*D. Bounding Box Tracking*

In this section explain how the weight vector is computed, by tracking the bounding box of the moving objects. In order to exploit weighted L1 optimization to solve the recovery problem for inferring prior information about the current foreground image from the previously decoded frames. Our solution consists in identifying the foreground objects and tracking the motion of the bounding boxes enclosing them, so that estimate the position of the objects in the current frame exploiting the past ones.

Let us assume that, at some time instant, the foreground image has been correctly obtained. In order to initialize the tracking algorithm, the absolute value of the foreground image is thresholded and the connected foreground pixels are labeled as being part of the same blob, so that the identified blobs represent the objects in the scene. In order to make the system robust to oversegmentation, in this section implemented a simple algorithm that merges blobs on the basis of a virtual merge evaluation criterion. The next step consists in assigning each blob to one of the detected objects. In other words, need to link each of the blobs identified in the current frame with the blob representing the same moving object in the previous frame. In this way successfully track the motion of the object across frames. The match is performed by associating each blob with the object that best describes it in terms of position and size.

Object tracking is performed by means of particle filtering. The problem can be formulated as the estimation of the a posteriori probability distribution of a random variable zt , representing the state of the system at time t (e.g., object position and velocity), given the available observations {y1…yt} (e.g., available video data). Particle filters model the a posteriori distribution of the state as a finite set of particles, each associated to a state vector ZJt and a particle weight w,t , which is proportional to the likelihood of the state vector ZJt with respect to the current observations. In this work use a sequential importance resampling (SIR) particle filter implementation, which requires the definition of a transition model P( Zt| Zt-1) , to define the dynamic evolution of the particle states, and a likelihood function P( yt| Zt) , to compute the particle weights.