Game Development Reference
In-Depth Information
Linear
Let us call λ the vector of parameters obtained from the image analysis and µ
the vector of FA parameters for the synthesis observed by
. The usual way to
λ
construct the linear estimator L , which best satisfies
= on the training
database, is to find a solution in the least square sense. We verify that this linear
estimator is given by
µ
λ
L
=
ΜΛ
T
ΛΛ
T
(4)
(
)
Μ
=
[
µ
µ
]
Λ
=
[
λ
λ
]
where
and
are the matrices obtained by concat-
d
d
vectors from the training set.
Valente, Andrés del Valle and Dugelay (2001) compare the use of a linear
estimator against an RBF (Radial Basis Functions) network estimator. In their
experiments,
enating all µ and
λ
are the set of the coefficients obtained from projecting an image
of the feature being analyzed ( imagette ) onto a PCA imagette database of the
feature recorded making different expressions under different lighting condi-
tions. µ contains the actions to apply on the model, in form of AUs, to generate
these different expressions. RBF networks find the relationship between a pair
of examples (input and output) of different dimensions, through the combination
of functions of simple variables whose main characteristic is that they are
continuous in
λ
and radial (Poggio & Girosi, 1990).
+
Neural networks
Neural networks are algorithms inspired on the processing structures of the
brain. They allow computers to learn a task from examples. Neural networks are
typically organized in layers. Layers are made up of a number of interconnected
“nodes,” which contain an “activation function.” (See Figure 5a.)
Most artificial neural networks, or ANNs, contain some form of learning rule
that modifies the weights of the connections according to the input patterns that
it is presented with. The most extensively used rule is the delta rule . It is utilized
in the most common class of ANNs called backpropagational neural net-
works (BPNNs). Backpropagation is an abbreviation for the backwards propa-
gation of error.
ANNs complement image-processing techniques that need to understand
images and in analysis scenarios where some previous training is permitted. In
Tian, Kanade and Cohn (2001), we find one fine example of the help neural
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