QUALITY PERCEPTION OF SIMPLIFIED MODELS: NSA V S.

QSLIM

Frutuoso G. M. Silva

IT - Networks and Multimedia Group

Department of Computer Science and Engineering

University of Beira Interior, Portugal

Samuel S. Silva

Institute of Electronics and Telematics Engineering of Aveiro

University of Aveiro, Portugal

Keywords:

Simpliﬁcation algorithms, Meshes, Quality perception.

Abstract:

Quality perception of simpliﬁed models is an important aspect for several applications. But, it is normally

evaluated only based on the analysis of geometrical errors of the simpliﬁed models. However, the analysis of

geometrical errors is not enough to evaluate the quality of the simpliﬁed models. The quality of the simpliﬁed

models and the execution times are the main aspects that distinguish the simpliﬁcation algorithms. These

algorithms are of great interest in a variety of areas, since they allow the replacement of large models by

approximations with far fewer cells for manipulation and visualization purposes.

This paper presents a comparison between two simpliﬁcation algorithms, NSA and Qslim, and shows the

difference between geometrical and graphical quality of the models. The comparison of results was made

using the PolyMeCo tool, which enables the analysis and comparison of meshes by providing an environment

where several visualization options and metrics are available and can be used in a coordinated way.

1 INTRODUCTION

The sophisticated modeling systems and 3D data ac-

quisition technologies enable us to create complex

and detailed geometric models. But in several appli-

cation ﬁelds these models are approximated by polyg-

onal meshes for manipulation purposes because of

their mathematical simplicity. However these mod-

els have normally redundant information that can be

removed.

Simplifying a polygonal mesh M

i

consists in gen-

erating another mesh M

j

with a lower number of cells.

The resulting mesh obeys a target criterion, which is

normally a measure of a maximum admissible error.

This error can be evaluated using different metrics and

the main difference between the algorithms is the met-

ric chosen. This metric has an inﬂuence in the quality

of generated meshes and also in the time performance

of the simpliﬁcation algorithm.

The quality of the model can be evaluated using

different tools and metrics, and it is important to eval-

uate the geometric and graphical quality of the mod-

els. Normally, most works present only the results of

geometric quality ignoring the graphical quality of the

models. But quality perception of the simpliﬁed mod-

els depends both on geometrical and graphical qual-

ity. Note that the graphical quality (i.e., the visual

quality of the model) depends on several factors and

not only of the geometric quality of the model.

In this work the geometrical and graphical qual-

ity of the simpliﬁed models was compared for NSA

and Qslim algorithms using the PolyMeCo tool. This

tool provides an environment with several visualiza-

tion options and metrics which allow their usage in a

systematic and efﬁcient way enabling a better percep-

tion of model quality.

Section 2 presents an overview of mesh compari-

son tools. The PolyMeCo tool is brieﬂy described in

Section 3. The NSA algorithm is presented in Section

4, and the experimental results are discussed in Sec-

tion 5. Finally, Section 6 presents some conclusions.

2 MESH COMPARISON TOOLS

Mesh comparison is usually carried out with the help

of dedicated software tools that provide a numerical

and visual representation of the data, for example, the

74

G. M. Silva F. and S. Silva S. (2008).

QUALITY PERCEPTION OF SIMPLIFIED MODELS: NSA V S. QSLIM.

In Proceedings of the Third International Conference on Computer Graphics Theory and Applications, pages 74-79

DOI: 10.5220/0001094900740079

Copyright

c

SciTePress

minimum, mean and maximum value for a metric and

a model colored according to the obtained values at

each mesh vertex/face.

A few tools allowing features evaluation and

comparison are described in the literature. The

Metro (Cignoni et al., 1998b) tool, allows compar-

ing two polygonal meshes by computing the geomet-

ric distance between them and by depicting the results

using a colored model. It also provides the computa-

tion of the Hausdorff distance. According to the lit-

erature, this is the most used tool for mesh compar-

ison. Another tool, proposed by Zhou et al. (Zhou

and Pang, 2001), introduces some additional mea-

sures (e.g., surface curvature) and provides a few dif-

ferent visualization options (e.g., side-by-side view of

models). The MESH tool, developed by Aspert et

al. (Aspert et al., 2002), uses the Hausdorff distance

to measure the difference between two models and

presents a model colored according to the obtained re-

sults. The MeshDev (Roy et al., 2004) tool allows the

computation of geometric, normal, and other mesh at-

tribute deviations such as color and texture. Its output

is a VRML model depicting the obtained results.

However, these tools provide a small amount of

quality measures and lack several features which

would enable a more systematic comparison process.

To evaluate the results obtained, for example, with

different simpliﬁcation methods, it is often necessary

to compare many models in order to reach a conclu-

sion. So, it is desirable that the mesh comparison tools

used support several models simultaneously for an ef-

ﬁcient comparison of the results.

PolyMeCo is such a tool, and an overview of its

main features will be presented in the next Section.

3 POLYMECO TOOL

PolyMeCo (Silva et al., 2005) is a tool under devel-

opment, which provides an integrated environment

where mesh analysis and comparison can be per-

formed using several quality measures. Besides, the

results are properly presented to the user using dif-

ferent visualization options. These options include,

among others:

- Original vs Processed vs Colored Model, which

allows the simultaneous view of both models being

compared and a model colored according to the data

obtained with a particular measure;

- Features Comparison which allows the visualization

of data distributions obtained with the same compu-

tational measure for several processed models. This

can be very useful in situations where the purpose is

to study different processing algorithms and compare

the obtained results. In order to allow a proper com-

parison using colored models, PolyMeCo allows us-

ing a common color map for all compared models,

i.e., the maximum data value across all models is ob-

tained and all models are colored according to it. To

the best of our knowledge, this feature is not avail-

able in any other tool for mesh analysis and compari-

son and can signiﬁcantly improve the way how users

explore the results. This option enables a better per-

ception of what is really happening with the analysed

models by inspecting the colored models only.

To analyse and compare polygonal meshes several

computational measures are available in PolyMeCo

and they can be divided in two groups: intrinsic prop-

erties and difference measures. Intrinsic

1

properties

allow the measurement of a particular property of a

mesh. Difference measures allow the comparison of

properties between two meshes, in general, the origi-

nal mesh and a processed version (e.g., through sim-

pliﬁcation or compression).

For more details about the intrinsic properties

and difference measures available in PolyMeCo tool

see (Silva et al., 2005). A version of PolyMeCo for

test purposes is available in http://www.ieeta.pt/

polymeco/.

4 THE NSA ALGORITHM

There are several types of algorithms for simplifying

a polygonal mesh (see (Cignoni et al., 1998a), (Puppo

and Scopigno, 1997) and (Luebke, 2001)). They can

be broadly categorized into three classes: cell deci-

mation, vertex clustering and edge collapse.

The edge collapse algorithms simpliﬁes a mesh by

iteratively collapsing edges into vertices. They tend to

preserve the topology but they may change it by col-

lapsing pairs of vertices that are not connected by an

edge (i.e., a ghost edge). The edge collapse operation

has the disadvantage that it may cause local surface

inversion.

The edge collapsing operation is standard. The

main difference between the various edge collapsing-

based simpliﬁcation algorithms is the criterion used to

choose the next edge to collapse. A different criterion

implies different mesh quality, as well as a distinct

processing time. Generally, all simpliﬁcation algo-

rithms make a trade-off between speed and the quality

of the resulting mesh.

QSlim algorithm follows a geometric criterion

that is based on the minimization of the error associ-

ated with each new vertex. This error is deﬁned as the

1

Meaning a property which can be obtained from a mesh

regardless of any other mesh.

QUALITY PERCEPTION OF SIMPLIFIED MODELS: NSA VS. QSLIM

75

sum of the squared distances to the set of planes sur-

rounding the pair of the original collapsing vertices.

Thus, this algorithm produces simpliﬁed meshes with

a very good geometric quality since it minimizes the

error associated with each new vertex.

The simpliﬁcation criterion used by NSA algo-

rithm is guided by the normal angle metric that is very

simple to compute. Thus, an edge is only collapsed

if the variation of the face normals around the target

edge (i.e., the faces that are incident on both vertices

adjacent to the edge) are within a given tolerance ε.

The value of ε is the threshold for the angle between

the current normal and the new normal after the edge

collapse operation.

In NSA algorithm the value of ε is adjusted auto-

matically according to the desirable reduction of the

number of faces of the mesh. A severe simpliﬁcation

of the model, i.e., a great reduction in the number of

faces, implies a large value of ε. A small simpliﬁca-

tion of the model implies a small value of ε. Note that

the number of faces of the mesh that will be created

is a input parameter to the NSA algorithm.

The normal angle criterion implies that the region

around the collapsing edge is nearly coplanar. In these

circumstances, we say that a region is quasi-coplanar.

But, the contrary is not true, i.e., the coplanarity does

not ensure a minimal variation of the face normals be-

cause we can have coplanar faces with opposite orien-

tations.

NSA algorithm guarantees the quasi-coplanarity

of the region to simplify and, at the same time, pre-

vents possible local folding or partial face overlapping

of the resulting mesh, because the edge collapse op-

eration is only allowed if the variation of the normals

is less than ε. Note that these situations have a great

variation of the face normals (see (Silva, 2007)).

Most authors distinguish between the simpliﬁca-

tion criterion (i.e., the criterion to choose the next

edge to collapse) and the criterion that validates the

edge collapse operation. On the contrary, NSA al-

gorithm uses the same normal-based criterion to sim-

plify and validate the edge collapse operation.

NSA algorithm preserves the mesh boundaries be-

cause the collapse operation is not allowed whenever

at least one edge neighboring the collapsing edge has

only a single face incident on it. This means that the

boundary edges are never collapsed, so the boundaries

are always preserved. Thus, it produces very good ap-

proximations preserving the original visual shape and

the boundaries of the original model.

Note that the NSA algorithm was developed ini-

tially for multiresolution purposes. But a new imple-

mentation of the NSA algorithm alone was created as

a general simpliﬁcation algorithm of meshes (Silva,

2007) and it is available for test purposes in

http://www.di.ubi.pt/

˜

fsilva/nsa/.

5 EXPERIMENTAL RESULTS

The comparisons are made with QSlim algo-

rithm (Garland and Heckbert, 1997) because it is re-

ferred in the literature as the algorithm that produces

better results quickly. Besides, QSlim is available

from http://www.cs.cmu.edu/

˜

garland, which

enabled running both algorithms in the same machine

for the same models.

Several models are used in the comparisons be-

tween NSA and QSlim, however, due to limited space

the results presented in this paper are based only on

the four models pictured in Figure 1. The tests were

performed with both algorithms on the same machine,

a PC Pentium(R) D at 3.20GHz with 4GB of RAM

running XP operating system.

Figure 1: The four models used in this work. The FLASCHE.

model has 85524 faces (left); the BUNNY model has 69473

faces (middle left); the FANDISK model has 12946 faces

(middle right); and the BLOCKFS model has 25542 faces

(right).

5.1 Time Performance

Table 1 shows the time performance for both algo-

rithms, NSA and QSlim. As we can see, the NSA

algorithm is always the fastest algorithm for all tested

models. However, the difference of times is more sig-

niﬁcant for CAD models (i.e., models with planar re-

gions as FANDISK and BLOCKFS). For example, with

the BLOCKFS and FANDISK models the NSA algo-

rithm is on average 8 to 10 times faster than QSlim

algorithm. But, with the BUNNY and FLASCHE mod-

els it is only on average 1.1 to 1.5 times faster than

QSlim algorithm.

The type of the model is important for the per-

formance of simpliﬁcation algorithms. For example,

the QSlim algorithm spends much more time to sim-

plify CAD models (see Table 1) than for other mod-

els. However, the run times for NSA algorithm show

us that NSA algorithm is more sensible to the number

of cells than to the type of model. Besides, the NSA

GRAPP 2008 - International Conference on Computer Graphics Theory and Applications

76

algorithm produces models with high graphical qual-

ity (i.e., a more regular mesh) compared with QSlim

algorithm, in particularly for CAD models as we will

see in the next Section.

Table 1: Simpliﬁcation times for NSA and QSlim.

Models # of faces NSA times QSlim times

Fandisk 8000 0.047 sec 0.687 sec

Fandisk 6000 0.062 sec 0.702 sec

Fandisk 4000 0.093 sec 0.717 sec

Fandisk 1200 0.125 sec 0.733 sec

BlockFS 15000 0.094 sec 1.421 sec

BlockFS 12000 0.125 sec 1.609 sec

BlockFS 8000 0.171 sec 1.749 sec

BlockFS 4000 0.203 sec 1.765 sec

BlockFS 2000 0.234 sec 1.796 sec

Bunny 34999 0.438 sec 0.702 sec

Bunny 24999 0.532 sec 0.843 sec

Bunny 14999 0.657 sec 0.952 sec

Bunny 5999 0.750 sec 1.030 sec

Flasche 45000 0.515 sec 0.702 sec

Flasche 35000 0.657 sec 0.796 sec

Flasche 20000 0.829 sec 0.937 sec

Flasche 8500 0.954 sec 1.046 sec

5.2 Model Quality

Model quality can be evaluated using different tools

and by different metrics. However, it is important

evaluating the geometric and graphical quality of the

models. Normally, most of the works present only

the results of geometric quality and ignore the results

of the graphical quality of the models. In this work

the geometrical and graphical quality was compared

using the PolyMeCo tool (Silva et al., 2007a). This

tool enable us a more systematic perception of the re-

sults, for example using a side-by-side viewing with a

equalized color scale.

5.2.1 Quality Metrics

There are several metrics available in PolyMeCo tool

to compare the obtained models, but for this work

we only use the most important of them to compare

the geometrical vs. graphical quality. Thus, we select

six metrics, three that compute the intrinsic proper-

ties and the other three that compute difference mea-

sures. Thus, the metrics used to evaluate the results

are the following: Geometric Deviation (GD), Nor-

mal Deviation (ND), Composed Deviation (COMP2),

Smoothness Analysis (SA3), Mean Curvature Analy-

sis (MCA) and Angle Analysis (AA).

The geometric deviation is the most commonly

used metric in the literature to compare polygonal

meshes. But, as said before, the results obtained do

not necessarily express the perceived quality of the

simpliﬁed models.

The normal deviation relates with the shape of the

model and particularly with how the model is viewed

due to the strong relation between surface normals

and light computation.

The composed deviation is a quality metric being

developed based upon perceived quality results ob-

tained using observer studies. Even though it still

needs to be further enhanced it proved to be a very

good estimator of user perceived quality in some spe-

ciﬁc conditions (Silva et al., 2007b).

The smoothness analysis measures how smooth is

a surface. It is considered as an important character-

istic of a surface which inﬂuences how its quality is

perceived (Karni and Gotsman, 2000).

The mean curvature is an important characteristic

of a surface, related with its shape, smoothness and,

consequently, surface normals.

Finally, the quality of the triangles composing a

mesh has been widely considered in Finite Element

Methods in order to obtain meshes with good numer-

ical characteristics. But, triangle quality (shape) is

also important when rendering the models, because

malformed (thin) triangles tend to result in visual ar-

tifacts which inﬂuence perceived quality.

Beyond all these quality metrics, PolyMeCo pro-

vides an additional (and important) feature to qual-

itatively evaluate perceptual quality. Its integrated

environment, where all tested models can be loaded

in a single work session, allows visually analy-

sis/comparison of the models which helps to under-

stand the meaning of the results obtained with the

quality metrics.

5.2.2 Analysis of Results

All the ﬁgures presented in this work use the same

color scale with a common color mapping among all

presented models, enabling us to see the real differ-

ences between the results of the algorithms.

Figure 2 shows the results of four metrics (GD,

ND, AA, and COMP) for a 8000-faces simpliﬁed

BLOCKFS model for both algorithms, NSA and QS-

lim. The Figures 2 a) to d) created by NSA and the

Figures 2 e) to h) created by QSlim show the met-

rics for the simpliﬁed model. In this case only the

geometric deviation is favorable to QSlim algorithm

while normal deviation, angle analysis and composed

analysis are favorable to NSA algorithm. Note that

the simpliﬁed BLOCKFS model produced by QSlim

has also geometric problems as show the Figures 3(b)

QUALITY PERCEPTION OF SIMPLIFIED MODELS: NSA VS. QSLIM

77

(a) GD (b) ND (c) AA (d) COMP

(e) GD (f) ND (g) AA (h) COMP

Figure 2: The simpliﬁed BLOCKFS. model. In the ﬁrst row

are the results of the NSA algorithm and in the second row

are the results of the QSlim algorithm.

(a) NSA (b) QSlim (c) NSA (d) QSlim

Figure 3: A 15000-faces simpliﬁed BLOCKFS. model cre-

ated by NSA and QSlim algorithms.

and (d) but, on the contrary, the simpliﬁed BLOCKFS

model produced by NSA algorithm is correct as show

the Figures 3(a) and (c).

Other model tested with both algorithms was the

FLASCHE model which has planar regions. In this

case only the angle analysis is favorable to NSA algo-

rithm, i.e., the graphical quality of the model created

by NSA algorithm is better than the graphical qual-

ity of the model created by QSlim algorithm. Thus,

the model created by NSA algorithm is more ade-

quate for visualization purposes because the mesh is

more regular. On the contrary, the geometrical qual-

ity of the model created by QSlim algorithm is better

than the geometrical quality of the model created by

NSA algorithm, i.e., the model created by QSlim have

smaller geometric errors (see (Silva, 2007)).

For the BUNNY model, all the results are favorable

to QSlim algorithm. This fact is due to the simpliﬁca-

tion criterion of the NSA algorithm which is based on

the planarity of the model surface. Since the BUNNY

model has not planar regions the meshes produced by

NSA algorithm have lower quality (see (Silva, 2007)).

Finally, the last model tested with both algorithms

is the FANDISK which have planar regions. Figure 4

shows a simpliﬁed 4000-faces FANDISK model. The

results for NSA algorithm are pictured in Figures 4

d), e), f), j), k) and l), and the results for QSlim al-

gorithm are pictured in Figures 4 g), h), i), m), n)

and o). The Figures 4 b) and c) show a 4000-faces

simpliﬁed FANDISK model created by NSA and QS-

lim algorithms, respectively. As you can see in this

case only the geometric deviation metric is favorable

to the QSlim algorithm (see Figures 4(d) and (g)). All

the others metrics (ND, COMP, AA, MCA, and SA)

are favorable to the NSA algorithm. We can also ob-

serve that the simpliﬁed model created by QSlim (Fig-

ure 4(c)) have geometric problems. On the contrary,

the model created by NSA algorithm have a correct

geometry as shows the Figure 4(b).

Both the models, FANDISK and BLOCKFS, have

planar regions where the QSlim algorithm generates

problems in the geometry as conﬁrmed by the simpli-

ﬁed models and by the angle analysis metric (AA) in

Figure 4 and Figure 2. Thus for models without pla-

nar regions the QSlim algorithm generates good sim-

pliﬁed models but always spends more time, as the

case of BUNNY model.

Thus for the models with planar regions we can

say that NSA algorithm produces better simpliﬁca-

tions than QSlim algorithm. For models without pla-

nar regions normally the QSlim algorithm produces

better simpliﬁcations than NSA algorithm, but some

times with inferior graphical quality.

6 CONCLUSIONS

The PolyMeCo tool provided the possibility of

analysing several simpliﬁed meshes using a large

range of metrics, which allowed a more precise eval-

uation of the simpliﬁcation algorithms. The available

visualization options allowed a clearer understanding

of the numerical values as well as the problems re-

lated to them. A clear example is the Angle Analysis

metric that detects thin triangles which are not ade-

quate for visualization.

The analysis and comparison of mesh properties

can be performed with the help of 3D models. For

example, a model is colored according to the value

obtained for each vertex/face. This coloring can be

performed by mapping the values range to a particular

color scale and it is important to use common color

maps among the compared models in order to attain a

correct perception of the results.

The NSA algorithm is faster than the QSlim algo-

rithm for all types of models, but in particularly for

CAD models. Besides, for CAD models the QSlim

algorithm generates simpliﬁed models with geomet-

ric/topological problems. On the contrary, the NSA

algorithm produces always valid geometric models.

GRAPP 2008 - International Conference on Computer Graphics Theory and Applications

78

The results show that even though Qslim always cre-

ated simpliﬁed models with high geometric quality

they sometimes have inferior graphical quality. Thus,

if the original model has a large number of planar re-

gions, and visual quality is the most important crite-

rion, then the QSlim algorithm might not be the algo-

rithm of choice. For these cases the NSA algorithm is

the right choice because it always creates valid mod-

els with a good graphical quality.

(a) Original (b) NSA version (c) QSlim version

(d) GD -nsa (e) ND - nsa (f) MCA - nsa

(g) GD - qslim (h) ND - qslim (i) MCA - qslim

(j) COMP - nsa (k) AA- nsa (l) SA - nsa

(m) COMP - qs-

lim

(n) AA- qslim (o) SA - qslim

Figure 4: The results of several metrics for a 4000-faces

simpliﬁed FANDISK. model for algorithms NSA and QS-

lim.

ACKNOWLEDGEMENTS

The second author would like to thank research unit

127/94 IEETA of the University of Aveiro for the

grant that supported his work.

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