DEBLOCKING FOR DYNAMIC TRIANGLE MESHES

Jan Rus and Libor V´aˇsa

Department of Computer Science and Engineering, Faculty of Applied Sciences

University of West Bohemia, Univerzitn´ı 8, Plzeˇn, Czech Republic

Keywords:

Static Triangle Meshes, Dynamic Triangle Meshes, Data Compression, Coddyac, Clustering, Blocking

Artifacts, Deblocking, Visual Quality.

Abstract:

Mesh segmentation (clustering) is a useful tool, which improves compression performance. On the other hand,

per-partes processing of meshes often leads to new types of artifacts - cracks and shifts on the borders between

clusters. These artifacts are detected by both, Human Visual System (HVS) and perceptually-motivated dis-

tortion metrics. In this paper, we present a post processing algorithm, which aims at reducing such artifacts

without needing any additional data - using only information about the cluster distribution that is already

present at the decoder. A rigid transformation, which minimises the border artifacts, is iteratively computed

and applied per cluster. Our experiments show that this approach leads to a reduction of distortion, as mea-

sured by the STED metric, by up to 18% for low bitrates. We also present visual results conﬁrming that the

improvement is well visible.

1 INTRODUCTION

The use of 3D data in the form of triangle meshes

is widespread. A great many examples of using this

kind of data can be found in engineering applications

or in ﬁlm and gaming industry. These examples in-

clude not only static, but also dynamic meshes — 3D

animations, which are usually represented by a series

of static triangle meshes, one mesh for each frame of

the animation. This kind of data representation is usu-

ally voluminous and needs to be compressed using a

specialised compressionalgorithm to achieveefﬁcient

storage and transmission.

Many of the most efﬁcient algorithms specialised

in static or dynamic mesh compression employ vertex

clustering or other mesh division technique. Unfor-

tunately, artifacts may appear in the form of cracks or

steps between individual clusters of the decompressed

triangle mesh (see ﬁgure 1). This kind of distortion

is concentrated in small areas of the triangle mesh

surface, thus it only slightly affects the total distor-

tion caused by compression itself as identiﬁed by the

usual measures (KG-error,for example), but may neg-

atively affect visual quality of the mesh. Similar ar-

tifacts are known in image and video compression,

where deblocking ﬁlters are used to handle them.

In this paper, we propose a method of post-

processing of decompressed triangle meshes, which

locally improvesthe visual quality with focus on com-

pression algorithms including mesh division tech-

niques. We choose clustered Coddyac (Rus and V´aˇsa,

2010) as a representative of this type of algorithms in

this paper, because it is currently the most efﬁcient

compression algorithm for dynamic meshes.

The rest of the paper is organised as follows. Sec-

tion 1.1 gives a brief overview of existing approaches

to dynamic mesh compression with clustering and

methods of improving the mesh appearance. Section

2 speciﬁes the scheme of Coddyac compression algo-

rithm and its clustering improvement. A description

of the mesh deblocking is presented in section 3 and

results of our experiments are reported in section 4.

Finally, we give conclusions in section 5.

1.1 Related Work

Many algorithms have been proposed for static and

dynamic mesh compression. There are also various

algorithms known dividing a given mesh into smaller

parts using geometry or connectivity criteria. Meshes

can be divided into semantic parts as well. In many

cases, efﬁcient compression schemes for static and

dynamic mesh compression combine compression al-

gorithms and algorithms of mesh segmentation (clus-

tering) to increase compression ratio.

One such method intended for static mesh com-

Rus J. and Váša L..

DEBLOCKING FOR DYNAMIC TRIANGLE MESHES.

DOI: 10.5220/0003829700480057

In Proceedings of the International Conference on Computer Graphics Theory and Applications (GRAPP-2012), pages 48-57

ISBN: 978-989-8565-02-0

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

pression has been proposed by Karni and Gotsman

(Karni and Gotsman, 2000). Spectral mesh compres-

sion expresses the triangle mesh data as a linear com-

bination of a set of orthogonal basis functions. As

in DCT-based image compression, these basis func-

tions are characterised by a frequency. Spectral mesh

compression needs only the triangle mesh connectiv-

ity to calculate the orthogonal basis, which consists of

eigenvectors of Laplacian matrix calculated from ver-

tex adjacency. Computation of the Laplacian eigen-

vectors is numerically expensive for meshes contain-

ing large number of vertices and thus the mesh must

usually be partitioned into submeshes and the cal-

culation must be performed separately for each part.

The mesh division is performed by MeTiS algorithm

(Karypis and Kumar, 1998) to obtain segments with

approximately the same number of vertices and mini-

mal number of edges between individual segments.

In contrast to the previous compression method,

method described by Lengyel (Lengyel, 1999) is one

of the ﬁrst compression methods intended for dy-

namic meshes. This method initially segments a

given dynamic mesh using information about rigid

body motions of the mesh. The motion of all ver-

tices of each segment is approximately described by

an afﬁne transformation. If one vertex is included in

more segments, weighted combination of afﬁne trans-

formations related to these segments is used. Weight-

ing coefﬁcients, transformation parameters and differ-

ences (residuals) between original and estimated ver-

tex positions are quantised and encoded. In order to

achieve compression efﬁciency, approximation resid-

uals are minimised using prediction techniques.

Differential 3D Mesh Coding scheme (D3DMC)

proposed by K. M¨uller, A.Smoli´c, M. Kautzner, P.

Eisert and T. Wiegand (M¨uller et al., 2005)is a predic-

tion based approach, which uses an octree data struc-

ture for spatial subdivision (clustering) of 3D mesh

animation with constant connectivity. D3DMC uses

an animation description similar to the usual video

compression schemes. Frames of animation are rep-

resented as sets of subsequent meshes called Groups

of Meshes (GOM) consisting of intra meshes (I mesh)

and predicted differential meshes (P mesh). I meshes

are compressed as a static meshes using 3DMC and

following P meshes are coded using octree motion

segmentation (spatial clustering) of difference vectors

of consecutive frames of the animation. I meshes are

typically used in the ﬁrst frame of compressed ani-

mation sequence or when the prediction in D3DMC

becomes too large.

The octree motion segmentation is also de-

scribed (Zhang and Owen, 2004) by Zhang and

Owen. Octree-based animated geometry compression

method only uses two consecutive frames of the ani-

mation to generate small set of motion vectors repre-

senting the motion of the geometry from the previous

frame to the current frame. The octree motion seg-

mentation starts with the minimum bounding box as a

topmost cell of the octree structure, which includes all

vertices. Eight motion vectors approximating the mo-

tion of all vertices enclosed within the octree cell are

associated with the cell, one motion vector for each

cell corner. If the motion of vertices is not approxi-

mated well using motion vertices, the cell is repeat-

edly split into eight octants until the approximation

reaches user deﬁned accuracy. Finally, the motion

vectors are uniformly quantised to reduce compressed

data entropy and thus enhance the compression ratio

of following context-adaptive binary arithmetic cod-

ing – CABAC, (Marpe et al., 2003). Only the set of

motion vectors and the octree structure are stored.

Another approach described by Sattler et al. (Sat-

tler et al., 2005) is based on clustered principal com-

ponent analysis (CPCA), analysing trajectories of all

vertices throughout the animation time. The division

of the mesh depends on similarity of these trajecto-

ries and usually leads to meaningful clusters, which

are separately encoded by shape-space PCA.

A similar approach to compression of dynamic

meshes was proposed by Amjoun and Straßer

(Amjoun and Straßer, 2007). Their method uses lo-

cal principal component analysis (LPCA) of vertex

motion. First, the set of vertices for each frame is

analysed, clustered and per-partes transformed from

world coordinate system into local coordinate sys-

tem of appropriate cluster. Local coordinate system

of each cluster is derived from the plane of its seed

triangle and the mesh division depends on the mo-

tion of vertices in this system. Finally, each cluster

is encoded using shape-space PCA and compressed

by arithmetic coding.

The Frame-based Animated Mesh Compression

(FAMC) method described by Mamou, Zaharia and

Prˆeteux (Mamou et al., 2008) uses mesh segmenta-

tion with respect to motion as well. It is based on a

skinning model. Each segment is described by a sin-

gle afﬁne transformation calculated for each frame of

the animation, such that the transformation matrix de-

scribes motion of vertices from the ﬁrst frame of the

animation to the desired frame of the animation. The

segmentation process is based on hierarchical deci-

mation of the original mesh using connectivitysimpli-

ﬁcations: two neighbouring vertices are merged into

a single vertex if their afﬁne motion and afﬁne motion

of all vertices merged previously is similar. The ﬁnal

number of segments corresponds to the number of re-

maining vertices.

DEBLOCKING FOR DYNAMIC TRIANGLE MESHES

Another approach by Rus and V´aˇsa (Rus and

V´aˇsa, 2010) is based on the Coddyac (V´aˇsa and Skala,

2007) compression algorithm with focus on the be-

haviour of trajectory-space PCA with respect to ver-

tex movement complexity. This algorithm transforms

geometry information of a dynamic mesh into the

form of a set of vertex trajectories and processes this

set by PCA. The PCA is used to reduce the set of ver-

tex trajectories necessary to express the mesh move-

ment. Efﬁciency of the algorithm directly depends

on the mesh movement complexity. Therefore the

movement is analysed ﬁrst and vertices with similar

movement are assigned into a common group - clus-

ter. This way the movement complexity is locally re-

duced and thus the compression algorithm efﬁciency

is improved.

As we already noted, mesh division is often used

in static and dynamic mesh compression algorithms

to improve their efﬁciency but it causes artifacts in

the form of cracks or steps on the boundaries between

individual clusters. These artifacts may be caused by

algorithms using octree subdivision as well.

Similar kinds of artifacts are well known in the

area of image and video compression. It is usu-

ally handled by a post-processing technique known

as deblocking. Deblocking ﬁlter reduces “blocking-

artifacts” by smoothing the sharp edges, often formed

between blocks of decompressed image or video

frame and thus improves its visual quality. In case

of (dynamic) mesh compression, only a negligible

part of the mesh data is distorted the way described

above, and thus the error identiﬁed by usually used

error measures, such as KG-error, is only slightly af-

fected by this distortion. We need a different metric

to measure the distortion related to artifacts caused

by mesh division techniques, which is small relative

to the distortion caused by compression itself but sig-

niﬁcant from the visual quality point of view.

One such error metric for static meshes is

MSDM2 (Lavou´e, 2011) and its ancestor MSDM

(Lavou´e et al., 2006), which is inspired by SSIM

(Wang et al., 2004) index expressing structural sim-

ilarity of two images. Both MSDM and MSDM2

exploit differences of local curvature statistics of

the mesh surface to assess the visual similarity be-

tween 3D meshes (original M

and distorted M

mesh). MSDM2 computes distortion maps for multi-

ple scales (radius of local neighbourhoodsof vertices)

and combines them into a global multi-scale distor-

tion map, which is used for computation of distortion

score. The metric is then computed as the average of

forward (M

→ M

) and backward (M

→ M

) global

distortion scores.

A suitable error measure for dynamic meshes –

STED (Spatio-temporal edge difference) – has been

presented in (V´aˇsa and Skala, 2011). STED is derived

from subjective testing of mesh distortion perception

and provides better correlation with human percep-

tion of quality loss between original and processed

dynamic meshes than any other metric we know of.

In this paper, we propose a method of improving

the mesh appearance similar to mesh fairing (Desbrun

et al., 1999). The mesh fairing is method of smooth-

ing the polygon mesh to improve its visual quality by

reducing its curvature variation. Both mesh fairing

and our approach move vertices of the mesh, while its

connectivity stays the same, to change its appearance.

In contrast with mesh fairing, our approach – mesh

deblocking – is focused on a speciﬁc kind of distor-

tion and affects only sharply deﬁned areas of the mesh

surface, thus the principle of our approach is closer to

the methods of deblocking ﬁlters known in image and

video compression.

1.2 Notation

In this paper we use the following notation:

F - number of frames of animation

V - number of mesh vertices

- trajectory vector of the i-th vertex, size 3F

A - average trajectory vector, size 3F

B - matrix of original animation, size 3F ×V

C - autocorrelation matrix, size 3F × 3F

- i-th eigenvector ofC, size of 3F

E - basis of the PCA subspace, size 3F × N

N - number of most important eigenvectors

S - matrix of samples, computed by subtracti-

on of A from columns of B, size 3F ×V

β - set of border triangles of the given cluster

Σ - set of surrounding triangles of the given

cluster belonging to surrounding clusters

- decompressed position of the i-th vertex

- predicted position of the i-th vertex

˜p

- transformed position of the i-th vertex

In the rest of this paper, the Rus and V´aˇsa ap-

proach, one of the most efﬁcient dynamic mesh com-

pression methods known at the time, is discussed and

used to demonstrate the inﬂuence of the mesh de-

blocking post-process on the dynamic mesh decom-

pression. The STED is used to measure changes

in distortion caused by implementing the deblocking

post-process.

GRAPP 2012 - International Conference on Computer Graphics Theory and Applications

2 CLUSTERED CODDYAC

ALGORITHM OVERVIEW

The Coddyac is a compression algorithm, which is

specialised in dynamic mesh compression and con-

tains two well known algorithms: Rossignac’s Edge-

breaker (Rossignac, 1999) and Principal Component

Analysis (PCA). In Coddyac, Edgebreaker is used for

triangle mesh connectivity compression and the PCA

is used for compression of the mesh geometry. The

Coddyac algorithm processes a sequence of meshes

with the same connectivity, which is represented as

set of vertex trajectories of individual vertices, each

described by a vector T of length 3F. Trajectory vec-

tor T

of the i-th vertex consist of its XYZ coordinates

in all F frames. The set of these trajectory vectors

is processed by PCA to ﬁnd the subspace where the

trajectories are located, and the trajectories are ex-

pressed in this subspace.

The original animated mesh is represented by ma-

trix B of size 3F ×V with columns corresponding to

vertex trajectories. Next, we compute the matrix of

samples S by subtracting the average trajectory vector

A from columns of the matrix B. Subsequently, the

autocorrelation matrix C of size 3F × 3F is computed

asC = S·S

. Dimension of the autocorrelation matrix

C is proportional to the number of frames F, thus the

computation complexity is independent of the num-

ber of mesh vertices V (in the contrast with spectral

mesh compression, for example). If the number of an-

imation frames (the dimension of the correlation ma-

trix) is too high, the frame sequence can be trivially

cut into several shorter pieces. Next, we use eigen-

value decomposition of the autocorelation matrix C

to obtain a set of eigenvectors E

, i = 1. . . 3F, whose

subset forms a basis of the desired subspace. This

subset consists of the N most important eigenvectors

(according to their respective eigenvalues), where N

is a user-speciﬁed parameter. The trajectory vector of

the i-th vertex is then expressed as:

= A +

∑

. (1)

To use this formula, we have to compute the matrix

of combination coefﬁcients c

by matrix multiplica-

tion C = S

· E. E is a matrix of a selected subset

of eigenvectors of size 3F × N, where each column

corresponds to one of these eigenvectors. The vec-

tor of combination coefﬁcients c

related with the i-th

vertex of the dynamic mesh is called a feature vec-

tor. Now, the mesh can be described by the matrix

of the selected subset of eigenvectors E, the matrix

of combination coefﬁcients C and the average trajec-

tory vector A. Finally, the COBRA (V´aˇsa and Skala,

2009) algorithm is used to compress the PCA basis

and thus reduce the size of this data by approximately

90% with respect to a direct encoding.

The PCA step of the compression algorithm can

be interpreted as a simple change of basis. This en-

ables us to use linear operators without any inﬂu-

ence on their results. This observation is used for

the following algorithm efﬁciency improvement: The

mesh surface is progressively traversed by expanding

the processed area by one edge-adjacent triangle at a

time. All three feature vectors of the vertices of the

ﬁrst processed triangle are stored without any modiﬁ-

cations, but each following feature vector correspond-

ing to an added triangle is predicted from already

compressed vectors using parallelogram prediction:

predicted

= c

left

+ c

right

− c

base

, j = 1. . . N, (2)

After the parallelogram prediction the residues be-

tween the original and the predicted feature vectors

are stored.

This compression scheme compresses vertex tra-

jectories using PCA and therefore the more compli-

cated the mesh movement is, the less information

about the mesh movement can be considered negli-

gible and the compression ratio decreases. In other

words, the efﬁciency of the Coddyac compression

algorithm directly depends on the mesh movement

complexity. By the movement complexity we under-

stand differences between individual vertex trajecto-

ries. The vertex trajectories can be complicated, but

if they are similar to each other, the movement com-

plexity of the set of these trajectories is low.

The clustering improvement of the basic Coddyac

algorithm lies in clustering the mesh vertices depend-

ing on mutual similarity of their trajectories, which

leads to local reduction of the movement complexity

(complexity in one cluster is lower than in the whole

mesh). Lower movement complexity enables short-

ening of feature vectors while maintaining the same

error and thus improves the compression ratio.

Experiments made in this area have shown that the

k-means (Kanungo et al., 2002) clustering of vertex

trajectories with L

distance norm is the most suitable

for Coddyac and it can improve compression bitrate

by 37%-46% without changing the error caused by

compression.

In the preceding text, N denotes a user-speciﬁed

number of basis vectors, but when clustering is a part

of the compression algorithm, then it is necessary

to change the approach to setting the number of ba-

sis vectors. Assuming that each vertex cluster has

different movement complexity, we also have to set

a different number of basis vectors to maintain the

DEBLOCKING FOR DYNAMIC TRIANGLE MESHES

same accuracy of movement of individual parts of the

compressed dynamic mesh. To do so, we use a sin-

gle scalar value instead of the set of N-values, which

represents a tolerable PCA-introduced error speciﬁed

by the user. The modiﬁed Coddyac algorithm calcu-

lates the number of basis vectors automatically for

each vertex cluster. The average amount of PCA-

introduced error using N basis vectors is expressed

as:

∆

PCA

∑

j=1

∑

i=1

−

, (3)

where l is the average edge length of the animation,

is the i-th component of the j-th original trajec-

tory and

is the i-th component of the j-th trajectory

reconstructed using N basis vectors. In order to se-

lect the number of basis vectors for a speciﬁc cluster,

we select the smallest possible N for which this aver-

age PCA-introduced error falls below a user-speciﬁed

value.

3 MESH DEBLOCKING

As mentioned in the introduction, some distortion of

a decompressed mesh may appear when using lossy

compression algorithms with clustering. A signiﬁcant

part of this distortion is usually caused by the data

quantisation step, which is essential for efﬁcient data

storage.

There are two basic ways in which this factor

may affect the mesh surface. First, all mesh vertices

are globally affected by noise-like distortion, inﬂicted

by quantisation of vertex coordinates. In this paper,

we are interested in the second kind of distortion,

which affects the mesh surface only locally and may

be caused for example by quantisation of PCA basis

vectors or quantisation of local coordinate systems of

vertex clusters. It is possible that artifacts in the form

of cracks or steps between individual vertex clusters

(parts of the mesh) are produced by mesh compres-

sion.

Using the exact knowledge of mesh division used

during the phase of mesh decompression, we are able

to locate borders of individual vertex clusters and thus

the areas of the mesh surfaces where the described

artifacts may appear. By mesh deblocking we want

to suppress or even remove these artifacts by mov-

ing vertices of triangles to a more suitable position

with respect to the problematic boundary of appropri-

ate clusters. The goal of this process is not to reduce

the distance between original and decompressed po-

sitions of vertices, but to increase the visual quality of

Figure 1: Comparison of decompressed, deblocked and

original frame of the dance animation. 13.6% improvement

of the STED error is achieved by deblocking.

the decompressed mesh. The result of such operation

can be seen in ﬁgure 1.

We avoid the deformation of the processed clus-

ter such as mesh smoothing, and thus bringing addi-

tional error to inner vertices of this cluster (not only

on the borders). We believe that a rigid transforma-

tion, which affects all cluster vertices regularly (in

the same way), is a better idea. This transformation

should meet two requirements:

• Minimal dihedral angle between pairs of triangles

on cluster boundaries is required to minimise the

step-like artifacts.

• Reasonable length of edges between clusters.

We can use a combination of the parallelogram

prediction with the rigid transformation to fulﬁl the

speciﬁed requirements and ﬁt the cluster boundaries

better to soften the transitions between them.

3.1 Algorithm Description

The mesh deblocking algorithm starts with ﬁnding

edges, that connect borders of different clusters. Tri-

angles containing these edges form a set of border tri-

angles (ﬁgure 2), deﬁning areas of mesh distortion de-

scribed earlier and potentially forming step-like arti-

facts between individual clusters.

CLUSTER1

CLUSTER3

CLUSTER2

PROCESSED

CLUSTER

Figure 2: Left: clusters surrounded by (darkened) border

triangles. Right: green Σ triangles and blue β triangles

surrounding processed cluster forming wedges. One of the

wedges W is highlighted in red.

Next, the best candidate cluster for transforma-

tion (deblocking) is selected. We choose such clus-

GRAPP 2012 - International Conference on Computer Graphics Theory and Applications

ter, which can bring the most signiﬁcant improvement

in the mesh visual quality using a proper rigid trans-

formation. Estimation of this improvement is based

on the width of the surrounding strip of correspond-

ing border triangles β (the distance of the transformed

cluster from the incident clusters).

Estimation of the artifact size reduction is calcu-

lated using an arithmetic average of the lengths of the

edges of the incident border triangles, which are con-

nected to adjacent clusters. Candidates for the de-

blocking transformation are iteratively selected and

transformed while the estimated reduction of artifact

size is decreasing. In other words, when the differ-

ence between two consecutive estimations is lower

than a speciﬁed threshold (we choose 0.1% in our ex-

periments), the iterative algorithm stops. Calculation

of an estimation of the artifact size reduction will be

described later in this section.

Once the candidate cluster for the transformation

is selected, the transformation algorithm ﬁnds all sur-

rounding triangles Σ from adjacent clusters, which

have one edge in common with any triangle in β.

These Σ triangles are used to form a set of triangle

wedges W consisting of one Σ triangle and one β tri-

angle sharing a common edge, as depicted in ﬁgure

In other words, each wedge includes an Σ trian-

gle lying out of the processed candidate cluster, which

can be used for a parallelogram prediction of the posi-

tion of the tip of the β triangle lying on the boundary

of the processed candidate cluster (see ﬁgure 3) and

thus wedges can be used for an estimation of position

of the vertices on the boundary of the processed clus-

ter after the desired deblocking transformation.

Figure 3: Green Σ triangle used for parallelogram prediction

of boundary vertex position of the processed cluster after

deblocking transformation.

Now, the position of the boundary vertices of the

processed cluster can be estimated using the parallel-

ogram prediction from clusters surrounding the pro-

cessed candidate cluster.

Parallelogram prediction is used to guarantee a

meaningful length of edges connecting the boundary

of the processed cluster with the rest of the mesh. It

also minimises the dihedral angles between the tri-

angles of the processed cluster and the surrounding

clusters.

A difference vector between the decompressed

position d

⊂ D and the predicted position p

⊂ P of

the i-th vertex belonging to the boundary of the pro-

cessed cluster is denoted as force f

⊂ F and deter-

mines the direction and the distance in which this ver-

tex has to be moved to fulﬁl the transformation re-

quirements. Each boundary vertex can be affected by

a number of forces and thus the total force vector af-

fecting this vertex is calculated as:

∑

j=1

− d

), (4)

where M

denotes the number of forces affecting the

i-th border vertex.

Using this approach, two sets of vertices are ob-

tained. A set of boundary vertices with the original

(decompressed) position D and a set of boundary ver-

tices with the desired position P, p

= d

+ f

, both of

the size of M elements. In the following step of de-

blocking algorithm a rigid transformation of D to P is

calculated. We do not use vertices with no force as-

signed to them in the following calculations, therefore

P, D and F have the same number of elements.

To ﬁnd the appropriate transformation, we use

SVD-based method of ﬁtting of two 3D point sets de-

scribed in (Arun et al., 1987) obtaining matrix of ro-

tation R and vector of translation t.

In some special cases, the calculation of the ma-

trix of rotation R may fail and thus R does not describe

the rotation we are looking for. In such cases, only the

translation vector t is calculated using the difference

between the centroids of the given sets. The calcula-

tion of the difference between the centroids of D and

P an thus the calculation of the vector of translation

as well is equivalent to the calculation of the average

force vector

t =

∑

i=1

−

∑

i=1

∑

i=1

+ f

) −

∑

i=1

∑

i=1

(5)

Finally, all vertices d

of the processed cluster are

transformed using the rigid transformation obtained

DEBLOCKING FOR DYNAMIC TRIANGLE MESHES

Figure 4: Frames 21 and 45 of the dance animation decompressed, deblocked and compared with the original animation. De-

spite the fact that the animation was compressed quite accurately with about 0.45 bpfv and STED 0.015, the mesh deblocking

brought almost 10% improvement of the STED error of this data.

by the application of SVD on the sets of border ver-

tices O and P. In other words, the whole cluster is ro-

tated and translated in order to minimise the size of

the artifacts on its boundary. The transformed vertex

position ˜p

⊂

P close to the predicted vertex position

of the i-th vertex of the processed cluster is then

calculated as follows:

˜p

= R · d

+ t (6)

If the calculation of the rotation matrix R fails, the

whole processed cluster is only translated in the di-

rection of average force vector

f. This cluster is dis-

carded from the list of possible candidates for the next

deblocking transformation iteration, because it could

be evaluated as the best candidate for transformation

again without any chance to further improve the vi-

sual quality of the mesh.

Earlier in the text, it was mentioned that the

change of the artifact size related to a given cluster

has to be estimated to identify which cluster should

be transformed to gain probably the most signiﬁcant

improvement of the visual quality of the mesh in the

current iteration. The estimation algorithm emulates

the transformation algorithm until it reaches the phase

of application of the rigid transformation on all cluster

vertices. Next, the average length l

avg

of force vectors

assigned to boundary vertices of the tested cluster is

computed:

avg

∑

i=1

| f

| (7)

The value of l

avg

is used as an approximation of

the visual quality improvement acquired by the ap-

plication of deblocking transformation on this clus-

ter. This average length value is calculated for each

cluster. The candidate cluster with the largest l

avg

chosen as the best candidate for the deblocking trans-

formation.

The whole deblocking algorithm is brieﬂy de-

scribed in the following pseudocode:

repeat

{

select the best candidate cluster for deblocking

-parallelogram prediction of border vertices

-computation of forces in border vertices

-calculation of average force length l_avg

-selection of the best candidate

if(best_l_avg > threshold * last_best_l_avg) break

else store best_l_avg as last_best_l_avg

calculate transformation for selected cluster

-parallelogram prediction of border vertices

-computation of forces in border vertices

-SVD to obtain rotation R and translation t

-if SVD failed, calculate translation t

if(SVD failed) translate cluster using t

else rotate and translate cluster using R and t

}

store deblocked mesh

4 EXPERIMENTAL RESULTS

The approach of the mesh visual quality improve-

ment described in this paper has been implemented

and subsequently, we have measured the impact of the

mesh deblocking on a set of selected dynamic meshes.

During our experiments, we were more interested in

the visual quality of the compressed meshes than in

the error measured by commonly used error metrics,

GRAPP 2012 - International Conference on Computer Graphics Theory and Applications

Figure 5: Comparison of meshes decompressed with deblocking and without deblocking.

Table 1: Comparison of results of mesh deblocking.

Animation Bitrate [bpfv] Original Error Deblocked Error Improvement

Chicken 0.1509 0.1311 0.1162 11.32%

0.4467 0.0383 0.0381 0.58%

0.5062 0.0298 0.0307 -3.19%

Cloth 0.1610 0.0620 0.0507 18.22%

0.3319 0.0184 0.0177 3.92%

0.6934 0.0105 0.0103 2.06%

Dance 0.2090 0.0680 0.0606 10.80%

0.2835 0.0448 0.0421 6.09%

0.4300 0.0191 0.0184 3.64%

Humanoid 0.1469 0.1030 0.0986 4.26%

0.3051 0.0268 0.0258 3.92%

0.3914 0.0127 0.0135 -6.32%

Jump 0.1576 0.1204 0.1124 6.65%

0.3308 0.0737 0.0716 2.86%

0.9749 0.0292 0.0292 -0.01%

such as KG-error. Therefore, STED has been chosen

to measure the impact of the mesh deblocking of the

decompressed meshes.

Spatio-temporal edge difference (STED) is a

novel method of measuring error caused by process-

ing of dynamic mesh. It has been derived from results

of a subjective testing of mesh distortion perception

published in (V´aˇsa and Skala, 2011). STED combines

the measurements of spatial and temporal deviation of

edge lengths caused by processing the mesh and it is

focused on local changes of error. The distortion is

evaluated only for a close neighbourhood of each ver-

tex and these values are summed to obtain the overall

error. STED error is deﬁned as a weighted combina-

tion of the spatial error STED

and the temporal error

STED

STED(d, w, dt, c) =

STED

(d)

+ c

· STED

(w, dt)

(8)

where c is a weighting coefﬁcient, dt is the temporal

distance between consecutive frames, d denotes topo-

logical distance (a vertex is maximally d edges distant

from the given vertex) and w represents the width of

the temporal window.

We tested the mesh deblocking algorithm on sev-

eral 3D dynamic meshes, such as Dance, Chicken and

Jump. These meshes contain only information about

vertex positions for individual frames and connectiv-

ity of their triangles. The experimental data-set con-

sists of artiﬁcial animations of single objects, multi-

ple separated objects and scanned real data. We have

experimented with different compression settings as

well. Unlike the original version, the decompressed

meshes processed by mesh deblocking can achieve

lower STED error while maintaining the same bi-

trate. The improvement of the STED error depends

on how precisely the mesh is compressed and thus

on the compression bitrate. A lower bitrate means

more distortion that can be suppressed by the mesh

deblocking. On the other hand, a high bitrate can lead

to a mesh so close to the original that the mesh de-

DEBLOCKING FOR DYNAMIC TRIANGLE MESHES

blocking can bring additional error, because it is only

estimating the correct shape of the mesh depending on

the close surroundings of the step-like artifacts. This

case of negative inﬂuence of the mesh deblocking

can be handled by additional information appended to

the compressed mesh, deﬁning whether it is advanta-

geous to adjust the mesh by the deblocking algorithm.

Even though the modiﬁcation of the mesh by de-

blocking affects only a close neighbourhoodof the tri-

angles forming the step-like artifacts between individ-

ual clusters, it can lead to a signiﬁcant improvement

of STED error and the visual quality of the mesh.

STED error can be decreased by up to 18% using

mesh deblocking, which can lead to a signiﬁcant im-

provement of visual quality of the mesh as well. It

may happen, that the dynamic mesh is compressed

so precisely that visible cracks or step-like artifacts

caused by clustering appear only in a small subset of

the animation frames (ﬁgure 4). Suppressing these

artifacts may lead to a small improvement of STED

error, while signiﬁcantly improving the visual quality

of the small subset of the frames of animation.

The results of the mesh deblocking for several dif-

ferent dynamic meshes are shown in ﬁgure 5. The re-

sults of the selected subset of experiments are given

in table 1. Only results of optimal conﬁgurations are

presented in the table. Rate-distortion optimal conﬁg-

urations (number of basis vectors, quantisation of ba-

sis vectors and quantisation of feature vectors) were

determined for the clustered Coddyac compression

of dynamic meshes with the deblocking post-process

and without it and compared to each other. There are

sub-optimal conﬁgurations with even larger improve-

ment (20%–35%) of the STED error in comparison

with the original (not deblocked) meshes, but it is dif-

ﬁcult to determine the contribution of such compres-

sion conﬁgurations which can not be compared with

optimal results derived from the rate-distortion curve.

Note that mesh deblocking becomes inefﬁcient

for compression conﬁgurations with bitrate close to

0.5 bpfv (bits per frame and vertex) or higher. The

reason for this behaviour is that the clustered Cod-

dyac compression algorithm is able to compress dy-

namic meshes with almost no distortion using such a

bitrate. Therefore, there is a low probability of the oc-

currence of the step-like artifacts between individual

clusters we are dealing with in this paper. For ex-

ample, the dance animation in ﬁgure 4 is compressed

with a bitrate of 0.46 bpfv and contains only 3 or 4

frames that are visibly distorted by the clustered Cod-

dyac compression. Two of these distorted frames are

shown in ﬁgure 4. Similarly the dance animation in

ﬁgure 1 is compressed with a bitrate of 0.19 bpfv and

contains visible step-like artifacts, but these artifacts

are successfully suppressed by the mesh deblocking.

5 CONCLUSIONS

We have presented a mesh deblocking algorithm

targeted on the reduction of artifacts in clustering-

based mesh compression schemes. We have demon-

strated its efﬁciency on the example of clustered

Coddyac algorithm and STED error measure for dy-

namic meshes, where we achieve a reduction of the

compression-introduced error by up to 18% without

the need for any additional data. Our result is con-

ﬁrmed in the presented images, where the artifact re-

duction is clearly visible. A similar implementation

may be used for post processing of static meshes,

which is also conﬁrmed by our preliminary experi-

ments in this application.

Apart from a thorough testing of the deblocking

process for static meshes, in the future, we also in-

tend to improve the processing speed of our algo-

rithm to allow the real-time processing of very large

meshes. We also intend to perform experiments with

more complex deblocking approaches using a trans-

formation that is smoothly changing across each clus-

ter rather than a rigid one, as in this work. We also

plan to use similar techniques to reduce temporal er-

rors (frame shaking) that may arise in dynamic mesh

processing.

ACKNOWLEDGEMENTS

This work has been supported by the Ministry of Ed-

ucation, Youth and Sports of the Czech Republic un-

der the research program LC-06008 (Center for Com-

puter Graphics).

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