Chaotic Invariants for Human Action
Recognition
Ali, Basharat, & Shah, ICCV 2007
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Premise: Moving reference joints carry
information about human actions
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Assumption: Human actions are
generated by a nonlinear dynamical
system
•Dynamical:
the system’s behaviour changes over time
•Nonlinear:
the rule(s) describing this change cannot be
written as a linear function
How to capture the nonlinear physics of
human actions?
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Assumption: Human actions are
generated by a nonlinear dynamical
system
•Movement trajectories of reference joints only
provide a low-dimensional observation of the
human action system
•But, they still carry information about the entire
(nonlinear) system
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Approach:
Chaotic Invariants
1. Reconstruct the dynamical behaviour of the
human action system based on movement
trajectories of reference joints
•
delay-embedding theorem (Takens, 1981)
2. Characterize this reconstructed dynamical
behaviour with chaotic invariants
3. Action recognition based on chaotic
invariants
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Example of application of delayembedding theorem:
•Lorenz system:
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Example of application of delayembedding theorem:
•Lorenz system:
strange attractor:
•plotting
x,
x - delay,
x -2*delay
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Appl. of delay-embedding theorem to
movements of reference joints:
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Characterisation of strange attractor
with chaotic invariants
•Maximum lyapunov exponent:
Quantifies the divergence of the strange
attractor
•Correlation integral:
Quantifies the density of points in the phase
space (using a threshold for nearby points)
•Correlation dimension:
Quantifies the sensitivity of the correlation
integral for the applied threshold
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9 Different Actions
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3 time series (x, y, and z) for 5
reference joints
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Results of activity classification using
chaotic invariants:
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