Game Development Reference
In-Depth Information
The second step is to derive movements of facial surface points that are not
sampled by markers in MUs. We use the radial basis interpolation function. The
family of radial basis functions (RBF) is widely used in face animation (Guenter
et al., 1998; Marschner, Guenter & Raghupathy, 2000; Noh & Neumann, 2001).
Using RBF, the displacement of a certain vertex
v is of the form
N
=
v
=
w
h
(
v
p
)
p
(2)
i
ij
i
j
j
j
1
p is its displacement.
h is a radial basis kernel function, and w ij are the weights. h and w ij need to be
carefully designed to ensure the interpolation quality. For facial deformation, the
muscle influence region is local. Thus, we choose a cut-off region for each
vertex. We set the weights to be zero for markers that are outside of the cut-off
region, i.e., they are too far away to influence the vertex. In our current system,
the local influence region for the i-th vertex is heuristically assigned as a circle,
with the radius r i as the average of the distances to its two nearest neighbors.
Similar to Marschner, Guenter & Raghupathy (2000), we choose the radial basis
p
where
, ( j = 1,..., N ) is the coordinate of a marker, and
j
j
i w to be
h
(
x
)
=
(
+
cos(
π
x
r
)
2
x
=
v
p
kernel to be
, where
. We choose
i
j
w . The lips and eye lids are
two special cases for this RBF interpolation, because the motions of the upper
parts of them are not correlated with the motions of the lower parts. To address
this problem, we add “upper” or “lower” tags to vertices and markers near the
mouth and eyes. Markers do not influence vertices with different tags. These
RBF weights need to be computed only once for one set of marker positions. The
weights are stored in a matrix, which is sparse because marker influence is local.
During synthesis, the movement of mesh vertices can be computed by one
multiplication of the sparse RBF matrix based on equation (2). Thus, the
interpolation is fast.
=
N
j
h
(
v
p
)
=
1
a normalization factor such that
ij
i
j
1
Temporal Facial Deformation
Temporal facial deformation model describes temporal variation of facial
deformation given constraints (e.g., key shapes) at certain time instances. For
compactness and usability, we propose to use an HMM-based model trained by
a standard HMM training algorithm, which employs only a few HMM states for
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