1 challenge the future chaotic invariants for human action recognition ali, basharat, & shah,...
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1Challenge the future
Chaotic Invariants for Human Action Recognition
Ali, Basharat, & Shah, ICCV 2007
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2Challenge the future
Premise: Moving reference joints carry information about human
actions
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3Challenge the future
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 functionHow to capture the nonlinear physics of
human actions?
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4Challenge the future
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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5Challenge the future
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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6Challenge the future
Example of application of delay-embedding theorem:
• Lorenz system:
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7Challenge the future
Example of application of delay-embedding theorem:
• Lorenz system:
• plotting x, x - delay, x -2*delay
strange attractor:
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8Challenge the future
Appl. of delay-embedding theorem to movements of reference joints:
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9Challenge the future
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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10Challenge the future
9 Different Actions
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11Challenge the future
3 time series (x, y, and z) for 5 reference joints
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12Challenge the future
Results of activity classification using chaotic invariants: