A Dynamic Programming Solution to Bounded Dejittering Problems

We propose a dynamic programming solution to image dejittering problems with bounded displacements and obtain efficient algorithms for the removal of line jitter, line pixel jitter, and pixel jitter.Comment: The final publication is available at link.springer.co

Optical flow estimation using steered-L1 norm

Motion is a very important part of understanding the visual picture of the surrounding environment. In image processing it involves the estimation of displacements for image points in an image sequence. In this context dense optical flow estimation is concerned with the computation of pixel displacements in a sequence of images, therefore it has been used widely in the field of image processing and computer vision. A lot of research was dedicated to enable an accurate and fast motion computation in image sequences. Despite the recent advances in the computation of optical flow, there is still room for improvements and optical flow algorithms still suffer from several issues, such as motion discontinuities, occlusion handling, and robustness to illumination changes. This thesis includes an investigation for the topic of optical flow and its applications. It addresses several issues in the computation of dense optical flow and proposes solutions. Specifically, this thesis is divided into two main parts dedicated to address two main areas of interest in optical flow. In the first part, image registration using optical flow is investigated. Both local and global image registration has been used for image registration. An image registration based on an improved version of the combined Local-global method of optical flow computation is proposed. A bi-lateral filter was used in this optical flow method to improve the edge preserving performance. It is shown that image registration via this method gives more robust results compared to the local and the global optical flow methods previously investigated. The second part of this thesis encompasses the main contribution of this research which is an improved total variation L1 norm. A smoothness term is used in the optical flow energy function to regularise this function. The L1 is a plausible choice for such a term because of its performance in preserving edges, however this term is known to be isotropic and hence decreases the penalisation near motion boundaries in all directions. The proposed improved L1 (termed here as the steered-L1 norm) smoothness term demonstrates similar performance across motion boundaries but improves the penalisation performance along such boundaries

Online learning the consensus of multiple correspondences between sets.

When several subjects solve the assignment problem of two sets, differences on the correspondences computed by these subjects may occur. These differences appear due to several factors. For example, one of the subjects may give more importance to some of the elements’ attributes than another subject. Another factor could be that the assignment problem is computed through a suboptimal algorithm and different non-optimal correspondences can appear. In this paper, we present a consensus methodology to deduct the consensus of several correspondences between two sets. Moreover, we also present an online learning algorithm to deduct some weights that gauge the impact of each initial correspondence on the consensus. In the experimental section, we show the evolution of these parameters together with the evolution of the consensus accuracy. We observe that there is a clear dependence of the learned weights with respect to the quality of the initial correspondences. Moreover, we also observe that in the first iterations of the learning algorithm, the consensus accuracy drastically increases and then stabilises

Low-rate non-intrusive load monitoring approaches via graph signal processing

The large-scale roll-out of smart metering worldwide brings many new application possibilities. One promising application is appliance-level energy feedback based on identifying individual loads from aggregate measurements. Driven by high application potentials, the research in this area has intensified. In particular, non-intrusive load monitoring (NILM), that is, estimating appliance load consumption from aggregate readings, using software means only, has attracted a lot of attention, since it does not require any additional hardware to be installed. This thesis first proposes two Graph Signal Processing (GSP)-based approaches for disaggregation of total energy consumption down to individual appliances used. The first approach uses the Graph Laplacian Regularisation (GLR) minimiser results as a starting point, adding further refinement via Simulated Annealing (SA). The second approach applies data segmentation and associates data segments with graph nodes. A Dynamic Time Warping (DTW) distance is applied for evaluating weights between graph nodes. GLR minimiser is again used for clustering. Finally, a generic optimisation based approach is proposed for improving the accuracy of existing NILM by minimising the difference between the measured aggregate load and the sum of estimated individual loads with the difference from original NILM approaches' results as regularisation. For all proposed methods, the competitive performance are demonstrated in terms of both accuracy and effciency compared to state-of-the-art approaches, using the public Personalised Retrofit Decision Support Tools For UK Homes Using Smart Home Technology (REFIT) dataset and Reference Energy Disaggregation Dataset (REDD) electrical load datasets.The large-scale roll-out of smart metering worldwide brings many new application possibilities. One promising application is appliance-level energy feedback based on identifying individual loads from aggregate measurements. Driven by high application potentials, the research in this area has intensified. In particular, non-intrusive load monitoring (NILM), that is, estimating appliance load consumption from aggregate readings, using software means only, has attracted a lot of attention, since it does not require any additional hardware to be installed. This thesis first proposes two Graph Signal Processing (GSP)-based approaches for disaggregation of total energy consumption down to individual appliances used. The first approach uses the Graph Laplacian Regularisation (GLR) minimiser results as a starting point, adding further refinement via Simulated Annealing (SA). The second approach applies data segmentation and associates data segments with graph nodes. A Dynamic Time Warping (DTW) distance is applied for evaluating weights between graph nodes. GLR minimiser is again used for clustering. Finally, a generic optimisation based approach is proposed for improving the accuracy of existing NILM by minimising the difference between the measured aggregate load and the sum of estimated individual loads with the difference from original NILM approaches' results as regularisation. For all proposed methods, the competitive performance are demonstrated in terms of both accuracy and effciency compared to state-of-the-art approaches, using the public Personalised Retrofit Decision Support Tools For UK Homes Using Smart Home Technology (REFIT) dataset and Reference Energy Disaggregation Dataset (REDD) electrical load datasets

Low-rank and sparse reconstruction in dynamic magnetic resonance imaging via proximal splitting methods

Dynamic magnetic resonance imaging (MRI) consists of collecting multiple MR images in time, resulting in a spatio-temporal signal. However, MRI intrinsically suffers from long acquisition times due to various constraints. This limits the full potential of dynamic MR imaging, such as obtaining high spatial and temporal resolutions which are crucial to observe dynamic phenomena. This dissertation addresses the problem of the reconstruction of dynamic MR images from a limited amount of samples arising from a nuclear magnetic resonance experiment. The term limited can be explained by the approach taken in this thesis to speed up scan time, which is based on violating the Nyquist criterion by skipping measurements that would be normally acquired in a standard MRI procedure. The resulting problem can be classified in the general framework of linear ill-posed inverse problems. This thesis shows how low-dimensional signal models, specifically lowrank and sparsity, can help in the reconstruction of dynamic images from partial measurements. The use of these models are justified by significant developments in signal recovery techniques from partial data that have emerged in recent years in signal processing. The major contributions of this thesis are the development and characterisation of fast and efficient computational tools using convex low-rank and sparse constraints via proximal gradient methods, the development and characterisation of a novel joint reconstruction–separation method via the low-rank plus sparse matrix decomposition technique, and the development and characterisation of low-rank based recovery methods in the context of dynamic parallel MRI. Finally, an additional contribution of this thesis is to formulate the various MR image reconstruction problems in the context of convex optimisation to develop algorithms based on proximal splitting methods

A discrete graph Laplacian for signal processing

In this thesis we exploit diffusion processes on graphs to effect two fundamental problems of image processing: denoising and segmentation. We treat these two low-level vision problems on the pixel-wise level under a unified framework: a graph embedding. Using this framework opens us up to the possibilities of exploiting recently introduced algorithms from the semi-supervised machine learning literature. We contribute two novel edge-preserving smoothing algorithms to the literature. Furthermore we apply these edge-preserving smoothing algorithms to some computational photography tasks. Many recent computational photography tasks require the decomposition of an image into a smooth base layer containing large scale intensity variations and a residual layer capturing fine details. Edge-preserving smoothing is the main computational mechanism in producing these multi-scale image representations. We, in effect, introduce a new approach to edge-preserving multi-scale image decompositions. Where as prior approaches such as the Bilateral filter and weighted-least squares methods require multiple parameters to tune the response of the filters our method only requires one. This parameter can be interpreted as a scale parameter. We demonstrate the utility of our approach by applying the method to computational photography tasks that utilise multi-scale image decompositions. With minimal modification to these edge-preserving smoothing algorithms we show that we can extend them to produce interactive image segmentation. As a result the operations of segmentation and denoising are conducted under a unified framework. Moreover we discuss how our method is related to region based active contours. We benchmark our proposed interactive segmentation algorithms against those based upon energy-minimisation, specifically graph-cut methods. We demonstrate that we achieve competitive performance

New Insights on Learning Rules for Hopfield Networks: Memory and Objective Function Minimisation

Hopfield neural networks are a possible basis for modelling associative memory in living organisms. After summarising previous studies in the field, we take a new look at learning rules, exhibiting them as descent-type algorithms for various cost functions. We also propose several new cost functions suitable for learning. We discuss the role of biases (the external inputs) in the learning process in Hopfield networks. Furthermore, we apply Newtons method for learning memories, and experimentally compare the performances of various learning rules. Finally, to add to the debate whether allowing connections of a neuron to itself enhances memory capacity, we numerically investigate the effects of self coupling. Keywords: Hopfield Networks, associative memory, content addressable memory, learning rules, gradient descent, attractor networksComment: 8 pages, IEEE-Xplore, 2020 International Joint Conference on Neural Networks (IJCNN), Glasgo

Statistical extraction of process zones and representative subspaces in fracture of random composite

We propose to identify process zones in heterogeneous materials by tailored statistical tools. The process zone is redefined as the part of the structure where the random process cannot be correctly approximated in a low-dimensional deterministic space. Such a low-dimensional space is obtained by a spectral analysis performed on pre-computed solution samples. A greedy algorithm is proposed to identify both process zone and low-dimensional representative subspace for the solution in the complementary region. In addition to the novelty of the tools proposed in this paper for the analysis of localised phenomena, we show that the reduced space generated by the method is a valid basis for the construction of a reduced order model.Comment: Submitted for publication in International Journal for Multiscale Computational Engineerin