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Nowadays, with the increased numbers of video cameras, the amount of recorded video is growing. Efficient video browsing and retrieval are critical issues when considering the amount of raw video data to be condensed. Activity-based video synopsis is a popular approach to solving the video condensation problem. However, conventional synopsis methods always consists of complicated and pairwise energy terms that involve a time-consuming optimization problem. In this paper, we propose a simple online video synopsis framework in which the number of collisions of objects is classified first. Different optimization strategies are applied according to different collision situations to maintain a balance among the computational cost, condensation ratio, and collision cost. Secondly, tube-resizing coefficients that are dynamic in different frames are adaptively assigned to a newly generated tube. Therefore, a suitable mapping result can be obtained in order to represent the proper size of the activity in each frame of the synopsis video. The maximum number of activities can be displayed in one frame with minimal collisions. Finally, in order to remove motion anti-facts and improve the visual quality of the condensed video, a smooth term is introduced to constrain the resizing coefficients. Experimental results on extensive videos validate the efficiency of the proposed method.

This paper is concerned with the stability analysis and control of a new smooth Chua's system. Firstly, the chaotic characteristic of the system is confirmed with the aid of the Lyapunov exponents. Secondly, it is proved that the system has globally exponential attractive set and positive invariant set. For the three unstable equilibrium points of the system, a linear controller is designed to globally exponentially stabilize the equilibrium points. Then, a linear controller and an adaptive controller are, respectively, proposed so that two similar types of smooth Chua's systems are globally synchronized, and the estimation errors of the uncertain parameters converge to zero as t tends to infinity. Finally, the numerical simulations are also presented.