Revista de Matemáticas Aplicadas y Computacionales

Tracking of humans in dynamic scenes has been an important topic of research. There has been considerable work in tracking humans and other objects in recent years. A real-time method for tracking multiple moving objects based on effective Gaussian Mixture Model (GMM), and identifying the moving objects with Joint Probability Data Association Filter (JPDAF) is proposed in this paper. Most tracking algorithms have better performance under static background but get worse results under background with fake motions. Therefore, most of the tracking algorithms are used in indoor environment. An adaptive Gaussian Mixtures has a nice property in resolving this problem. This paper uses recursive equations to constantly update the parameters of a Gaussian Mixture Model and to simultaneously select the appropriate number of components for each pixel. Therefore, this method is more time and memory efficient than the common GMM with the fixed component number. In tracking multiple moving objects, problems occur when objects pass across each other. The JPDAF method is used in this paper to solve this problem. Moreover, it can effectively deal with the various scenes such as the indoor scene, the outdoor scene, and the cluttered scene. The experimental results on our test sequence demonstrate the high efficiency of the proposed method.

This paper deals with the periodic boundary value problems where is a constant and in which case the associated Greens function may changes sign. The existence result of positive solutions is established by using the fixed point index theory of cone mapping.