PhDRecent advances in robust subspace estimation have made dimensionality reduction and
noise and outlier suppression an area of interest for research, along with continuous
improvements in computer vision applications. Due to the nature of image and video
signals that need a high dimensional representation, often storage, processing, transmission,
and analysis of such signals is a difficult task. It is therefore desirable to obtain a
low-dimensional representation for such signals, and at the same time correct for corruptions,
errors, and outliers, so that the signals could be readily used for later processing.
Major recent advances in low-rank modelling in this context were initiated by the work of
Cand`es et al. [17] where the authors provided a solution for the long-standing problem of
decomposing a matrix into low-rank and sparse components in a Robust Principal Component
Analysis (RPCA) framework. However, for computer vision applications RPCA
is often too complex, and/or may not yield desirable results. The low-rank component
obtained by the RPCA has usually an unnecessarily high rank, while in certain tasks
lower dimensional representations are required. The RPCA has the ability to robustly
estimate noise and outliers and separate them from the low-rank component, by a sparse
part. But, it has no mechanism of providing an insight into the structure of the sparse
solution, nor a way to further decompose the sparse part into a random noise and a structured
sparse component that would be advantageous in many computer vision tasks. As
videos signals are usually captured by a camera that is moving, obtaining a low-rank
component by RPCA becomes impossible. In this thesis, novel Approximated RPCA
algorithms are presented, targeting different shortcomings of the RPCA. The Approximated
RPCA was analysed to identify the most time consuming RPCA solutions, and
replace them with simpler yet tractable alternative solutions. The proposed method is
able to obtain the exact desired rank for the low-rank component while estimating a
global transformation to describe camera-induced motion. Furthermore, it is able to
decompose the sparse part into a foreground sparse component, and a random noise
part that contains no useful information for computer vision processing. The foreground
sparse component is obtained by several novel structured sparsity-inducing norms, that
better encapsulate the needed pixel structure in visual signals. Moreover, algorithms for
reducing complexity of low-rank estimation have been proposed that achieve significant
complexity reduction without sacrificing the visual representation of video and image
information. The proposed algorithms are applied to several fundamental computer
vision tasks, namely, high efficiency video coding, batch image alignment, inpainting,
and recovery, video stabilisation, background modelling and foreground segmentation,
robust subspace clustering and motion estimation, face recognition, and ultra high definition
image and video super-resolution. The algorithms proposed in this thesis including
batch image alignment and recovery, background modelling and foreground segmentation,
robust subspace clustering and motion segmentation, and ultra high definition
image and video super-resolution achieve either state-of-the-art or comparable results to
existing methods
