each group is individually encoded by PCA. This type
of method supports progressive transmission. The
drawback of this approach is it is computationally ex-
pensive.
In predictive methods, for each frame, the differ-
ence between the predicted and the current locations
is encoded with very few bits. These approaches are
simple, not expensive, lossless and well suited for
real-time applications. The drawback of these meth-
ods is that they don’t support progressive transmis-
sion.
Affine transformations well approximate the be-
havior of sets of vertices relative to the initial posi-
tion (the first frame, eventually the I-frame). This
type of method is very effective for animations based
on motion capturing, if the mesh is well partitioned
into almost rigid parts, since the vertices are attached
to the bones and move according to their represen-
tative joints. Therefore, exploiting the coherence in
this animation and finding the transformation that best
matches each group of vertices is easier than finding
a transformation that approximates each part in de-
formed meshes (like a cow animation). The draw-
back of this technique is that it can be computation-
ally expensive depending on the splitting process or
the affine transformation optimization.
In this paper, we propose a new compression algo-
rithm based on predictive and DCT transform in the
local coordinate systems.
The method is inspired from video coding. We
first split the animated mesh into severalclusters (sim-
ilar to macroblocks in video coding) using a simple
and efficient clustering process (Amjoun and Strasser,
2006). Then, we perform a prediction in the local co-
ordinate systems. Finally, we transform the resulting
delta vectors (between the predicted and the original
vertex locations) of each cluster in each frame into the
frequency domain using Discrete Cosine Transform.
2 STATE-OF-ART
During the last decade, extensive research has been
done on static mesh compression, producing a large
number of schemes (see, e.g., (Rossignac, 2004)
or (Alliez and Gotsman, 2005) for comprehensive
surveys of the developed techniques). While re-
search still focuses on efficient compression for huge
static meshes (Isenburg and Gumhold, 2003) ani-
mated meshes have become more and more important
and useful every where. However, the current tech-
niques for the compression of sequences of meshes
independently are inefficient.
Lengyel (Lengyel, 1999) suggested the decom-
posing of the mesh into submeshes whose motions
are described by rigid body transformations. The
compression was achieved by encoding the base sub-
meshes, the parameters of the rigid body transforma-
tions, and the differences between the original and the
estimated locations. Zhang et al. (Zhang and Owen,
2004) used an octree to spatially cluster the vertices
and to represent their motion from the previous frame
to the current frame with a very few number of motion
vectors. The algorithm predicts the motion of the ver-
tices enclosed in each cell by tri-linear interpolation
in the form of weighted sum of eight motion vectors
associated with the cell corners. The octree approach
is later used by K. Mueller et al. (Muller et al., 2005)
to cluster the difference vectors between the predicted
and the original positions. Very recently, Mamou et
al. (Mamou et al., 2006) proposed skinning based rep-
resentation. In their algorithm, the mesh is also par-
titioned, then each submesh in each frame is associ-
ated an affine motion and each vertex is estimated as a
weighted linear combination of the clusters motions.
Finally, the prediction errors are compressed using a
temporal DCT coding.
In prediction techniques, assuming that the con-
nectivity of the meshes doesn’t change, the neigh-
borhood in the current and previous frame(s) of the
compressed vertex is exploited to predict its loca-
tion or its displacement (J.H. et al., 2002; Ibarria
and Rossignac, 2003). The residuals are compressed
up to a user-defined error. For example, Ibarria and
Rossignac (Ibarria and Rossignac, 2003) extended the
parallelogramprediction used in static mesh compres-
sion to animation case and introduced two predictors:
Extended Lorenzo Predictor, a perfect predictor for
translations, and Replica Predictor, which is capa-
ble of perfectly predicting the location of the vertices
undergoing any combinations of translation, rotation,
and uniform scaling.
In PCA based approaches, Alexa et al. (Alexa and
M¨uller, 2000) used PCA to achieve a compact repre-
sentation of animation sequences. Later, this method
is improved by Karni and Gotsman (Karni and Gots-
man, 2004), by applying second-order Linear Pre-
diction Coding (LPC) to the PCA coefficients such
that the large temporal coherence present in the se-
quence is further exploited. Sattler et al. (Sattler et al.,
2005) proposed a compression scheme that is based
on clustered PCA. The mesh is segmented into mean-
ingful clusters which are then compressed indepen-
dently using a few PCA components only. Amjoun
et al. (Amjoun et al., 2006) suggest the use of local
coordinates rather the world coordinates in the local
PCA based compression. They showed that the local
coordinate systems are more compressable with PCA
PREDICTIVE-SPECTRAL COMPRESSION OF DYNAMIC 3D MESHES
31