Robust Subspace Estimation Using Low-rank Optimization. Theory And Applications In Scene Reconstruction, Video Denoising, And Activity Recognition.

In this dissertation, we discuss the problem of robust linear subspace estimation using low-rank optimization and propose three formulations of it. We demonstrate how these formulations can be used to solve fundamental computer vision problems, and provide superior performance in terms of accuracy and running time. Consider a set of observations extracted from images (such as pixel gray values, local features, trajectories . . . etc). If the assumption that these observations are drawn from a liner subspace (or can be linearly approximated) is valid, then the goal is to represent each observation as a linear combination of a compact basis, while maintaining a minimal reconstruction error. One of the earliest, yet most popular, approaches to achieve that is Principal Component Analysis (PCA). However, PCA can only handle Gaussian noise, and thus suffers when the observations are contaminated with gross and sparse outliers. To this end, in this dissertation, we focus on estimating the subspace robustly using low-rank optimization, where the sparse outliers are detected and separated through the `1 norm. The robust estimation has a two-fold advantage: First, the obtained basis better represents the actual subspace because it does not include contributions from the outliers. Second, the detected outliers are often of a specific interest in many applications, as we will show throughout this thesis. We demonstrate four different formulations and applications for low-rank optimization. First, we consider the problem of reconstructing an underwater sequence by removing the iii turbulence caused by the water waves. The main drawback of most previous attempts to tackle this problem is that they heavily depend on modelling the waves, which in fact is ill-posed since the actual behavior of the waves along with the imaging process are complicated and include several noise components; therefore, their results are not satisfactory. In contrast, we propose a novel approach which outperforms the state-of-the-art. The intuition behind our method is that in a sequence where the water is static, the frames would be linearly correlated. Therefore, in the presence of water waves, we may consider the frames as noisy observations drawn from a the subspace of linearly correlated frames. However, the noise introduced by the water waves is not sparse, and thus cannot directly be detected using low-rank optimization. Therefore, we propose a data-driven two-stage approach, where the first stage “sparsifies” the noise, and the second stage detects it. The first stage leverages the temporal mean of the sequence to overcome the structured turbulence of the waves through an iterative registration algorithm. The result of the first stage is a high quality mean and a better structured sequence; however, the sequence still contains unstructured sparse noise. Thus, we employ a second stage at which we extract the sparse errors from the sequence through rank minimization. Our method converges faster, and drastically outperforms state of the art on all testing sequences. Secondly, we consider a closely related situation where an independently moving object is also present in the turbulent video. More precisely, we consider video sequences acquired in a desert battlefields, where atmospheric turbulence is typically present, in addition to independently moving targets. Typical approaches for turbulence mitigation follow averaging or de-warping techniques. Although these methods can reduce the turbulence, they distort the independently moving objects which can often be of great interest. Therefore, we address the iv problem of simultaneous turbulence mitigation and moving object detection. We propose a novel three-term low-rank matrix decomposition approach in which we decompose the turbulence sequence into three components: the background, the turbulence, and the object. We simplify this extremely difficult problem into a minimization of nuclear norm, Frobenius norm, and `1 norm. Our method is based on two observations: First, the turbulence causes dense and Gaussian noise, and therefore can be captured by Frobenius norm, while the moving objects are sparse and thus can be captured by `1 norm. Second, since the object’s motion is linear and intrinsically different than the Gaussian-like turbulence, a Gaussian-based turbulence model can be employed to enforce an additional constraint on the search space of the minimization. We demonstrate the robustness of our approach on challenging sequences which are significantly distorted with atmospheric turbulence and include extremely tiny moving objects. In addition to robustly detecting the subspace of the frames of a sequence, we consider using trajectories as observations in the low-rank optimization framework. In particular, in videos acquired by moving cameras, we track all the pixels in the video and use that to estimate the camera motion subspace. This is particularly useful in activity recognition, which typically requires standard preprocessing steps such as motion compensation, moving object detection, and object tracking. The errors from the motion compensation step propagate to the object detection stage, resulting in miss-detections, which further complicates the tracking stage, resulting in cluttered and incorrect tracks. In contrast, we propose a novel approach which does not follow the standard steps, and accordingly avoids the aforementioned diffi- culties. Our approach is based on Lagrangian particle trajectories which are a set of dense trajectories obtained by advecting optical flow over time, thus capturing the ensemble motions v of a scene. This is done in frames of unaligned video, and no object detection is required. In order to handle the moving camera, we decompose the trajectories into their camera-induced and object-induced components. Having obtained the relevant object motion trajectories, we compute a compact set of chaotic invariant features, which captures the characteristics of the trajectories. Consequently, a SVM is employed to learn and recognize the human actions using the computed motion features. We performed intensive experiments on multiple benchmark datasets, and obtained promising results. Finally, we consider a more challenging problem referred to as complex event recognition, where the activities of interest are complex and unconstrained. This problem typically pose significant challenges because it involves videos of highly variable content, noise, length, frame size . . . etc. In this extremely challenging task, high-level features have recently shown a promising direction as in [53, 129], where core low-level events referred to as concepts are annotated and modelled using a portion of the training data, then each event is described using its content of these concepts. However, because of the complex nature of the videos, both the concept models and the corresponding high-level features are significantly noisy. In order to address this problem, we propose a novel low-rank formulation, which combines the precisely annotated videos used to train the concepts, with the rich high-level features. Our approach finds a new representation for each event, which is not only low-rank, but also constrained to adhere to the concept annotation, thus suppressing the noise, and maintaining a consistent occurrence of the concepts in each event. Extensive experiments on large scale real world dataset TRECVID Multimedia Event Detection 2011 and 2012 demonstrate that our approach consistently improves the discriminativity of the high-level features by a significant margin

Feature Selection Based on Sequential Orthogonal Search Strategy

This thesis introduces three new feature selection methods based on sequential orthogonal search strategy that addresses three different contexts of feature selection problem being considered. The first method is a supervised feature selection called the maximum relevance–minimum multicollinearity (MRmMC), which can overcome some shortcomings associated with existing methods that apply the same form of feature selection criterion, especially those that are based on mutual information. In the proposed method, relevant features are measured by correlation characteristics based on conditional variance while redundancy elimination is achieved according to multiple correlation assessment using an orthogonal projection scheme. The second method is an unsupervised feature selection based on Locality Preserving Projection (LPP), which is incorporated in a sequential orthogonal search (SOS) strategy. Locality preserving criterion has been proved a successful measure to evaluate feature importance in many feature selection methods but most of which ignore feature correlation and this means these methods ignore redundant features. This problem has motivated the introduction of the second method that evaluates feature importance jointly rather than individually. In the method, the first LPP component which contains the information of local largest structure (LLS) is utilized as a reference variable to guide the search for significant features. This method is referred to as sequential orthogonal search for local largest structure (SOS-LLS). The third method is also an unsupervised feature selection with essentially the same SOS strategy but it is specifically designed to be robust on noisy data. As limited work has been reported concerning feature selection in the presence of attribute noise, the third method is thus attempts to make an effort towards this scarcity by further exploring the second proposed method. The third method is designed to deal with attribute noise in the search for significant features, and kernel pre-images (KPI) based on kernel PCA are used in the third method to replace the role of the first LPP component as the reference variable used in the second method. This feature selection scheme is referred to as sequential orthogonal search for kernel pre-images (SOS-KPI) method. The performance of these three feature selection methods are demonstrated based on some comprehensive analysis on public real datasets of different characteristics and comparative studies with a number of state-of-the-art methods. Results show that each of the proposed methods has the capacity to select more efficient feature subsets than the other feature selection methods in the comparative studies

Emotion and Stress Recognition Related Sensors and Machine Learning Technologies

This book includes impactful chapters which present scientific concepts, frameworks, architectures and ideas on sensing technologies and machine learning techniques. These are relevant in tackling the following challenges: (i) the field readiness and use of intrusive sensor systems and devices for capturing biosignals, including EEG sensor systems, ECG sensor systems and electrodermal activity sensor systems; (ii) the quality assessment and management of sensor data; (iii) data preprocessing, noise filtering and calibration concepts for biosignals; (iv) the field readiness and use of nonintrusive sensor technologies, including visual sensors, acoustic sensors, vibration sensors and piezoelectric sensors; (v) emotion recognition using mobile phones and smartwatches; (vi) body area sensor networks for emotion and stress studies; (vii) the use of experimental datasets in emotion recognition, including dataset generation principles and concepts, quality insurance and emotion elicitation material and concepts; (viii) machine learning techniques for robust emotion recognition, including graphical models, neural network methods, deep learning methods, statistical learning and multivariate empirical mode decomposition; (ix) subject-independent emotion and stress recognition concepts and systems, including facial expression-based systems, speech-based systems, EEG-based systems, ECG-based systems, electrodermal activity-based systems, multimodal recognition systems and sensor fusion concepts and (x) emotion and stress estimation and forecasting from a nonlinear dynamical system perspective

Safety and Reliability - Safe Societies in a Changing World

The contributions cover a wide range of methodologies and application areas for safety and reliability that contribute to safe societies in a changing world. These methodologies and applications include: - foundations of risk and reliability assessment and management - mathematical methods in reliability and safety - risk assessment - risk management - system reliability - uncertainty analysis - digitalization and big data - prognostics and system health management - occupational safety - accident and incident modeling - maintenance modeling and applications - simulation for safety and reliability analysis - dynamic risk and barrier management - organizational factors and safety culture - human factors and human reliability - resilience engineering - structural reliability - natural hazards - security - economic analysis in risk managemen