G-LBM: Generative Low-Dimensional Background Model Estimation from Video Sequences
In this paper, we propose a computationally tractable and theoretically supported non-linear low-dimensional generative model to represent real-world data in the presence of noise and sparse outliers. The non-linear low-dimensional manifold discovery of d
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Abstract. In this paper, we propose a computationally tractable and theoretically supported non-linear low-dimensional generative model to represent real-world data in the presence of noise and sparse outliers. The non-linear low-dimensional manifold discovery of data is done through describing a joint distribution over observations, and their low-dimensional representations (i.e. manifold coordinates). Our model, called generative low-dimensional background model (G-LBM) admits variational operations on the distribution of the manifold coordinates and simultaneously generates a low-rank structure of the latent manifold given the data. Therefore, our probabilistic model contains the intuition of the non-probabilistic low-dimensional manifold learning. GLBM selects the intrinsic dimensionality of the underling manifold of the observations, and its probabilistic nature models the noise in the observation data. G-LBM has direct application in the background scenes model estimation from video sequences and we have evaluated its performance on SBMnet-2016 and BMC2012 datasets, where it achieved a performance higher or comparable to other state-of-the-art methods while being agnostic to different scenes. Besides, in challenges such as camera jitter and background motion, G-LBM is able to robustly estimate the background by effectively modeling the uncertainties in video observations in these scenarios. (The code and models are available at: https://github.com/brezaei/G-LBM.) Keywords: Background estimation · Foreground segmentation · Non-linear manifold learning · Deep neural network · Variational auto-encoding
Electronic supplementary material The online version of this chapter (https:// doi.org/10.1007/978-3-030-58610-2_18) contains supplementary material, which is available to authorized users. c Springer Nature Switzerland AG 2020 A. Vedaldi et al. (Eds.): ECCV 2020, LNCS 12357, pp. 293–310, 2020. https://doi.org/10.1007/978-3-030-58610-2_18
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Introduction
Many high-dimensional real world datasets consist of data points coming from a lower-dimensional manifold corrupted by noise and possibly outliers. In particular, background in videos recorded by a static camera might be generated from a small number of latent processes that all non-linearly affect the recorded video scenes. Linear multivariate analysis such as robust principal component analysis (RPCA) and its variants have long been used to estimate such underlying processes in the presence of noise and/or outliers in the measurements with large data matrices [6,17,41]. However, these linear processes may fail to find the low-dimensional structure of the data when the mapping of the data into the latent space is non-linear. For instance background scenes in realworld videos lie on one or more non-linear manifolds, an investigation to this fact is presented in [16]. Therefore, a robust representation of the data should find the underlying non-linear structure of the real-world data as well as its uncertainties. To this end, we propose a ge
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