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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 / CORNERBOUNDARYCOMPLEX

SIMPLE INTERIOR_EDGECORNER

FEATURE EDGES

Normal

Classification

User-Specified

Criteria

DISTANCE

TO PLANE

DISTANCE

TO EDGE

SIMPLE INTERIOR_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 triangles 50% 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 variationWith normal variation

Original 20,003 triangles 12% 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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