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Top1. Introduction
Moving object detection is the first step as a pre-processing task for many computer vision applications, e.g., visual surveillance (Javed, Shafique, & Shah, 2007; Huang & Chen, 2014), behavior recognition (Gowsikhaa, Abirami, & Abiram, 2014), video retrieval (Chen & Huang, 2014) and video compression (Tong et al., 2014; Hadizadeh & Bajic, 2013). The objective of this task is to obtain the accurate foreground-background segmentation as an input for the high level analysis. Despite of its key importance, most traditional approaches (Hadizadeh & Bajic, 2013; Doretto et al., 2003) fail in the dynamic scenes. In some realistic scenarios shot by the static camera, the dynamic behaviors are caused by background elements, e.g., falling snow, moving water, rain, fountain, waves and swaying trees. In this case, objects of interest are moving among the complicated scene motion. Some scenes are static, but monitored by the moving or distant camera, or the static scenes are with ego- motion. It is very challenging to detect objects of interest in these dynamic scenes for computer vision community.
Recently, it is more successful in modeling the dynamic scenes as samples from a linear dynamical system (Doretto et al., 2003; Mahadevan & Vasconcelos, 2009; Gopalakrishnan, Rajan, & Hu, 2012). These works have demonstrated that DT as a probabilistic motion model is much more powerful than the classic background models. In fact, DT has the amazed ability to account for the various complex patterns of motion and appearance, while jointly modeling the spatiotemporal characteristics of the stochastic visual processes. One major limitation is that DT parameters estimation is based on batch-PCA. The complexity of the batch PCA is dominated by taking the SVD of a high-dimensional matrix. Let the observed data matrix be 
the complexity of SVD of 
is 
. So, the batch-PCA is a computationally inefficient method for high-dimensional vectors.
Besides, in the realm of DT, the dimension of state space 
is given or set experimentally. In practice, the parameter 
should be inferred from the observed data. DT represents the dynamic process as the output of the linear dynamic system driven by white, zero-mean Gaussian noise. If 
is set high as the order of the model, much noise will be included in the useful variable components, if not, some useful components will be removed. Therefore, the suitable selection of the parameter 
becomes very important.