Tracking using CONDENSATION: Conditional Density Propagation

Transcription

1 Tracking using CONDENSATION: Conditional Density Propagation Goal Model-based visual tracking in dense clutter at near video frae rates M. Isard and A. Blake, CONDENSATION Conditional density propagation for visual tracking, Int. J. Coputer Vision 29(1), 1998, pp Exaple of CONDENSATION Algorith Approach Probabilistic fraework for tracking objects such as curves in clutter using an iterative sapling algorith Model otion and shape of target Top-down approach Siulation instead of analytic solution 1

2 Probabilistic Fraework Object dynaics for a teporal Markov chain p Observations, z t, are independent (utually and w.r.t process) Use Bayes rule ( x Χ ) p( x x ) t t 1 t t 1 t 1 (, x X ) p( x X ) p( z x ) p Z t 1 t t 1 t t 1 i 1 i i X Z p(x) p(z) Notation State vector, e.g., curve s position and orientation Measureent vector, e.g., iage edge locations Prior probability of state vector; suarizes prior doain knowledge, e.g., by independent easureents Probability of easuring Z; fixed for any given iage p(z X) Probability of easuring Z given that the state is X; copares iage to expectation based on state p(x Z) Probability of X given that easureent Z has occurred; called state posterior Tracking as Estiation Copute state posterior, p(x Z), and select next state to be the one that axiizes this (Maxiu a Posteriori (MAP) estiate) Measureents are coplex and noisy, so posterior cannot be evaluated in closed for Particle filter (iterative sapling) idea: Stochastically approxiate the state posterior with a set of N weighted particles, (s, π), where s is a saple state and π is its weight Use Bayes rule to copute p(x Z) Factored Sapling Generate a set of saples that approxiates the posterior p(x Z) ( 1) ( N) Saple set s { s,..., s } generated fro p(x); each saple has a weight ( probability ) π i N p j 1 z p ( s z ( i ) ( s p z ( x) p( z x) ) ( j ) ) 2

3 Factored Sapling Estiating Target State N15 X CONDENSATION for one iage p ( X Z) Bayes Rule This is what you can evaluate This is what you want. Knowing p(x Z) will tell us what is the ost likely state X. This is what you ay know a priori, or what you can predict p( Z X) p( X) p( Z) This is a constant for a given iage CONDENSATION Algorith 1. Select: Randoly select N particles fro {s t-1 } based on weights π t-1 ; sae particle ay be picked ultiple ties (factored sapling) 2. Predict: Move particles according to deterinistic dynaics (drift), then perturb individually (diffuse) 3. Measure: Get a likelihood for each new saple by coparing it with the iage s local appearance, i.e., based on p(z t x t ); then update weight accordingly to obtain {(s t, π t )} 3

4 Posterior at tie k-1 Predicted state at tie k Posterior at tie k observation density s s k k s 1, π k, π k 1 k drift diffuse easure Notes on Updating Enforcing plausibility: Particles that represent ipossible configurations are discarded Diffusion odeled with a Gaussian Likelihood function: Convert goodness of prediction score to pseudo-probability More arkings closer to predicted arkings higher likelihood State Posterior State Posterior Aniation 4

5 Object Motion Model For video tracking we need a way to propagate probability densities, so we need a otion odel such as X t+1 A X t + B W t where W is a noise ter and A and B are state transition atrices that can be learned fro training sequences The state, X, of an object, e.g., a B-spline curve, can be represented as a point in a 6D state space of possible 2D affine transforations of the object φ Evaluating p(z X) x ρ z 2 if x p( z x) qp( z clutter) + p( z x, φ ) p( φ ) 1 where φ {true easureent is z } for 1,,M, and q 1 - Σ p(φ ) is the probability that the target is not visible M z otherwise < δ Dancing Exaple Hand Exaple 5

6 Pointing Hand Exaple Glasses Exaple 6D state space of affine transforations of a spline curve Edge detector applied along norals to the spline Autoregressive otion odel 3D Model-based Exaple 3D state space: iage position + angle Polyhedral odel of object Minerva Museu tour guide robot that used CONDENSATION to track its position in the useu Desired Location Exhibit 6

7 Advantages of Particle Filtering Nonlinear dynaics, easureent odel easily incorporated Copes with lots of false positives Multi-odal posterior okay (unlike Kalan filter) Multiple saples provides ultiple hypotheses Fast and siple to ipleent 7