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determine feasible combinations of joint angles. We can also incorporate either hard
or soft
dynamical
constraints on the velocities and accelerations of joints, based on
biomechanical analysis of how quickly humans can move.
Finally, we can take an alternate approach of fitting the kinematicmodel tomotion
capture data using a
physics-based
cost function (e.g., see [
584
]). That is, we assume
that the kinematic model is subjected to forces (e.g., from springs that relate the
markers to the skeleton, and from friction with the ground) and its pose corresponds
to achieving the most “comfortable” position.
7.4.3
Model-Based Inverse Kinematics
A natural next step is to incorporate learned models for natural human motion,
extracted by analyzing training data from previously collected motion capture ses-
sions. That is, we want to find inverse kinematics solutions that are not only
biomechanically feasible but also likely for a human to take.
One approach is to build a principal component analysis (PCA) model based on
training samples of
to reduce its dimensionality, and minimize cost functions like
example, Safonova et al. [
416
] reduced an approximately sixty-dimensional joint
parameter vector to about eight dimensions using PCA. Their inverse kinematics
cost function was a weighted sum of squared torques, joint accelerations, and PCA
coefficient magnitudes.
A more sophisticated approach is to use the training data to build a probability
density function that can be used to estimate the likelihood of a given pose,
L
θ
.
Higher likelihoods mean that the pose is more likely to be taken by a human. Then
the general problem is to maximize the likelihood of the probabilistic model given
a set of constraints. For example, Grochow et al. [
179
] proposed to use a nonlinear
dimensionality reduction technique called the Scaled Gaussian Process Latent Vari-
able Model. They used the initial portion of a motion capture sequence to learn the
“style” of a performer, and used the learnedmodel to estimate poses for the rest of the
sequence, even in the presence of missing markers. Urtasun et al. [
507
] extended this
type of approach to include dynamics using a Gaussian Process Dynamical Model.
We'll discuss simpler dynamical systems in the context of markerless motion capture
(Section
7.7
).
The poses estimated by learned-model-based methods seem much more natural
to the human eye than those produced by themethods in Section
7.4.1
and
7.4.2
. This
makes sense since they're trained on a large number of motion capture sessions of
real performers instead of simply imposing generic constraints. On the other hand,
model-based methods are extremely dependent on the quality and nature of the
training data. The methods produce the best results when the training data all has a
similar type, such as historical motion capture data of boxers that's applied to solve
the inverse kinematics problem for a new boxer. The methods perform more poorly
if a general mix of motion capture data is used for input, and they performbadly if the
training data doesn't match the online problem at all (for example, if training data
(
θ
)
11
The PCA should only be applied to the relative joint angles, and not the position and orientation
of the root.
