Auto-regressive dynamical models Continuous form of Markov process Linear Gaussian model Hidden states and stochastic observations (emissions) Statistical filters: Kalman, Particle EM learning Mixed states

Configuration AR model Parametric shape/texture model, eg curve model: Auto-regressive dynamical model driven by independent noise ARP order possibly nonlinear

Deformable curve model Planar affine + learned warps Active shape models (Cootes&Taylor, 93) Residual PCA (“Active Contours”, Blake & Isard, 98) Active appearance models (Cootes, Edwards &Taylor, 98) curve model:

Configuration Linear Gaussian AR model Prior shape “Steady state” prior Linear AR model (“Active Contours”, Blake and Isard, Springer 1998) (1 st order)

Gaussian processes for shape & motion intra-classsingle object (Reynard, Wildenberg, Blake & Marchant, ECCV 96)

Stochastic observer Kalman filter (Forward filter) Kalman smoothing filter (Forward-Backward) Kalman filter independent noise (Gelb 74) alsoetc.

Classical Kalman filter

Visual clutter

Visual clutter  observational nonlinearity

Particle Filter: Non-Gaussian Kalman filter

Particle Filter (PF) continue

particles “sprayed” along the contour “JetStream”: cut-and-paste by particle filtering

Propagating Particles particles “sprayed” along the contour particles “sprayed” along the contour contour smoothness prior contour smoothness prior

Branching

MLE Learning of a linear AR Model Direct observations: “Classic” Yule-Walker Learn parameters by maximizing: which for linear AR process  minimizing Finally solve: where “sufficient statistics” are:

Handwriting -- simulation of learned ARP model “Scribble” -- disassembly

Simulation of learned Gait -- simulation of learned ARP model

Walking Simulation (ARP)

Walking Simulation (ARP + HMM) (Toyama & Blake 2001)

Dynamic texture (S. Soatto, G. Doretto, Y. N. Wu, ICCV 01; A. Fitzgibbon, ICCV01)

Speech-tuned filter (Blake, Isard & Reynard, 1985)

EM learning Stochastic observations z:unknown -- hidden unavailable – classic EM: M-step E-step i.e. FB smoothing

PF: forward only

PF: forward-backward continue

Juggling (North et al., 2000)

State lifetimes and transition rates also learned Learned Dynamics of Juggling

Juggling

Perception and Classification Ballistic (left)Catch, carry, throw (left)

Underlying classifications

Learning Algorithms EM-P

1D  Markov models 1D  Markov models 2D Markov models

EM-PF Learning Forward-backward particle smoother (Kitagawa 96, Isard and Blake, 98) for non-Gaussian problems:particle smoother Generates particles with weights Autocorrelations: Transition Frequencies: