![](bg2.png)
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
49