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 temporal evolution of histograms can not be well described by linear dynamic systems. Instead, we employ the concept of (KLDS) which model the observations in a kernel feature space. The parameters describing the KLDS are the representations of the visual processes employed in his work. Using these descriptors in the context of supervised learning requires the definition of a dissimilarity measure. The available literature on KLDSs offers a manageable number of dissimilarity measures that perform insufficiently on the SoB descriptors used in this work, as will be shown in the experimental Section , which may be due to the fact that they put too much emphasis on the dynamic part of the KLDS parameters, whereas in the setting discussed in this work, static information, i.e. the information not related to the temporal context has a considerable significance. The KLDS itself was introduced in @cite_11 and motivated by the recognition of dynamic textures. As a dissimilarity measure, a kernelized version of the widely adopted Martin distance @cite_20 was applied.
@cite_20 @cite_11
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Abstract We define a notion of subspace angles between two linear, autoregressive moving average, single-input–single-output models by considering the principal angles between subspaces that are derived from these models. We show how a recently defined metric for these models, which is based on their cepstra, relates to the subspace angles between the models. The dynamic texture is a stochastic video model that treats the video as a sample from a linear dynamical system. The simple model has been shown to be surprisingly useful in domains such as video synthesis, video segmentation, and video classification. However, one major disadvantage of the dynamic texture is that it can only model video where the motion is smooth, i.e. video textures where the pixel values change smoothly. In this work, we propose an extension of the dynamic texture to address this issue. Instead of learning a linear observation function with PCA, we learn a non-linear observation function using kernel-PCA. The resulting kernel dynamic texture is capable of modeling a wider range of video motion, such as chaotic motion (e.g. turbulent water) or camera motion (e.g. panning). We derive the necessary steps to compute the Martin distance between kernel dynamic textures, and then validate the new model through classification experiments on video containing camera motion.