In the specific application scenario addressed in this work, Zt = \ct, st, ut] represents the state vector, where the components are the bounding box centroid position (ct G □ 2 ) , size (st G □ 2 ) and velocity ( ut G □ 2 ) of the objects to be tracked, while the observation vector yt is set equal to the blob representing the object in the recovered foreground ft .

The state transition model expresses the a priori knowledge about the motion evolution of the target and provides a prediction based on the past state values. At each time instant, the state of each particle is updated according to the following model, and constructed upon the equation of motion:

Where |^cj , Sj ,uj is the predicted state vector associated with the j th particle, DT is the time sample interval and Xc, Xs, X are random terms which provide the system with a diversity of hypotheses. At each time instant, the bounding box centroid position, size and velocity are estimated according to the following equations:

Where (Xc, (Xu are two parameters that adjust the adaptation rates.

The particle weight w,t is computed to be proportional to the matching between the bounding box represented by the state vector ZJt to be more precise, it can be use the following formula:

wt = ER -dBB (6)

Two terms are used to composing the weights. The first term represents the energy ratio Er , which is defined as the ratio between the energy of the portion of the blob contained in the bounding box and the total energy of the blob. The second term is the bounding box density dbb , defined as the percentage of pixels contained in the bounding box having an intensity value greater than a fixed threshold. In fact, a correctly positioned over-dimensioned bounding box would exhibit maximum energy ratio, as it would completely enclose the blob, but also low density, since many pixels belonging to the bounding box but not to the blob would have negligible intensity values.

Therefore, the bounding box would be correctly assigned with a low weight, since it does not provide a satisfactory representation of the blob. On the other hand, a large weight is assigned to a bounding box which correctly matches both the position and size of the blob, since it is characterized by maximum energy ratio and very high density.