techniques can then be used to ex-
plore surface shapes in detail.
Intersection contours When using the shadow-casting sur-
face glyphs, the researchers noted that intersection contours
are important to help distinguish between glyphs and inter-
sections. The presence of these contours also helped the re-
searchers to better perceive the intersecting surface visual-
izations in general.
Relevance The researchers see the benefit of suppressing
small differences using a threshold. However, they indi-
cated several points where the current visualization should
be improved. First, the visual complexity of the current
implementation is too high. Thresholding being performed
on both surfaces separately clutters rather than suppresses
these areas in the visualization. Because of this clutter, visu-
alizations which included the thresholding technique were

S. Busking et al.
ranked very low in the evaluation. More work should be
done to reduce the visual complexity of the masked areas,
e.g., using illustrative techniques. The presence of a third
color (white) is acceptable in these visualizations, as the
color has a well-defined meaning (areas with no relevant
differences). Second, comparing thresholding to color map-
ping, the researchers indicated a need for better visualiza-
tion of the values in non-masked areas. Additionally, a color
scale should be used to highlight particularly large or signif-
icant differences in the unmasked areas.
Point-correspondence information While not normally
available for general surface-to-surface comparison, corre-
spondence information is essential for shape model valida-
tion (scenario 3), and should therefore always be included in
these visualizations. The point-correspondence glyphs ful-
fill this requirement, but can be enhanced in several ways.
Color mapping the glyphs by their length can help show the
distance between corresponding points. Similarly to surface
thresholding by distance, an option should also be added to
filter glyphs that are too short to be relevant by thresholding,
and the user should be able to toggle their display interac-
tively.
One thing to note is that for single-surface visualizations,
point-correspondence glyphs may point inside the surface.
This makes such areas impossible to distinguish from areas
of no change, unless the surface is made transparent (thereby
causing other perceptual issues). The intersecting surfaces
visualizations always show all point-correspondence glyphs.
It was mainly for this reason that this was a preferred com-
bination for the researchers.
5.5 Lessons learned
A recurring concern during the evaluation was the high vi-
sual complexity of the intersecting surfaces visualizations,
especially when deforming surfaces are involved. Despite
this, intersecting surfaces were ranked higher than single-
surface visualizations for all scenarios. Overall, the re-
searchers feel that the visualizations can be easily inter-
preted after some use. However, the initial learning curve
is rather steep, and the additional complexity introduced by
our fogging and thresholding techniques added to this. For
exploration of the variation in a shape model, the researchers
considered information about exact differences less impor-
tant than for the other scenarios. This means techniques like
thresholding, color mapping and the point-correspondence
glyphs are best omitted in this scenario, in order to reduce
visual complexity.
Scenario 3 furthermore showed the importance of tuning
visualizations to application-specific requirements. The pre-
ferred visualization chosen by both researchers consisted of
a basic combination of intersecting surfaces with contours
and shadow-casting surface glyphs to aid perception of the
shape of the transparent surfaces. However, due to the nature
of statistical shape models, this visualization should also in-
clude point-corresponding glyphs, which can be colored by
distance, filtered by relevance and toggled on or off by the
user.
5.6 Summary and outlook
In this case study, we applied our technique to real-world
data and problems to gauge their effectiveness. Our expert
evaluation agrees with most of our own findings as well
as those from Weigle’s studies. However, it also indicates
that more work should be done on reducing the visual com-
plexity of the depth cuing (fogging) and relevance masking
(thresholding) techniques, as well as of the intersecting sur-
faces technique in general. Given this, there is no absolute
winner among the visualizations considered in this study.
Due to this visual complexity, we need to tune the combi-
nation of techniques to answer specific questions rather than
simply including every bit of information. Interactive per-
formance in changing the visualization and its parameters
certainly helps in making this process easy for the user.
We intend to continue the collaboration in future work to
apply our technique to shape model comparison and popula-
tion studies. Additionally, user studies should be performed
at a larger scale to more thoroughly evaluate the techniques.
6 Conclusions and future work
We have presented technique for the interactive visualiza-
tion and exploration of surface differences using intersecting
surfaces. Our main points of contribution are:
– A new image-based formulation of the proven intersect-
ing surfaces visualization, based on our new layered ren-
dering pipeline. Our formulation provides interactive per-
formance, even when the objects being compared are de-
formed or moved relative to each other. This interactivity
enables intersecting surface techniques to be applied in
new domains such as shape model visualization.
– Enhancements to the original intersecting surfaces tech-
nique. These include object-intersection contours, as well
as the integration of local difference measures in the form
of view-dependent depth cues and view-independent dis-
tance fields. Furthermore, we extend the intersecting sur-
faces visualization to a three-way segmentation of surface
differences, where the visual impact of insignificant dif-
ferences is reduced.
– A case study, exploring the usefulness of intersecting sur-
faces techniques for the visualization and comparison of
statistical shape models.

Image-based rendering of intersecting surfaces for dynamic comparative visualization
Our layered rendering formulation offers a flexible frame-
work for various rendering techniques which are otherwise
not straightforward to implement. The approach has strong
parallels with ray casting, in that information is propagated
from the viewer into and through the geometric scene. This
enables image-based implementation of various ray-casting-
like algorithms for layered surfaces, such as CSG operations
and fogging inside objects. However, as the method is still
based on rasterization, performance is much higher than that
of a ray-casting technique and the technique can take full
advantage of hardware acceleration. Furthermore, due to the
formulations sharing a common framework, techniques can
be combined in a straightforward way.
Based on the layered rendering formulation, our tech-
nique creates an interactive visualization for the comparison
of surfaces. As indicated by Weigle [23], this interactivity
is an important aid for understanding the shapes of objects
being compared. Interactivity during object manipulations
such as relative movement and/or deformation also enables
new applications for the intersecting surfaces visualization,
such as the visualization of statistical shape models explored
in our case study.
Our visualization addresses the requirements defined in
Sect. 1: The visualization of differences is local and explicit,
and we presented methods for the suppression of irrelevant
differences in the visualization. The distance cues and rele-
vance filtering techniques can be used with various distance
metrics, as long as it is possible to create a distance field for
such a metric.
Furthermore, our enhanced intersecting surfaces tech-
nique addresses most limitations of the original technique:
Contour lines remove ambiguity between intersections, oc-
clusions and surface glyphs, distance cues add additional
inter-surface distance information at any point on the sur-
faces, and relevance filtering hides irrelevant information.
Regarding the visualization of highly different objects or
dealing with occlusion, we provide both suggestions and
(through our framework) opportunities for solving these in
future work.
The resulting visualization can provide an overview of
differences for any given pair of surfaces. This can assist
a researcher in selecting areas of interest and/or choosing
further techniques to apply to quantitatively analyze these
differences. Our evaluation has shown that intersecting sur-
faces can also be a useful technique for comparing dy-
namic objects, provided that: (1) The visualization is prop-
erly adapted to the problem domain, e.g., by adding corre-
spondence feedback in the case of our shape models; (2) The
visual complexity of the visualizations is kept as low as pos-
sible. For example, rather than combining the various tech-
niques and enhancements, a better option is to allow switch-
ing between them one-by-one, based on user interests.
6.1 Future work
Further improvements can be made in the use of texture pat-
terns to show local surface shape as well as differences. In
particular, if a surface is deformed, comparison of the de-
formed pattern to the original may yield more insight into
the nature of the deformation. Texture-based techniques,
possibly shown on cross sections of the data, could help to
illustrate these changes.
The use of (linked) cross-sectional views could also help
to reduce the perceived visual complexity of our visualiza-
tions. On-demand slicing has the potential to show differ-
ences which are hard to interpret in 3D clearly in a 2D plane.
Another option not yet explored in this work is the effect of
adding legends and similar tools to aid interpretation of the
visualizations. For instance, fogging could be easier to in-
terpret if some simple geometry was used as a “legend”: this
legend could consist of two planes intersecting in the middle
along a scale of distances, visualized using the same settings
as the current visualization.
In our case study we applied our technique to the visu-
alization of statistical shape models. The statistical aspects
of these models are currently missing from the visualiza-
tions. In work [39] performed subsequently to that presented
in this paper, we presented an application for the visualiza-
tion of high-dimensional shape spaces. We plan to integrate
the intersecting surfaces techniques into our software in the
future, as well as to extend these visualizations to include
feedback on the statistical properties of the model.
Given two shape models for different populations, statis-
tically significant differences can be determined between the
models themselves [37]. By including such statistical infor-
mation, our visualizations could help to link such statistical
differences to physical differences in shape. This would aid
both in understanding the causes and in validating the statis-
tical models.
Finally, there is a need for intuitive methods for the in-
teractive exploration of differences within the data. Our use
of layered rendering already enables objects to be manipu-
lated interactively. We are looking for ways to guide this in-
teraction in order to select and eliminate certain differences
which are not relevant to the application domain. Addition-
ally, we plan to integrate linked cross-sectional views and
probing tools to provide quantitative statements about dif-
ferences. Combined, these techniques will enable better ex-
ploration and visualization of relevant differences.
Acknowledgements This research is supported by the Nether-
lands Organization for Scientific Research (NWO), project number
643.100.503 “Multi-Field Medical Visualization”.

S. Busking et al.
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01684.x

Image-based rendering of intersecting surfaces for dynamic comparative visualization
Stef Busking received both B.Sc.
(2005) and M.Sc. degrees (2006) in
Computer Science from the Tech-
nische Universiteit Eindhoven. He
is currently a Ph.D. candidate at
Delft University of Technology. His
research interests include illustra-
tive rendering, real-time interaction,
comparative visualization and visual
exploration of data sets.
Charl P. Botha is Assistant Profes-
sor in the Visualization Group of
the Delft University of Technology,
the Netherlands, where he leads the
Medical Visualization research ac-
tivities. He is also a visiting scien-
tist at the LKEB research group, De-
partment of Radiology, Leiden Uni-
versity Medical Center. Dr. Botha
holds an M.Sc. in Electronic Engi-
neering (1999) and a Ph.D. in Com-
puter Science (2005).
Luca Ferrarini works as a re-
searcher in the field of neuroimag-
ing/neuroscience at the Division of
Image Processing (LKEB) of the
Leiden University Medical Center
(LUMC), in Leiden, the Nether-
lands. He received his Ph.D. cum
laude in neuroimaging from Leiden
University in 2008, and his M.Sc.
cum laude in Information Engineer-
ing from the University of Modena
and Reggio Emilia (Italy) in 2003.
His research interests include sta-
tistical analysis of morphological
changes in the brain due to neurode-
generative diseases, as depicted by structural MRI, and the character-
ization of functional connectivity networks in the resting brain using
graph theory and resting state fMRI.
Julien Milles is Assistant Profes-
sor in the Department of Radiol-
ogy of the Leiden University Med-
ical Center, the Netherlands, where
he works since 2004. He previously
worked as a research associate at the
Cardiovascular Research Institute
of Maastricht (2003) and the CRE-
ATIS laboratory (Lyon, France) be-
tween 1999 and 2003. He received
his M.Sc. degree in Electrical Engi-
neering from the Polytechnic Insti-
tute of Grenoble and Ph.D. from the
Applied Science Institute of Lyon in
1999 and 2002 respectively. His re-
search interests include cardiovascular and neurological MR imaging,
image enhancement, motion estimation, and quantitative analysis.
Frits H. Post is Associate Professor
of Computer Science at TU Delft,
where he leads a research group
in data visualization. He received
an M.Sc. degree in Industrial De-
sign Engineering from TU Delft in
1979. His research interests include
flow visualization, medical visual-
ization, virtual reality and 3D inter-
action. He has (co-)authored more
than 100 publications in many ar-
eas of data visualization. He is the
chairman of the Eurographics Steer-
ing Committee on Data Visualiza-
tion and a co-founder of the annual
joint Eurographics-IEEE EuroVis Symposium. He is a Fellow of the
Eurographics Association.