Techniques for Face Motion & Expression Analysis on Monocular Images - 3D Modeling and Animation: Synthesis and Analysis Techniques for the Human Body - page 217

AUs. These two approaches differ in the image processing techniques and
parameters they use to describe the image characteristics introduced as input to
the neural network.

A model for motion — Hidden Markov models

By collecting data from real human motion, we can model behavior patterns as
statistical densities over configuration space. Different configurations have
different observation probabilities. One very simple behavior model is the
Gaussian Mixture Model (GMM), in which the probability distribution is modeled
as a collection of Gaussians. In this case the composite density is described by:

N

∑ =

P ⋅ Pr( O λ = k )

(5)

k

k

where P k is the observed prior probability of sub-model k . The mixture model
represents a clustering of data into regions within the observation space. Since
human motion evolves over time, in a complex way, it is advantageous to
explicitly model temporal dependence and internal states. A hidden Markov
model is one way to do this, and has been shown to perform quite well recognizing
human motion. Figure 5b illustrates their graphical representation.
Hidden Markov models (HMM) are a powerful modern statistical technique. A
Markov process not only involves probability, but also depends on the “memory”
of the system being modeled. An HMM consists of several states. In the
formulation of HMMs, each state is referred to individually, and thus practical
and feasible examples of these models have a small number of states. In an
HMM, a system has a number of states S 1 … S n . The probability that the system
passes from state i to state j is called P ( i , j ). The states of the system are not
known, but the system does have one observable parameter on output, which has
m possible values from 1 to m . For the system in state i , the probability that output
value v will be produced is called O ( i , v ). We must point out that it is required that
the transition probabilities depend on the state, not the output.
We refer the reader to the tutorial on HMMs by Rabiner (1989), where
theoretical bases are further discussed and examples of the most common
applications can be found. In Metaxas (1999), the author presents a framework
to estimate human motion (including facial movements) where the traditional use
of HMMs is modified to ensure reliable recognition of gesture. More specifically,
Pardàs and Bonafonte (2002) use an HMM to deduce the expression of faces