We consider the problem of tracking the boundary contour of a moving and deforming object from a sequence of images. If the motion of the “object” or region of interest is constrained (e.g. rigid or… (More)

We study the change detection problem in partially observed nonlinear dynamic systems. We assume that the change parameters are unknown and the change could be gradual (slow) or sudden (drastic). For… (More)

Definitions: 1. A hidden Markov model (HMM) refers to a set of " hidden " states X 0 with the following joint PMF or PDF: p(x 0:T , y 1:T) = [p(x 0)[ T ∏ τ =1 p(x τ |x τ −1)]][[ T ∏ τ =1 p(y τ |x… (More)

We study the change detection problem in general HMMs, when change parameters are unknown and the change could be gradual (slow) or sudden (drastic). Drastic changes can be detected easily using the… (More)

Consider the following state space model (signal and observation model). Y t = H t X t + W t , W t ∼ N (0, R) (1) X t = F t X t−1 + U t , U t ∼ N (0, Q) (2)

We propose a particle filtering algorithm for tracking continuous closed curves which form the boundary of objects in images. This can be used for tracking moving and deforming objects from a… (More)

1. First, assume a scalar unknown parameter θ (a) Min classical MSE estimator: ˆ θ(X) = arg minˆθ E X [(θ − ˆ θ(X)) 2 2 ] (b) Often the resulting estimator is not realizable, i.e. it depends on θ.

• Proof: X is j G implies that V = uX is G with mean uμ and variance uΣu. Thus its characteristic function, CV (t) = e ituμe−t 2uTΣu/2. But CV (t) = E[e itV ] = E[e TX ]. If we set t = 1, then this… (More)