  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. G-LBM
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 the background scenes in
videos. 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.
