Adaptive surface data compression

Abstract

Three-dimensional (3D) visualization techniques are becoming an important tool for medical applications. Computer-generated 3D reconstructions of the human skull are used to build stereolithographic models, which can be used to simulate surgery or to create individual implants. Anatomy-based 3D models are used to simulate the physical behaviour of human organs. These 3D models are usually displayed by a polygonal description of their surface, which requires hundreds of thousands of polygons. For interactive applications this large number of polygons is a major obstacle. We have improved an adaptive compression algorithm that significantly reduces the number of triangles required to model complex objects without losing visible detail and have implemented it in our surgery simulation system. We present this algorithm using human skull and skin data and describe the efficiency of this new approach.ZusammenfassungComputerbasierte dreidimensionale Visualisierungstechniken haben im letzten Jahrzehnt Einzug in die Medizin gehalten. Aus den computergenerierten dreidimensionalen Rekonstruktionen des Gesichtsschädels werden unter anderem mittels Stereolithographie reale Modelle erstellt, an denen geplante chirurgische Eingriffe simuliert werden können, oder aber die 3D-Rekonstruktionen dienen dazu, patientenangepaβte Implantate herzustellen. Die Geometrie solch komplexer 3D Modelle wird im allgemeinen mit Hilfe hunderttausender einzelner, planarer Polygone beschrieben. Eine interaktive Darstellung dieser Modelle ist oftmals nicht mehr möglich. In dieser Arbeit beschreiben wir ein erweitertes adaptives Verfahren zur signifikanten Reduzierung von Polygonoberflächen, ohne daβ damit ein Detailverlust in der Darstellung verbunden ist. Dieses Reduzierungsverfahren wurde in ein Operationsplammgssystem integriert und umfassend verifiziert. An zwei medizinischen Datensätzen, der 3D Rekonstruktion der Hautoberfläche und des Gesichtsschädels, wird die Leistungsfähigkeit dieses neuen Verfahrens aufgezeigt.RésuméLes techniques de visualisation tri-dimensionnelle sont en train de devenir un outil important pour les applications médicales. Des reconstructions 3D du squelette humain générées par ordinateur sont utilisées pour construire des modèles stéréolithographiques qui peuvent être utilisés pour simuler une opération chirurgicale ou pour créer des implants individuels. Des modèles tri-dimensionnels basés sur l'anatomie sont utilisés pour simuler le comportement physique d'organes humains. Ces modèles 3D sont en général affichés à l'aide d'une description polygonale de leur surface, ce qui nécessite des centaines de milliers de polygones. Pour les applications interactives, ce grand nombre de polygones est un obstacle majeur. Nous avons amélioré un algorithme de compression adaptatif qui réduit significativement le nombre de triangles requis pour modéliser des objets complexes sans perdre de détails visibles, et nous l'avons implémenté dans notre système de simulation de chirurgie. Nous présentons cet algorithme en utilisant des données de squelette et de peau humains et décrivons l'efficacité de cette nouvelle approche.

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Special Issue of Signal Processing on Medical Image Compression1997
Erwin Keeve, Stefan Schaller, Sabine Girod, Bernd GirodAdaptive Surface Data Compression
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Adaptive Surface Data Compression
Erwin Keeve *, Stefan Schaller **, Sabine Girod ***, Bernd Girod **
Invited paper
* Surgical Planning Laboratory, Dept. of Radiology, Brigham and Women’s Hospital, Harvard Medical School
75 Francis Street, Boston, MA 02115, USA, Email: keeve@bwh.harvard.edu
** Telecommunications Institute, University of Erlangen-Nuremberg
Cauerstraße 7, 91058 Erlangen, Germany, Email: {girod, schaller}@nt.e-technik.uni-erlangen.de
*** Department of Oral and Maxillofacial Surgery, University of Erlangen-Nuremberg
Glückstraße 11, 91054 Erlangen, Germany, Email: sabine.girod@mkg.med.uni-erlangen.de
Keywords: medical image compression, surface reconstruction, interactive simulation and visualization
Abstract: Three-dimensional visualization techniques are becoming an important tool for medical applications.
Computer generated 3D reconstructions of the human skull are used to build stereolithographic models, which can be
used to simulate surgery or to create individual implants. Anatomy-based three-dimensional models are used to simulate
the physical behaviour of human organs. These 3D models are usually displayed by a polygonal description of their
surface, which requires hundreds of thousands of polygons. For interactive applications this large number
a major obstacle. We have improved an adaptive compression algorithm that significantly reduces the number of triangles
required to model complex objects without losing visible detail and have implemented it in our surgery simulation
system. We present this algorithm using human skull and skin data and describe the efficiency of this new approach.
of polygons is
Zusammenfassung: Computerbasierte dreidimensionale Visualisierungstechniken haben im letzten Jahrzehnt Einzug
in die Medizin gehalten. Aus den computergenerierten dreidimensionalen Rekonstruktionen des Gesichtsschädels werden
unter anderem mittels Stereolithographie reale Modelle erstellt, an denen geplante chirurgische Eingriffe simuliert werden
können, oder aber die 3D-Rekonstruktionen dienen dazu, patientenangepaßte Implantate herzustellen. Die Geometrie solch
komplexer 3D Modelle wird im allgemeinen mit Hilfe hunderttausender einzelner, planarer Polygone beschrieben. Eine
interaktive Darstellung dieser Modelle ist oftmals nicht mehr möglich. In dieser Arbeit beschreiben wir ein erweitertes
adaptives Verfahren zur signifikanten Reduzierung von Polygonoberflächen, ohne daß damit ein Detailverlust in der
Darstellung verbunden ist. Dieses Reduzierungsverfahren wurde in ein Operationsplanungssystem integriert und
umfassend verifiziert. An zwei medizinischen Datensätzen, der 3D Rekonstruktion der Hautoberfläche und des
Gesichtsschädels, wird die Leistungsfähigkeit dieses neuen Verfahrens aufgezeigt.

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1.Introduction
Computer-based three-dimensional visualization
techniques have made a great impact on the field of
medicine in the last decade [Zon94]. Physical models of
the skull can be created through computer-generated
reconstruction [Bil95], individual implants can be
produced [Weh95], or surgical operations can be
simulated using state-of-the-art graphics workstations
[Kee96a] [Kee96b] [Kee96c] [Kee96d]. Such modern
visualization methods also allow the use of surgery
robots that help with the exact positioning of surgical
instruments, especially in neurosurgery [Haß95].
The visualization of such three-dimensional
objects takes place by using volume or surface
rendering techniques [Fol92]. Volume rendering - the
direct rendering of data represented as 3D scalar fields -
is becoming an important branch of computer graphics.
It allows the visualization of three-dimensional
transparent datasets without obscuring the interior of
objects. Although there exists several compression
algorithms for volume visualization [Nin92] [Nin93]
there is still an even greater need for hardware speed
than with surface rendering, since volume datasets are
generally much larger.
In most cases medical objects are visualized using
surface rendering techniques.
primitives, the object surface is described and visualized
through common computer graphics hardware. Since a
single polygon is planar, a large number of primitives
is required to capture the detail of complex, curved
objects such as anatomical structures. One algorithm
that extracts isodensity surfaces from volume data is
“Marching Cubes“ [Lor87]. Developed for medical
applications, “Marching Cubes“ generates typically
500,000 to 1,000,000 triangular primitives from a 512
by 512 by 100 CT-dataset of an anatomical object, such
as a skull. Sampling devices such as a Cyberware 3D-
laser scanner obtain models of the human head using
500,000 triangles. This large number of polygons
slows down the rendering and inhibits real-time
interaction. Even today’s graphics workstation have
trouble storing and rendering models of this size.
Therefore a surface compression technique is required
which speeds up the rendering while preserving the
visible detail of such anatomy-based models.
Using polygonal
In this paper we present an adaptive surface data
compression algorithm which classifies the surface
primitives by their topology, geometry, neighbouring
normals and user-specified criteria. After outlining other
work related to surface data compression, we describe
our approach and its implementation in detail. Results
show how this technique reduces human skin and skull
data without sacrificing the visible detail of the
anatomical models.
2.Related Work
There are two main categories in surface data
compression; filter-based and adaptive approaches.
Filter-based techniques are well-known and proceed
on a large number of samples to remove or replace
them. Examples of this technique are sub-sampling and
averaging. Sub-sampling uses every n’th sample, while
averaging combines neighbouring primitives to reduce
the size of the dataset.
Adaptive techniques reduce primitives only if
specified criteria are satisfied. For example, Yoshida et
al. decimate a triangle mesh in smooth areas by
degenerating one edge of a triangle toward a point
[Yos93]. Schmitt starts with rough bi-cubic patch
approximations to sample data, then subdivides those
patches that are not sufficiently close to the underlying
samples [Sch86]. De Hämer extends this technique to
reduce polygonal meshes [DeH92]. Turk randomly
places a given number of vertices on a polygonal mesh
and then specifies a new mesh by retriangulation
[Tur92]. To yield the topological structure of the
original mesh, all new vertices are first introduced to
the existing mesh and then the original samples are
discarded. Deformable models are another adaptive
technique to resample a given dataset [Mil91]. An
initial surface model is deformed until it fits the
implicit surface that exists within a sampled volume.
Also adaptive meshing techniques [Ter91] that are
employed in [Wat95] are used to reduce the large data
acquired by a 3D-laser scanner into a parsimonious
geometric model of the face that can be animated
efficiently [Lee95]. To create new views of 3D models
from arbitrary camera positions Levoy and Hanrahan
developed a method which simple combines and
resamples the available images [Lev96].
Another adaptive compression technique, which
considers the local topological and geometrical structure
of a polygonal mesh, was developed by Schroeder,
Zarge and Lorensen, in 1992 [Sch92]. The presented
surface data compression approach is based on the work
by Schroeder et al. and improves this technique for
medical applications [Sch95].

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3.Compression Algorithm
The goal of the presented adaptive compression
algorithm is to reduce the amount of triangles used to
represent complex anatomical structures without
sacrificing the visible detail of the models. This is done
by using a subset of the original vertices. There is no
creation of new vertices; instead vertices which meet
user-specified criteria are removed from the dataset.
Starting by classifying the surface primitives by
their topology, geometry and their normals, an indicator
is set for each primitive vertex whether it can be
considered for removal or not. If a marked vertex meets
the user-specified compression criterion, the vertex and
all primitives that use it, are deleted. A new local
triangulation with fewer primitives is formed to patch
the resulting “hole”. This process is repeated until a
termination criterion is satisfied.
3.1 Data Aquisition
The compression algorithm is used in a surgery
planning system which
operations [Kee96a] [Kee96d]. This system obtains data
from a Cyberware scanner, which measures exactly the
geometry of the skin surface [Cyb93]. By providing
colour information as well, this 3D laser scanner makes
an additional contribution to the photorealistic
appearance of the patient’s face. The system also
requires skull data, which are generated through
computer tomography. The “Marching-Cubes“ method
is used to build a 3D model from this CT dataset
[Lor87].
simulates craniofacial
3.2 Data Structure
There are many approaches to represent polygonal
data structures [Wei85]. Because we have a large
amount of data, the chosen data structure must be
efficient, while still providing the functionality that we
need. It must allow the efficient retrieval of all vertices
of a given primitive, the finding of all primitives of a
given vertex and the finding of all neighbouring vertices
of a given vertex. The only primitives being used in
our approach are triangles, since they capture the detail
of complex, curved objects well and can be rendered
efficiently using common graphics hardware. The brute
force approach would be to save a list of all triangles
and their vertex coordinates, but this is inefficient,
because the coordinates of shared vertices are multiply
stored. Another approach lessens storage space by only
storing the vertex coordinates once and maintaining a
primitive list with references to these coordinates. This
index list is efficient but does not easily provide the
above functionality. A more useful data structure is the
Winged-Edge representation by Baumgart [Bau75],
which keeps a list of all primitive edges and therefore is
not as efficient.
Our implementation uses a space-efficient vertex-
triangle hierarchical ring structure [Sch92]. This
consists of a list of all triangles whose indices refer to a
vertex coordinate array. Connections are built from the
coordinate array back to the triangle list by lists of
triangles using each vertex. Additionally another list is
maintained that contains an index of all neighbouring
vertices for each vertex. Edge definitions are not
explicitly defined, instead they are implicitly given by
the order of the vertex indices in the triangle list. Figure
1 shows this data structure.
Vertex
List
1
2
3
coordinates
xyz
coordinates
xyz
coordinates
xyz
coordinates
xyz
Triangle
List
vertex 1
vertex 2
vertex 0
vertex 0
vertex 2
vertex 3
vertex 1
vertex 2
vertex 3
vertex 0
vertex 2
vertex 0
vertex 1
vertex 3
vertex 0
vertex 2
Triangle lists
for each vertex
Neighboring
vertices
vertex 3
0
vertex 2
vertex 0
vertex 1
triangle 1
triangle 2
Figure 1: Implemented data structure

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3.3 Classification
Each vertex is classified by three criteria; by its
topology, by its geometry and by its neighbouring
normals. We only continue to consider vertices that
successfully pass each successive criterion. After the
topological and geometrical classification steps there are
five possible cases; two of which are never allowed to
be decimated, and three of which proceed to further
normal testing. If the normal criterion is also
successful, then user-specified criteria are applied.
Figure 2 shows an overview of all classification steps.
Topological
Classification
Geometrical
Classification
SIMPLE / INTERIOR_EDGE / CORNERBOUNDARY COMPLEX
SIMPLEINTERIOR_EDGE CORNER
FEATURE EDGES
Normal
Classification
User-Specified
Criteria
DISTANCE
TO PLANE
DISTANCE
TO EDGE
SIMPLEINTERIOR_EDGEBOUNDARY
Figure 2: Classification
Topological Classification: The first step is
to classify each vertex according to the topology of its
neighbouring triangles. There are three possible
topological classifications; COMPLEX, BOUNDARY and
SIMPLE / INTERIOR_EDGE / CORNER. A triangle is called
two-manifold if its edges belong to at most two
primitives
[Fol92]. Under
classification, a vertex whose triangle is not two-
manifold is labeled as COMPLEX and is not further
the topological
considered for reduction. Figure 3 shows two COMPLEX
vertices. BOUNDARY vertices, which are those that are
not completely surrounded by triangles, do not pass
through the geometry classification, but proceed to
further normal and user-specified testing. All vertices
which are completely surrounded by triangles are
grouped together as SIMPLE / INTERIOR_EDGE / CORNER
and will be further classified according to geometry.
Figure 3: COMPLEX vertices
Geometrical Classification: The SIMPLE /
INTERIOR_EDGE / CORNER vertices are further separated
into three categories; SIMPLE, INTERIOR_EDGE and
CORNER. Each triangle edge is examined with respect to
the angle between the normals of its adjacent triangles.
This edge is labeled as a FEATURE EDGE if the angle
exceeds a given user-specified FEATURE EDGE ANGLE, as
shown in Figure 4. Each vertex is classified by the
number of FEATURE EDGES which are connected to it. If
a vertex has no connecting FEATURE EDGES then it is
labeled as SIMPLE. If it has two connecting FEATURE
EDGES it is labeled as INTERIOR_EDGE. Otherwise, it is
labeled CORNER and is not considered for reduction.
SIMPLE and INTERIOR_EDGE vertices will further proceed
to normal and user-specified testing.
FEATURE EDGE
Normal Vectors
Figure 4: FEATURE EDGE
Normal Classification: Because normals have
a great impact on the appearance of rendered anatomical
structures, an additional normal criterion is defined. All
SIMPLE, INTERIOR_EDGE and BOUNDARY vertices are
analysed with respect to the normals of their
neighbouring vertices; if the angle between the normal
of each vertex and its adjacent vertices is larger than a
user-specified NORMAL VARIATION ANGLE, the vertex is
not considered for removal. Otherwise it is passed
through to the final user-specified testing.

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3.4 User-Specified Criteria
After assigning each vertex to one of SIMPLE,
INTERIOR_EDGE, CORNER, BOUNDARY or COMPLEX
categories, user-specified decimation criteria can be
defined for each class. To keep the topological structure
of the mesh, COMPLEX vertices are never considered for
removal. Also CORNER vertices are not reduced, in order
to preserve sharp edges.
SIMPLE vertices are tested using the user-specified
DISTANCE TO PLANE criterion, as shown in Figure 5. An
AVERAGE PLANE is constructed from the neighbouring
vertices. If the distance from the vertex to the AVERAGE
PLANE is greater than the user-specified value, the vertex
is retained. If the distance is less, then the vertex can be
considered for removal.
d
AVERAGE PLANE
Figure 5: DISTANCE TO PLANE criterion
INTERIOR_EDGE and BOUNDARY vertices are tested
by the user-specified DISTANCE TO EDGE criterion, as
shown in Figure 6. By definition, these vertices are
connected to two FEATURE EDGES or they build part of
the boundary. The distance from the vertex to the line
defined by the pair of vertices forming the FEATURE
EDGES or to the line defined by the two other vertices
forming the boundary segment, is determined. If this
distance is less than the user-specified value, the vertex
can be considered for removal and otherwise it is
retained.
d
FEATURE EDGES
INTERIOR_EDGE
d
BOUNDARY
Figure 6: DISTANCE TO EDGE criterion
3.5 Retriangulation
After these classification steps, each vertex is now
marked with an indicator whether it could be removed or
not. In a further step we consider the submesh around
each positively marked vertex and attempt to
retriangulate the remaining polygons without it. If the
retriangulation is not successful, we must retain the
vertex and its triangles.
If we remove a SIMPLE or BOUNDARY marked
vertex from a submesh, we are left with one remaining
polygon, which must be retriangulated. However, if we
remove an INTERIOR_EDGE marked vertex we are left
with two remaining polygons, which both must be
retriangulated. Figure 7 shows this.
INTERIOR_EDGEBOUNDARY SIMPLE
Figure 7: Remaining polygons
When we retriangulate the remaining polygons we
have two goals to take into consideration; the new
triangulation must approximate the original shape well
and each triangle should be within a user-specified
TRIANGLE ASPECT RATIO. To do this, we split each
remaining polygon into two halves. This splitting
procedure is recursively repeated until each half has only
three vertices forming a new triangle. If we could not
split the remaining polygon into new triangles within
an user-specified aspect ratio, the vertex under
consideration and all of its triangles must be retained.
The remaining polygon can be split along a few
possible lines. We enumerate all of the possible SPLIT
LINES between pairs of non-neighbouring vertices and
build SPLIT PLANES along these lines orthogonal to the
AVERAGE PLANE, as shown in Figure 8. For each
possible SPLIT PLANE, we calculate the distance from
each vertex to it and take the ratio of the smallest
distance to the length of the SPLIT LINE. The SPLIT LINE
with the greatest ratio will deliver new triangles with
the best aspect ratio.
As it follows from the Euler relation the removal
of a SIMPLE or a INTERIOR_EDGE vertex reduces the
submesh by two triangles [Pre88]. Removal of a
BOUNDARY vertex reduces the submesh by one triangle.

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d
AVERAGE PLANE
SPLIT PLANE
SPLIT LINE
Figure 8: SPLIT PLANE
After all vertices have passed through these
different decimation steps, the loop is started again until
a user-specified NUMBER OF ITERATIONS is reached.
3.6 Special Cases
There exists several special cases in general, which
must be taken into account. However, because we are
using only triangle meshes generated by the “Marching-
Cubes“ algorithm or directly reconstructed from
Cyberware scanner data, attention must be given to
only two special cases during retriangulation.
• If there is a topological hole in the triangle mesh
it might be possible to remove a vertex from this
hole's boundary. This could cause the hole to
collapse and would change the topology.
• Also for a simple closed surface such as a
tetrahedon removing of one vertex changes the
topology of the mesh.
To prevent this,
retriangulation to insure that dublicate triangles or
triangle edges are not generated.
checks are made during
3.7 Software Implementation
The algorithm is part of a surgical simulation
system which is implemented in C++ on Silicon
Graphics workstations, using the object-oriented 3D
graphics library Open Inventor [Wer94]. The user-
interface was created with the Motif library and is
shown in Figure 9. It provides flexibility by allowing
the user to set the following parameters
• DISTANCE TO PLANE
• DISTANCE TO EDGE
• FEATURE EDGE ANGLE
• TRIANGLE ASPECT RATIO
• NORMAL VARIATION ANGLE
• NUMBER OF ITERATIONS
Additionally, to simplify the user interaction, an
OVERALL QUALITY LEVEL is provided which takes
reasonable default parameter values.
Figure 9: User-interface
4.Results
As described above, in our surgical planning
system we use two different types of data - Cyberware
scanner skin data and “Marching-Cubes“ reconstructions
of the skull from computer tomography. Although the
initial meshes are generated by different methods, all
results are produced by the same compression
algorithm.
As shown in Figure 10 on a extract of human skin
data, our algorithm reduces the original dataset from
46,000 to 5,390 triangles (compression ratio 8.5:1)
without sacrificing the visible detail of the model.
Texture mapping further improves the appearance. The
differences between the reduced and original dataset are
visualized in the lower row. The maximal error for the

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compression rate 2:1 is 0.25 mm and for the
compression rate 8.5:1 is 0.4 mm. The compression of
the skin data takes less than one minute on a common
graphics workstation, such as a SGI Indigo High
Impact. Afterwards, the reduced dataset can be used
interactively in our surgery simulation system running
on the same platform. This would not be possible
without compression.
Figure 11 shows the compression of skull data.
The algorithm reduces the original dataset from 343,696
to 95,808 triangles (compression ratio 3.5:1). In this
application the compression ratio is less than in the
above example, because the surface structure in the area
of the teeth and vertebrae is more complex and highly
curved.
We compared our improved method (with normal
variation) with the original approach developed by
Schroeder et al. (without normal variation). As shown
in Figure 12 on a extract of human skin data the surface
looks more smooth with the improved method.
5.Conclusions
We have improved an adaptive compression
algorithm developed by Schroeder et al. by adding an
additional normal classification step to it. The
implemented algorithm can reduce the number of
triangles required to model complex objects by
approximately 8:1 without losing visible detail. We
have implemented this algorithm and it enables
interactive manipulation of
objects, which is a fundamental prerequisite of a
surgical simulation system. The interface gives users
the flexibility to easily tailor parameters to suit the
needs of their application. The presented results
demonstrate the efficiency and strengths of this
approach.
complex anatomical
Acknowledgement: This work is supported by
Deutsche Forschungsgemeinschaft (DFG) research grant
Gi 198/2-4 and by German Academic Exchange Service
(DAAD) research grant D/96/17570.
This software is available
http://splweb.bwh.harvard.edu:8000/pages/ppl/keeve
via internet under

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Original, 46,000 triangles50% of original data, 23,007 triangles
(compression ratio 2:1)
12% of original data, 5,390 triangles
(compression ratio 8.5:1)
Wireframe
Phong shaded
Texture shaded
Error visualization
Figure 10: Skin data

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Original, 343,696 triangles48% of original data, 166,717 triangles
(compression ratio 2:1)
27% of original data, 95,808 triangles
(compression ratio 3.5:1)
Wireframe
Phong shaded
Figure 11: Skull data
Without normal variation With normal variation
Original 20,003 triangles12% of original data, 2,407 triangles
(compression ratio 8.5:1)
12% of original data, 2,409 triangles
(compression ratio 8.5:1)
Figure 12: Comparison

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