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Primitives
for Human Motion: a Dynamical Approach
D. Del Vecchio, R.M. Murray, P. Perona
Abstract.
Using tools from d dynamical systems theory and systems identification
theory we develop the study of primitives for human motion which we
refer to as movemes. We introduce basic definitions of dynamical independence
of LTI systems and segmentability of signals and we develop classification
and segmentation algorithms for two dimensional motions. We test our
ideas on data sampled from four human subjects who were engaged in a
simple reallife activity including two movemes. Our experiments show
that we are able to distinguish between the two movemes and recognize
them even when they take place in an activity containing more than one
moveme.
Introduction and Motivation: Building systems that can detect and recognize
human actions and activities is an important goal of modern engineering.
Applications range from humanmachine interfaces, to security to entertainment.
The first fundamental problem in achieving this goal is one of representation.
Our point of view is that human activity should be decomposed into its
building blocks which belong to an ``alphabet'' of elementary actions
that the machine knows. We refer to these primitives of motion as movemes.
This word first came up in the work by (Bregler and Malik, 1997). Their
approach
Figure
1
D oes not include an input and therefore is only applicable to periodic
or stereotypical motions, such as walking or running where the motion
is always the same. (Goncalves et al., 1998) also proposed to divide
human motion into elementary trajectories called movemes. They dealt
with the problem in a phenomenological and noncausal way: each moveme
was parameterized by goal and style parameters. We attempt here to define
movemes in terms of causal dynamical systems; this way a moveme could
be parameterized by a small set of dynamical parameters and by an input
which drives the overall dynamics. Our aim is to build an ``alphabet
of movemes'' which one can compose to represent and describe human motion
similar to the way phonemes are used in speech. Two more problems we
address are the ones of segmentation and classification: can a continuous
trajectory of the human body be decomposed automatically into its component
movemes? We validate our ideas by analyzing the mouse trajectories generated
by computer users as they ``pointandclick'' (we call this the reach
moveme) and trace straight lines (we call this the draw moveme).
APPROACH: represent movemes as causal dynamical systems
Figure
2
Dynamically
independent sets of dynamical systems are roughly defined in Fig.2 :
they are systems parameterized by parameters which lie in separated
subsets of the parameter space (see figure). Then the elements MR and
MD of the set {MR,MD} of mutually dynamically independent systems are
said to be movemes. The trajectories in space that we can measure are
then represented by a sequence in time of moveme's outputs y(t), see
Fig.3.
 We
say in this case that the signal y(t) is segmentable since it can be
decomposed into two moveme outputs S1(t) and S2(t)
Figure
3
Do movemes exist in practice?
In other words can we observe human actions whose underling dynamics
are characterized by parameters that in parameter space separate as
in Fig.2? It is clear that if this were the case there would exist human
activities which can be classified and recognized on the basis of their
dynamics. On the basis of the computer experiments we carried out the
answer seems to be yes, movemes exist. In particular we found two actions
which can be defined as movemes: reach moveme and draw moveme. The sequences
of experiments are represented in Fig.4. In the draw sequence the user
had to redraw a randomly appearing line, while in the reach sequence
the user had to reach three randomly appearing points
Figure
4
Figure
5
The resulting
parameters plotted in parameter space are represented in Fig.5. From
such figures we find the two sets CR and CD in parameter space that
we defined in Fig.2. Such sets are linearly separable with small errors
(the training error is about 4%). At this point we can claim that the
two sets CR and CD parameterize two dynamical model sets that we previously
called MR and MD which according to the definition are dynamically independent
and therefore they form a set {MR,MD} of movemes. We say also that the
set {MR,MD} constitute an alphabet of movemes. Thanks to the mutual
positions of the sets CR and CD we can solve a classification problem,
that is: given a signal y(t) (that is a reach or a draw action) determine,
on the basis of our alphabet, what is the moveme y(t) is more likely
to come from. The results of the classification problem are reported
in the second column of the table in Fig.5, and they are satisfactory.
Segmentation problem. Once the classification problem has been solved,
we want to solve the problem of recognizing a reach or a draw action
even when it takes place in a composed activity:
Effective
segmentation point and segmentation point which results from the segmentation
algorithm
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