Advances in Vision-Based Human Body Modeling - 3D Modeling and Animation: Synthesis and Analysis Techniques for the Human Body - page 6

1989). A mathematical model will include the parameters that describe the links,
as well as information about the constraints associated with each joint. A model
that only includes this information is called a kinematic model and describes the
possible static states of a system. The state vector of a kinematic model consists
of the model state and the model parameters. A system in motion is modeled
when the dynamics of the system are modeled as well. A dynamic model
describes the state evolution of the system over time. In a dynamic model, the
state vector includes linear and angular velocities, as well as position (Wren &
Pentland, 1998).
After selecting an appropriate model for a particular application, it is necessary
to develop a concise mathematical formulation for a general solution to the
kinematics and dynamics problem, which are non-linear problems. Different
formalism have been proposed in order to assign local reference frames to the
links. The simplest approach is to introduce joint hierarchies formed by indepen-
dent articulation of one DOF, described in terms of Euler angles. Hence, the body
posture is synthesized by concatenating the transformation matrices associated
with the joints, starting from the root. Despite the fact that this formalism suffers
from singularities, Delamarre & Faugeras (2001) propose the use of composi-
tions of translations and rotations defined by Euler angles. They solve the
singularity problems by reducing the number of DOFs of the articulation.
3D Human Body Coding Standards
As it was mentioned in the previous section, an HBM consists of a number of
segments that are connected to each other by joints. This physical structure can
be described in many different ways. However, in order to animate or inter-
change HBMs, a standard representation is required. This standardization allows
compatibility between different HBM processing tools (e.g., HBMs created
using one editing tool could be animated using another completely different tool).
In the following, the Web3D H-anim standards, the MPEG-4 face and body
animation, as well as MPEG-4 AFX extensions for humanoid animation, are
briefly introduced.
The Web3D H-Anim Standards
The Web3D H-anim working group (H-anim) was formed so that developers
could agree on a standard naming convention for human body parts and joints.
The human form has been studied for centuries and most of the parts already