Recent research in image and video recognition indicates that many visual processes can be thought of as being generated by a time-varying generative model. A nearby descriptive model for visual processes is thus a statistical distribution that varies over time. Specifically, modeling visual processes as streams of histograms generated by a kernelized linear dynamic system turns out to be efficient. We refer to such a model as a system of bags. In this paper, we investigate systems of bags with special emphasis on dynamic scenes and dynamic textures. Parameters of linear dynamic systems suffer from ambiguities. In order to cope with these ambiguities in the kernelized setting, we develop a kernelized version of the alignment distance. For its computation, we use a Jacobi-type method and prove its convergence to a set of critical points. We employ it as a dissimilarity measure on Systems of Bags. As such, it outperforms other known dissimilarity measures for kernelized linear dynamic systems, in particular the Martin distance and the Maximum singular value distance, in every tested classification setting. A considerable margin can be observed in settings, where classification is performed with respect to an abstract mean of video sets. For this scenario, the presented approach can outperform the state-of-the-art techniques, such as dynamic fractal spectrum or orthogonal tensor dictionary learning.
The novelty of this work is to explore the framework of SoB in the context of dynamic scene and large-scale dynamic texture recognition and to develop an appropriate dissimilarity measure. To this end, we adopt the framework of the from @cite_3 and develop a kernelized version suitable for the comparison of SoBs. Unlike the mentioned dissimilarity measures for SoBs, impact of the static and dynamic components can be chosen depending on the employed generative image model. Besides, its property of being the square of a metric and its simple definition based on the Frobenius distance allows for the definition of @cite_14 . This is crucial for the classification via the (NCC) @cite_35 . A part of this work is dedicated to the computation of abstract means of sets of KLDSs for avoiding the memory burden of (1-NN) classification.
@cite_35 @cite_14 @cite_3
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The research context of this article is the recognition and description of dynamic textures. In image processing, the wavelet transform has been successfully used for characterizing static textures. To our best knowledge, only two works are using spatio-temporal multiscale decomposition based on the tensor product for dynamic texture recognition. One contribution of this article is to analyze and compare the ability of the 2D+T curvelet transform, a geometric multiscale decomposition, for characterizing dynamic textures in image sequences. Two approaches using the 2D+T curvelet transform are presented and compared using three new large databases. A second contribution is the construction of these three publicly available benchmarks of increasing complexity. Existing benchmarks are either too small not available or not always constructed using a reference database. Feature vectors used for recognition are described as well as their relevance, and performances of the different methods are discussed. Finally, future prospects are exposed. We introduce a framework for defining a distance on the (non-Euclidean) space of Linear Dynamical Systems (LDSs). The proposed distance is induced by the action of the group of orthogonal matrices on the space of statespace realizations of LDSs. This distance can be efficiently computed for large-scale problems, hence it is suitable for applications in the analysis of dynamic visual scenes and other high dimensional time series. Based on this distance we devise a simple LDS averaging algorithm, which can be used for classification and clustering of time-series data. We test the validity as well as the performance of our group-action based distance on synthetic as well as real data and provide comparison with state-of-the-art methods.