A FRAMEWORK FOR DATA-DRIVEN PROGRESSIVE MESH

COMPRESSION

Gabriel Cirio

∗

, Guillaume Lavou

†

and Florent Dupont

∗

Universit

e de Lyon, CNRS, France

∗

Universit

e Lyon 1, LIRIS, UMR5205, F-69622, France

†

INSA-Lyon, LIRIS, UMR5205, F-69621, France

Keywords:

Progressive mesh compression, Associated properties, Data-driven, Kd-tree.

Abstract:

Progressive mesh compression techniques have reached very high compression ratios. However, these tech-

niques usually do not take into account associated properties of meshes such as colors or normals, no matter

their size, nor do they try to improve the quality of the intermediate decompression meshes. In this work, we

propose a framework that uses the associated properties of the mesh to drive the compression process, resulting

in an improved quality of the intermediate decompression meshes. Based on a kd-tree geometry compression

algorithm, the framework is generic enough to allow any property or set of properties to drive the compression

process provided the user deﬁnes a distance function for each property. The algorithm builds the kd-tree struc-

ture using a voxelisation process, which recursively separates the set of vertices according to the associated

properties distances. We evaluate our method by comparing its compression ratios to recent algorithms. In

order to evaluate the visual quality of the intermediate meshes, we carried a perceptive evaluation with human

subjects. Results show that at equal rates, our method delivers an overall better visual quality. The algorithm

is particularly well suited for the compression of meshes where geometry and topology play a secondary role

compared to associated properties, such as with many scientiﬁc visualization models.

1 INTRODUCTION

Nowadays, 3D models are widely used in many ﬁelds

involving 3D graphics such as scientiﬁc visualization,

engineering, virtual reality, gaming, e-commerce and

education. They are becoming as popular as other

media types like audio, image and video. In recent

years, due to improvements in three dimensional data-

acquisition, storing and display devices, the demand

for high resolution models has exploded. This in-

crease in the complexity of 3D models brought the

need to use efﬁcient compression techniques in or-

der to satisfy the requirements of graphic applications

in terms of compact storage and fast transmission of

models. The increasing use of networked applica-

tions, low computational power devices (such as mo-

bile phones or PDAs) and huge size meshes calls for

progressive visualization of models through interme-

diate quality meshes.

A 3D mesh is made of geometry data and connec-

tivity data. However, in many cases there are prop-

erties associated to the mesh’s elements, most com-

monly to vertices. These properties can be colors,

normals, or, such as in the case of scientiﬁc visual-

ization, density or temperature values. Most recent

mesh compression algorithms focus only on geometry

and connectivity data compression. However, prop-

erty data can be as large or even larger in size than

geometry and connectivity data together, hence ded-

icated compression algorithms could greatly improve

coding efﬁciency. Moreover, existing techniques are

driven by geometry or connectivity, meaning that only

the geometry or the connectivity is taken into account

to optimize the compression, while associated prop-

erties play a secondary role.

In this work, we describe a framework that takes

into account vertex-bound associated properties for

the driving of the compression (the technique is there-

fore called data-driven), and that compresses the asso-

ciated properties together with the geometry and the

connectivity data. We believe that a compression pro-

cess driven by the associated properties will deliver

better results in terms of visual quality during decom-

pression, particularly for meshes where geometry and

topology play a secondary role compared to associ-

ated properties, such as with many scientiﬁc visual-

Cirio G., Lavoué G. and Dupont F. (2010).

A FRAMEWORK FOR DATA-DRIVEN PROGRESSIVE MESH COMPRESSION.

In Proceedings of the International Conference on Computer Graphics Theory and Applications, pages 5-12

DOI: 10.5220/0002813500050012

 SciTePress

ization models.

In the next section, we survey the existing tech-

niques for progressive mesh compression and asso-

ciated properties compression, and we describe the

few algorithms that take into account associated prop-

erties for data-driving. In section 3 we present our

algorithm for data-driven compression. In section 4

we compare our results with recent techniques and

present a perceptive evaluation of the quality of the

compressed meshes.

2 RELATED WORK

2.1 Progressive Mesh Compression

In this section, we brieﬂy describe the different ex-

isting approaches for progressive mesh compression.

For a more comprehensive review, we refer the reader

to (Peng et al., 2005).

Connectivity-based approaches ﬁrst process con-

nectivity data, with the vertices positions playing a

secondary role. (Hoppe, 1996) reported the ﬁrst tech-

nique, where he simpliﬁes the mesh by performing a

sequence of edge collapses. Later techniques focused

on improving the compression ratio by Vertex deci-

mation techniques, as in (Alliez and Desbrun, 2001),

or by extending single-rate methods to achieve pro-

gressivity such as in (Taubin and Rossignac, 1998).

More recent research has focused on geometry-

based approaches, achieving higher compression ra-

tios. (Gandoin and Devillers, 2002) proposed a kd-

tree space subdivision technique, where they recur-

sively subdivide the space in two cells and encode the

number of vertices contained in one of the child cells.

The geometry compression relies on the bit sharing

property, since grouping vertices in a common cell

makes them share the ﬁrst high-level bits of their po-

sitions. (Peng and Kuo, 2005) improve the technique

by using an octree subdivision and efﬁcient prediction

schemes, but at the cost of restricting the algorithm to

triangular meshes only. (Bordignon et al., 2006) ex-

tend (Gandoin and Devillers, 2002) algorithm by us-

ing a BSP-tree, in order to obtain child cells with the

same number of vertices and therefore maximize the

bit sharing property.

Other approaches for progressive mesh compres-

sion techniques exist, but are not well suited for our

requirements. (Karni and Gotsman, 2000) spectral

coding does not allow a local control of the com-

pression algorithm, making it inappropriate for data

driving. (Khodakovsky et al., 2000) wavelet based

compression requires special mesh properties, such as

regularity or piecewise regularity, and often a remesh-

ing pre-processing step. Since many applications can-

not afford these constraints, we do not consider these

techniques in our work.

2.2 Property Compression

The compression of mesh associated properties plays

a secondary role in recent compression schemes.

However, mesh properties can often be of greater size

than other mesh components: if we consider a color

3 ﬂoating-point value property attached to vertices,

both geometry and color data are equally important

in size. Here, we survey existing techniques that deal

with the progressive compression of these associated

properties.

(Waschbsch et al., 2004), while recursively con-

tracting pairs of neighboring vertices in point-clouds,

also contract their YUV color data. They encode the

color of the resulting point by delta coding with one

of the contracted points. The same method is ap-

plied for the coding of normals, using the normals

spherical coordinates. (Huang et al., 2008), with

their octree-based geometry compression data struc-

ture, further improve properties compression ratios

by using progressive normal quantization. The nor-

mal unit sphere, ﬁrst represented by an octahedron,

is subdivided along the mesh, and each normal of the

intermediate mesh is mapped to a facet of the sub-

divided octahedron, which leads to a progressive in-

crease in precision. The normal of a cell is the av-

erage of the normals of the vertices inside the cell.

For color compression, they use an optimized custom

color frame and adaptive quantization. Each compo-

nent is encoded through delta coding.

2.3 Data-driven Compression

Little research has been conducted to exploit asso-

ciated property data to drive the compression of the

geometry, in order to achieve a higher quality of the

intermediate meshes. The aim has been improving

the compression ratios and not necessarily the decom-

pression quality. To the best of our knowledge, there

are few papers which make the ﬁrst steps into data-

driven progressive mesh compression.

(Peng et al., 2006) recursively split the initial set

of vertices of the mesh into several child sets, through

the use of a distance metric applied on the geome-

try data and the normal property data. However, no

compression ratio is given. (Waschbsch et al., 2004),

as previously mentioned, recursively contract pairs of

neighboring points. In order to decide which pairs

will be contracted, and in order to obtain the best set

GRAPP 2010 - International Conference on Computer Graphics Theory and Applications

of pairs, they solve a minimum weight perfect match-

ing graph problem. The weight of each edge of the

graph is the sum of the distance between the two ver-

tices for each associated property, together with their

Euclidean distance. Each distance is given by a dis-

tance function that returns the difference between two

instances of the same property. In the examples given,

they use the normals as driving associated property,

and the distance between two normals is the cosine of

their enclosing angle. By taking into account normal

data, both techniques lead to an increased quality of

the intermediate levels of detail.

These algorithms show an initial concern for data-

driving the progressive compression of meshes. How-

ever, they do not provide a generic approach for

any kind of property or they exploit these properties

in a limited way. Inspired from (Waschbsch et al.,

2004) distance functions and based on (Gandoin and

Devillers, 2002) kd-tree compression technique, we

propose a framework for the data-driven progressive

compression of arbitrary meshes.

3 OUR DATA-DRIVEN

FRAMEWORK

The space subdivision techniques ((Gandoin and Dev-

illers, 2002) (Peng and Kuo, 2005) (Bordignon et al.,

2006)), while achieving high compression ratios, use

data structures that allow a certain ﬂexibility in the

splitting of a cell: the position of the cutting plane.

Our algorithm exploits this degree of freedom by

choosing, similarly to the BSP-tree algorithm from

(Bordignon et al., 2006), the position of the cutting

plane for each cell subdivision. The position is se-

lected according to a set of variables which are, in

our work, the associated properties. Due to the or-

thogonality constraint in the kd-tree cutting planes, a

kd-tree structure is cheaper to code than a BSP-tree.

We chose the kd-tree over the BSP-tree in a trade-off

between degrees of freedom and data overhead, and

over the octree for ﬂexibility reasons, since the oc-

tree requires cutting along each dimension iteratively,

while the kd-tree allows two or more consecutive cuts

along the same dimension.

The kd-tree structure is built by recursively split-

ting the cells in two, starting at the bounding box of

the mesh. The data-driven splitting algorithm, the

main contribution of our work, is described in sec-

tion 3.1. Then, in a bottom to top pass, connectivity

data is updated as described in (Gandoin and Dev-

illers, 2002). During the same pass, the associated

properties data are also updated, with each property

of the parent cell being the average of the correspond-

ing properties of the child cells. The property average

is computed through an average function associated

to each property type, as described in section 3.2. In

a third pass, from top to bottom, the data is encoded.

Along with the geometry and connectivity data en-

coding achieved in (Gandoin and Devillers, 2002), we

encode the cutting plane as described in section 3.3.

The associated properties data are encoded using delta

encoding.

3.1 Data-driven Cell Splitting

At each cell split we want to subdivide a set of ver-

tices into two sets through a plane orthogonal to an

axis of the reference frame. We deﬁne a discrete set

of equidistant planes orthogonal to each dimension of

the cell, and we compute a saliency value for each of

them. The saliency value represents the overall aver-

age weighted distance between the properties associ-

ated to the vertices on each side of the plane. We pick

the plane with the highest saliency value.

3.1.1 Local Voxelisation

The splitting process is represented in Figure 1 for

a 2D cell. We ﬁrst voxelise the entire cell as a pre-

processing step. The boundaries of the voxels are

deﬁned by the discrete set of planes for the cell, as

detailed in section 3.1.2. The properties of the ver-

tices inside each voxel are averaged so that each voxel

is represented by only one instance of each property.

Then, for each plane, each voxel in the plane neigh-

borhood is evaluated with its symmetric voxel with

respect to the plane, hence computing the distance of

every property for every pair of voxels. The saliency

value s of a plane is given by the average of the dis-

tance values d

i, p

for P properties p

to p

of the N

voxels on each side of its neighborhood:

s =

∑

j=0

(

∑

i=0

i, p

) (1)

This technique allows a local analysis of data,

which leads to a local vertex segmentation driven by

the associated properties. The plane with the high-

est saliency value is the one that captures the most

visible property difference according to the distance

criterion. Figure 2 compares the ﬁrst two cuts of the

data-driven and the non data-driven compression of

an example model with a simple color distribution.

3.1.2 Adaptive Precision

When a cell is voxelised, the number of planes of the

discrete set on each dimension deﬁnes the number

A FRAMEWORK FOR DATA-DRIVEN PROGRESSIVE MESH COMPRESSION

Figure 1: The cell (a) is voxelised (b) according to the dis-

crete planes, and each voxel averages the properties of the

vertices it contains. The algorithm iterates through the dis-

crete planes ( (c), (d), (e), (f) ), computing the property dis-

tances for every pair of symmetric voxels. The saliency

value of the plane is the weighted average of the average

property distances. The plane with the highest saliency

value is selected (g), and the cell is split according to the

selected plane (h).

Figure 2: Illustration of the ﬁrst two cuts (4 cells) of a sim-

ple model for the non data-driven (left) and the data-driven

(right) versions of the algorithm. The non data-driven cuts

subdvide the parent cell into 2 equal children cells, while

the data-driven cuts follow the color borders.

of voxels in the cell. The size of a voxel and the

efﬁciency of the split are directly related to the

number of planes. This number is computed for each

cell, and for each dimension, following 2 criteria:

The Cell Size. For a constant number of planes,

the bigger the cell the larger the separation between

planes, and hence the lower the accuracy of the split.

A bigger cell requires a larger discrete set of planes.

If l

is the length of the longest side of a cell C and

is the length of the corresponding side of the mesh

bounding box, the size criterion S is given by S =

The Number of Vertices of the Cell. The higher the

number of vertices in a cell, the larger the number of

planes should be in order to accurately separate the

set of vertices in two. Hence, we need to quantize the

surplus or the lack of vertices for a given cell volume.

For that, we normalize the number of vertices with the

expected number of vertices of the cell, which is the

number of vertices the cell would have if the vertices

were homogeneously distributed inside the bounding

box. If V

is the volume of C, V

is the volume of the

bounding box, P

is the number of vertices of C and

is the total number of vertices, the ratio criteron R

is given by R =

∗V

∗P

The number of discrete planes N

of a cell C is

therefore given by the following formula:

= N

max

∗ S

∗ R

where N

max

is the maximum number of planes set by

the user. We choose α = β =

to obtain a stagnating

behavior of N

. N

is bounded by 1 and N

max

in or-

der to avoid particular cases of extreme out-of-range

values.

3.2 Distance and Average Functions

For each associated property, we need to deﬁne

a distance and an average function. The distance

function is used in the subdivision process, while the

average function is used in the encoding process.

Distance Function. The distance function compares

two instances of a property and returns a positive

value representing a difference between them. It is

used in Equation 1 to compute the plane saliency.

For the color property, we can deﬁne the distance

between two colors as their Euclidean distance in

the Luv space, as proposed in (Waschbsch et al.,

2004). The Luv space is better suited for human

perception of colors than the RGB space, since

distances between colors in the Luv space are closer

to distances perceived by a human eye than their

corresponding RGB space distances. Moreover, the

Luv space decorrelates color information redundant

in the RGB space, which improves coding efﬁciency.

Average Function. The average function should re-

turn a property instance that closely represents both

input instances. For the color property, an appropriate

average function is the 3-tuple of the averages of each

Luv space component.

3.3 Plane Coding

Two extra values need to be encoded for each non-

empty cell in order to recover the cutting planes dur-

ing the decompression process: the dimension to

which the cutting plane is orthogonal to, and the index

of the cutting plane among the discrete set of planes

GRAPP 2010 - International Conference on Computer Graphics Theory and Applications

(a) (b) (c) (d) (e) (f)

Figure 3: Some models from the Princeton Shape Benchmark repository data set: birdy (a), cleaver (b), gangster (c), dice (d),

dog (e), montgolf (f).

of that dimension of the cell. The dimension is arith-

metically encoded, using the parent and the grand-

parent cutting planes dimension as context. This re-

duces the cost of coding the dimension by around

60%. Since the number of discrete planes N

is cell

dependent and can be computed at decompression

time, the index of the cutting plane is arithmetically

encoded with N

as context.

4 RESULTS

In the following section we quantitatively and qualita-

tively evaluate the compression ratios and decompres-

sion qualities of sets of colored meshes. We use the

color mesh property to drive the compression process

with the color distance and average functions previ-

ously described.

We quantitatively evaluate the geometric quality

of the intermediate levels of detail of several 3D

models using the METRO (Cignoni et al., 1998)

rate/distortion evaluation tool. However, this geomet-

ric distance does not reﬂect the perceptual visual qual-

ity of the meshes, which depends in part on the color

property. Therefore, we also carried perceptive eval-

uations through subjective experiments with human

subjects (experts and non experts) in order to compare

the results of our algorithm with its non data-driven

version. The non data-driven version splits cells at

their center, as in (Gandoin and Devillers, 2002).

A ﬁrst set of colored meshes was chosen among

the original meshes of the Princeton Shape Bench-

mark repository (Shilane et al., 2004). We selected a

set of 8 heterogeneous models that we used through-

out our quantitative tests and subjective experiments.

Some of the models are shown in Figure 3. The num-

ber of vertices ranged from 4000 to 17000.

A second set of 8 colored meshes was provided

by EDF R&D (Energie de France Research and De-

velopment) division. The meshes are examples of

CAD machinery parts and scientiﬁc computation out-

puts of thermal ﬂows. Unfortunately, this data set is

conﬁdential, with the exception of the radiator sam-

Figure 4: The radiator, from the EDF R&D data set.

ple shown in Figure 4. The number of vertices of the

meshes of this data set ranges from 26000 to 322000.

This dataset was used during a perceptive evaluation

performed by EDF R&D experts.

4.1 Rate/Distortion

In order to evaluate the geometry quality of the in-

termediate meshes, we computed distortion values at

several bitrates. The geometry distortion value for a

particular bitrate is given by the Hausdorff distance

between the original (lossless) mesh and the inter-

mediate mesh at that particular bitrate. We used the

METRO (Cignoni et al., 1998) tool for the computa-

tions. Results are given in Figure 5, which show the

rate-distortion (R-D) curves of the data-driven and the

non data-driven compression of 3 different models of

the ﬁrst set of meshes.

At low bitrates, the data-driven method performs

worse than the non data-driven version, in terms of

geometric distortion. This behaviour was expected,

since the algorithm is optimized for higher associated

properties quality, while the METRO tool judges ge-

ometry quality. At higher bitrates, we can notice that

both versions of the meshes are roughly equivalent in

geometry. It is interesting to point out that the distor-

tion difference remains small for the tested dataset,

meaning that the gain on the associated properties

side is achieved at a small cost. Since a purely ge-

ometric distance is not well suited to evaluate the vi-

sual quality of a mesh, particularly for colored meshes

where color may carry an important part of the visual

A FRAMEWORK FOR DATA-DRIVEN PROGRESSIVE MESH COMPRESSION

Figure 5: R-D curves for 3 of the evaluated meshes (birdy, dice and gangster). Abscissa: bitrates (in bits per vertex). Ordinates:

Hausdorff distances.

information, we proceeded to human perceptive eval-

uations through subjective experiments.

4.2 Perceptive Evaluation

In order to demonstrate that our data-driven method

increases the visual quality of the intermediate

meshes compared to its non data-driven counterpart,

we have conducted two subjective experiments using

human observers. These two experiments share the

same evaluation protocol. However, the data sets and

the expertise of the human observers are different.

4.2.1 Evaluation Protocol

The evaluation protocol was as follows: we presented

to each evaluator 4 intermediate meshes at a time, to-

gether with the original lossless model. The inter-

mediate meshes were composed of 2 data-driven in-

termediate meshes and their corresponding non data-

driven version of the same bitrates, in random posi-

tions. The evaluator could rotate, scale and translate

the models. A transformation applied to one of the

meshes was also automatically applied to all the other

meshes on the screen, in order to keep a consistent

point of view. The evaluator was asked to provide

a score for each object, reﬂecting the degree of per-

ceived visual similarity with the original, from 1 (no

similarity) to 6 (highest similarity). The Mean Opin-

ion Score (MOS) is then computed for each interme-

diate mesh of each model of each corpus:

MOS

∑

j=1

i j

where MOS

is the mean opinion score of the i

ob-

ject, n is the number of evaluators, and m

i j

is the score

(∈ [1, 6]) given by the j

evaluator to the i

object.

For each model of the data sets, we evaluated

4 different bitrates, which required 8 intermediate

meshes (4 data-driven, 4 non data-driven). Since only

4 intermediate meshes could be shown on the screen

at a time for a confortable visualization, each model

was fully evaluated in two independent steps: the low

step, with the 2 lower bitrates, and the high step, with

the other 2 bitrates. The high step immediately fol-

lowed the low step.

Since we noticed that, at high resolutions, our al-

gorithm performs roughly equally than the non data-

driven version, we believed it was more interesting to

compare the two algorithms at low bitrates. The color

property was compressed with 9, 6 and 6 bits per color

component (L, u and v) respectively. Geometry was

compressed with 14 bits per coordinate.

4.2.2 First Experiment: Princeton Shape

Benchmark Data Set

Eight color models from the Princeton Shape Bench-

mark repository data set (Figure 3) were evaluated

by 12 human subjects, from the research staff of the

LIRIS laboratory in Lyon, France, with different de-

grees of knowledge in the computational geometry

and computer graphics ﬁeld. For this experiment, we

chose 4 ﬁxed bitrates: 2, 3, 4 and 6 bits per vertex

(bpv). Hence our corpus was composed of 64 ob-

jects (8 models * (4 data driven version + 4 non-data-

driven version) ). Table 1 details the Mean Opinion

Scores (MOS) for the models of the dataset, accord-

ing to the bitrate and the method (data-driven vs. non

data-driven).

The results show a positive evaluation for most of

the meshes of the set, where the data-driven algorithm

is evaluated from roughly equal (no MOS difference)

to considerably better (more than 1 point in MOS dif-

ference) than its non data-driven counterpart. Clear

examples are the dog (Figure 6) and cleaver (Figure

7) models, where different color regions can be dis-

tinguished from an early stage in the data-driven ver-

sion, hence the overall visual quality is clearly im-

proved even if the geometric distorsion is higher than

for the non-data-driven version. However, for some

models (for instance montgolf) the geometric distor-

tion breaks the overall shape of the model, and there-

fore the data-driven version has lower MOS than its

non data-driven couterpart, regardless of the color vi-

GRAPP 2010 - International Conference on Computer Graphics Theory and Applications

sual quality of the data-driven model.

Table 1: Mean Opinion Scores for the models of the Prince-

ton Shape Benchmark data set, at all tested bitrates, for the

data-driven and the non data-driven algorithms.

Non data-driven Data-driven

2 3 4 6 2 3 4 6

dog 2.8 4.1 4 4.4 3 4.2 4.6 5.2

cleaver 4.1 4.5 4.1 4.3 4.5 4.6 4.6 5

montgolf 3.5 4 3.6 4 2.3 3 2.8 3.7

tuna 3.7 4.1 4.4 5.1 4.3 4.9 5 5.2

dice 2.3 2.7 3 3.5 2.9 3.3 3.4 3.8

gangster 3 3.5 3.4 3.9 3.3 3.4 3.7 4.1

chair 3.3 3.6 4 4.2 3.1 3.5 3.8 4

birdy 3.5 3.6 4.3 4.5 4 4.2 4.9 5

Average 3.28 3.76 3.85 4.24 3.43 3.89 4.1 4.5

Figure 6: The non data-driven (left) and the data-driven

(right) intermediate meshes for the dog model at 3 bpv.

Figure 7: The non data-driven (left) and the data-driven

(right) intermediate meshes for the cleaver model at 2 bpv.

For many of the models, the MOS at a particu-

lar bitrate with the data-driven algorithm was equal

or higher than the MOS of the next (higher) bitrate

with the non data-driven algorithm, like with bitrates

4 and 6 of the dog model, for instance. In such cases,

both the compression ratio and the visual quality are

improved by our method.

It is interesting to see that, even if our data-

driving algorithm exhibits a rate-distorsion compro-

mise slightly worse than the non data-driven one, on

the contrary the rate-quality compromise is greatly

improved.

4.2.3 Second Experiment: EDF Data Set

Five color models from EDF R&D Clamart were eval-

uated by 7 EDF physicists and 3D experts. There

were considerable differences in the number of poly-

gons among the models of this dataset. Therefore,

instead of using ﬁxed bitrates for all the models, we

chose bitrates corresponding to 5, 10, 15 and 20%

of the ﬁle size of the non data-driven lossless com-

pressed model. Resolutions under 5% were usually

too coarse for any visual evaluation, and resolutions

higher than 20% were less interesting due to the close

ressemblance between the results of both algorithms.

For this experiment, we included the normal data in

the compression process, but only as encoded data,

not as a driving property. This produced intermediate

meshes of a higher rendering quality, for both algo-

rithms.

The data-driven algorithm produced higher qual-

ity intermediate meshes for 3 of the 5 models (higher

MOS), as shown in Table 2. The models where the

data-driven algorithm was rated lowerer than its non

data-driven counterpart were the radiator and a sec-

ond model where color regions were hard to distin-

guish even in its lossless version. For the case of the

radiator, the compressed version presented an impor-

tant visual distortion, due to its rough parallelepipedal

shape, with any break in the continuity of the con-

tours being easily noticeable, decreasing distortion

tolerance. Figure 8 compares the result of the algo-

rithms for a bitrate where the data-driven algorithm

was given a higher grade.

Table 2: Mean Opinion Scores for the models of the EDF

data set, at all tested bitrates, for the data-driven and the non

data-driven algorithm.

Non data-driven Data-driven

5% 10% 15% 20% 5% 10% 15% 20%

1 2.8 3.4 3.9 4.3 2.3 3.2 3.8 4.3

radiator 2.2 3.7 2.2 4 1.3 2.5 2.5 3.5

3 2.8 3.1 3 3.4 3.3 3.7 3.8 4

4 2.6 2.7 3 3.3 2.3 2.5 3 3.6

5 3.1 3.4 3.5 4.2 3.4 3.6 3.6 4.2

Average 2.7 3.26 3.12 3.84 2.52 3.1 3.34 3.92

Figure 8: The non data-driven (left) and the data-driven

(right) intermediate meshes for the radiator model at 6 bpv

(15%).

A FRAMEWORK FOR DATA-DRIVEN PROGRESSIVE MESH COMPRESSION

An interesting remark can be made based on the re-

sults of the evaluation. Two of the evaluators sys-

tematically gave a lower grade to the data-driven al-

gorithm, for every model at every evaluated bitrate.

Even in situations where all of the other evaluators

gave a signiﬁcant advantage to the data-driven al-

gorithm, these 2 evaluators graded it lower. We

could therefore think that some individuals are or be-

come more sensitive to geometry distortion than oth-

ers. These two subjective experiments have shown

that driving the compression with attributes like color

can improve the rate-quality compromise, whereas

producing a slighty higher geometric distorsion. Of

course this improvement depends on the geometric

structure of the object and on the importance of the

attributes in its visual appearance: we have noticed

that it is more interesting to use our compression tech-

nique on objects where the important data is color,

instead of meshes where the geometry-color tradeoff

can dramatically deteriorate the overall visual quality.

5 CONCLUSIONS

We have presented a framework for the data-driven

progressive compression of meshes. It allows the use

of any associated property, and the behavior of the

compression process can be customized through a sin-

gle distance function per property. We showed an ex-

ample of color data-driving and compression of the

color property. At equal bitrates, it improves the vi-

sual quality of the decompressed meshes compared to

the non data-driven version. This algorithm is well

suited for the compression of meshes where geome-

try and topology play a secondary role compared to

associated properties, such as with scientiﬁc visual-

ization models. This work sets the bases for further

research around the concept of data-driven compres-

sion. The performance of the algorithm relies in part

on efﬁcient distance functions. Other properties will

be considered for testing, such as normals. More

complex and efﬁcient distance functions could be de-

ﬁned for intrinsic properties such as curvature tensors

and connectivity data, in order to improve the geo-

metric shape of the intermediate meshes. Moreover,

a BSP-tree could be used to allow more ﬂexible cuts.

However, special attention would have to be given to

plane coding and overall processing time.

ACKNOWLEDGEMENTS

This work has been supported by French National Re-

search Agency (ANR) through SCOS project (ANR-

06-TLOG-029) and COSINUS program (project

COLLAVIZ ANR-08-COSI-003). The authors would

like to thank R. Marc and C. Mouton from EDF for

their help regarding the perceptive evaluation.

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