94 research outputs found
Background Subtraction via Generalized Fused Lasso Foreground Modeling
Background Subtraction (BS) is one of the key steps in video analysis. Many
background models have been proposed and achieved promising performance on
public data sets. However, due to challenges such as illumination change,
dynamic background etc. the resulted foreground segmentation often consists of
holes as well as background noise. In this regard, we consider generalized
fused lasso regularization to quest for intact structured foregrounds. Together
with certain assumptions about the background, such as the low-rank assumption
or the sparse-composition assumption (depending on whether pure background
frames are provided), we formulate BS as a matrix decomposition problem using
regularization terms for both the foreground and background matrices. Moreover,
under the proposed formulation, the two generally distinctive background
assumptions can be solved in a unified manner. The optimization was carried out
via applying the augmented Lagrange multiplier (ALM) method in such a way that
a fast parametric-flow algorithm is used for updating the foreground matrix.
Experimental results on several popular BS data sets demonstrate the advantage
of the proposed model compared to state-of-the-arts
Weighted Low Rank Approximation for Background Estimation Problems
Classical principal component analysis (PCA) is not robust to the presence of
sparse outliers in the data. The use of the norm in the Robust PCA
(RPCA) method successfully eliminates the weakness of PCA in separating the
sparse outliers. In this paper, by sticking a simple weight to the Frobenius
norm, we propose a weighted low rank (WLR) method to avoid the often
computationally expensive algorithms relying on the norm. As a proof
of concept, a background estimation model has been presented and compared with
two norm minimization algorithms. We illustrate that as long as a
simple weight matrix is inferred from the data, one can use the weighted
Frobenius norm and achieve the same or better performance
Online and Batch Supervised Background Estimation via L1 Regression
We propose a surprisingly simple model for supervised video background
estimation. Our model is based on regression. As existing methods for
regression do not scale to high-resolution videos, we propose several
simple and scalable methods for solving the problem, including iteratively
reweighted least squares, a homotopy method, and stochastic gradient descent.
We show through extensive experiments that our model and methods match or
outperform the state-of-the-art online and batch methods in virtually all
quantitative and qualitative measures
Convex and Network Flow Optimization for Structured Sparsity
We consider a class of learning problems regularized by a structured
sparsity-inducing norm defined as the sum of l_2- or l_infinity-norms over
groups of variables. Whereas much effort has been put in developing fast
optimization techniques when the groups are disjoint or embedded in a
hierarchy, we address here the case of general overlapping groups. To this end,
we present two different strategies: On the one hand, we show that the proximal
operator associated with a sum of l_infinity-norms can be computed exactly in
polynomial time by solving a quadratic min-cost flow problem, allowing the use
of accelerated proximal gradient methods. On the other hand, we use proximal
splitting techniques, and address an equivalent formulation with
non-overlapping groups, but in higher dimension and with additional
constraints. We propose efficient and scalable algorithms exploiting these two
strategies, which are significantly faster than alternative approaches. We
illustrate these methods with several problems such as CUR matrix
factorization, multi-task learning of tree-structured dictionaries, background
subtraction in video sequences, image denoising with wavelets, and topographic
dictionary learning of natural image patches.Comment: to appear in the Journal of Machine Learning Research (JMLR
Weighted Low-Rank Approximation of Matrices and Background Modeling
We primarily study a special a weighted low-rank approximation of matrices
and then apply it to solve the background modeling problem. We propose two
algorithms for this purpose: one operates in the batch mode on the entire data
and the other one operates in the batch-incremental mode on the data and
naturally captures more background variations and computationally more
effective. Moreover, we propose a robust technique that learns the background
frame indices from the data and does not require any training frames. We
demonstrate through extensive experiments that by inserting a simple weight in
the Frobenius norm, it can be made robust to the outliers similar to the
norm. Our methods match or outperform several state-of-the-art online
and batch background modeling methods in virtually all quantitative and
qualitative measures.Comment: arXiv admin note: text overlap with arXiv:1707.0028
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