1. 1 Challenge the future Chaotic Invariants for Human Action Recognition Ali, Basharat, & Shah, ICCV 2007

2. 2 Challenge the future Premise: Moving reference joints carry information about human actions

3. 3 Challenge 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 function How to capture the nonlinear physics of human actions?

4. 4 Challenge 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

5. 5 Challenge 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

6. 6 Challenge the future Example of application of delay- embedding theorem: Lorenz system:

7. 7 Challenge the future Example of application of delay- embedding theorem: Lorenz system: plotting x, x - delay, x -2*delay strange attractor:

8. 8 Challenge the future Appl. of delay-embedding theorem to movements of reference joints:

9. 9 Challenge 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

10. 10 Challenge the future 9 Different Actions

11. 11 Challenge the future 3 time series (x, y, and z) for 5 reference joints

12. 12 Challenge the future Results of activity classification using chaotic invariants: