This paper presents an extended MCMC method for tracking and an extended HMM method for learning/recognizing multiple moving objects in videos with jittering backgrounds. A GUI with enhanced usability is also proposed. Previous MCMC and HMM based methods are known to suffer performance impairments, degraded tracking and recognition accuracy and higher computation costs, when challenged with appearance and trajectory changes such as occlusion, interaction, and varying numbers of moving objects. This paper proposes a cost reduction method for the MCMC approach by taking moves, i.e., birth and death, out of the iteration loop of the Markov chain when different moving objects interact. For stable and robust tracking, an ellipse model with stochastic model parameters is used. Moreover, our HMM method integrates several different modules in order to cope with multiple discontinuous trajectories. The GUI proposed herein offers an auto-allocation module of symbols from images and a hand-drawing module for efficient trajectory learning and for interest trajectory addition. Experiments demonstrate the advantages of our method and GUI in tracking, learning, and recognizing spatio-temporal smooth and discontinuous trajectories.