Graphics Reference
In-Depth Information
37
TensorTextures bases of the coins image
ensemble. (From [Vasilescu and Terzopoulos 04]
c
230400
×
21
×
Figure 9.23
A partial visualization of the
T ∈
R
2004 ACM, Inc. Included here by
permission.)
Z
where
is the core tensor in the
M
-mode SVD above, and
U
x
is the texel mode
matrix. Figure 9.23 illustrates part of
T
for the tensor illustrated in Figure 9.20.
A more efficient way of computing the TensorTextures basis is
T
=
D ×
L
U
L
×
V
U
V
.
(9.15)
In order to create a compact multilinear BTF model,
U
L
,
U
V
and
are dimen-
sionally reduced by truncation and optimized using an alternating least squares
algorithm.
As is illustrated in Figure 9.24, the TensorTextures basis can be used as a
generative
model to synthesize textures according to the expression
T
d
new
L
l
new
×
v
new
,
=
T ×
(9.16)
V
Figure 9.24
TensorTextures texture synthesis. The lower left image is rendered by modulating each
of the TensorTextures basis vectors with the coefficients in the view coefficient vector
v
T
=[
v
1
v
2
v
3
...
]
and illumination coefficient vector
l
T
=[
l
1
l
2
l
3
...
]
. (From [Vasilescu
and Terzopoulos 04] c
2004 ACM, Inc. Included here by permission.)
