Virtual Character Definition and Animation within the MPEG-4 Standard - 3D Modeling and Animation: Synthesis and Analysis Techniques for the Human Body - page 62

effects by modifying the value of the offset , see Equation (10); and (2) reshaping
of the regular reference grid. The latter form of animation can be done on a
hierarchical multi-resolution basis, and will be exploited for the bone-based
animation of the humanoid.
A particularity of the M ESH G RID representation is that the hierarchical structure
of the reference grid allows the coordinates of the reference grid points of any
resolution-level R l +1 to be recomputed whenever the coordinates of the reference
grid points of the lower resolution-level R l are modified, for instance by the bone-
based animation script. For that purpose, “Dyn's four-point scheme for curves”
interpolation (Dyn, 1987) is applied.

The compact and scalable M ESH G RID stream

The particularities of the M ESH G RID representation allow a very compact
encoding of the model. In addition, the information inside the compressed stream
is organized in regions of interest and levels of refinement such that the needed
portions of the mesh can be retrieved at the appropriate resolution and quality
level. The high encoding performance is achieved by combining different coding
techniques for the different components of the M ESH G RID representation, as
follows:

1. The surface mesh can be obtained from the connectivity-wireframe by

performing a triangulation procedure using some of the same connectivity
rules as described in Salomie (2002a). It is, however, more efficient to
encode the connectivity-wireframe than the triangulated mesh because of
the smaller number of edges that have to be described. For encoding the
connectivity-wireframe, a new type of 3D extension of the Freeman chain-
code is used, requiring only between one and two bits per edge.

2. The reference grid is a smooth vector field defined on a regular discrete 3D

space, each reference grid point being identified by a discrete position
( u , v , w ). The ( x , y , z ) coordinates are efficiently compressed using an embed-
ded 3D wavelet-based multi-resolution intra-band coding algorithm.

By combining and applying these coding techniques to multi-resolution objects,
the compressed M ESH G RID stream can be 2.5 times more compact than the
corresponding multi-resolution 3DMC (Taubin, 1998a) stream. When M ESH G RID
is configured in homogeneous triangular or quadrilateral mesh mode, its com-
pression performances are close to that of WSS, dedicated to triangular or
quadrilateral meshes. The encoding performance of the WSS 3D-detail informa-
tion is, indeed, very high and difficult to surpass. Nevertheless, M ESH G RID does