How Conditional Random Fields Learn Dynamics: An Example-Based Study

In this paper we investigate how Conditional Random Fields (CRFs) learn dynamics. To demonstrate the ability of CRF in learning dynamics, a discriminative probabilistic framework, Temporal Conditional Random Fields, is presented for the modeling of the object motion and tracking. The main drawback of generative models, such as HMM and MRF is that they can simply employ the relation between states without considering the relation between states and measurements, while discriminative frameworks can model any arbitrary relation between measurements and states. To facilitate such a powerful graphical model to learn the object motion, and to achieve a CRF-based estimation based upon the advantage of the discriminative framework, a set of graphical temporal relations is proposed for the object tracking, including feature functions, such as optical flow (calculated based upon consequent frames) and line field features. Based on temporal feature function, we show the ability of CRF in dynamic learning mathematically. As it is assumed that the object motion is nearly constant and that the current measurement is not available when TCRF estimates the target state, therefore, the changing of the object motion is addressed by utilizing a template matching in order to determine and then retrain TCRF. The proposed method is validated using synthetic and real data sequences. This shows that the TCRF estimation error is approximately zero.