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

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

Signals and Images in Sea Technologies

Life below water is the 14th Sustainable Development Goal (SDG) envisaged by the United Nations and is aimed at conserving and sustainably using the oceans, seas, and marine resources for sustainable development. It is not difficult to argue that signals and image technologies may play an essential role in achieving the foreseen targets linked to SDG 14. Besides increasing the general knowledge of ocean health by means of data analysis, methodologies based on signal and image processing can be helpful in environmental monitoring, in protecting and restoring ecosystems, in finding new sensor technologies for green routing and eco-friendly ships, in providing tools for implementing best practices for sustainable fishing, as well as in defining frameworks and intelligent systems for enforcing sea law and making the sea a safer and more secure place. Imaging is also a key element for the exploration of the underwater world for various scopes, ranging from the predictive maintenance of sub-sea pipelines and other infrastructure projects, to the discovery, documentation, and protection of sunken cultural heritage. The scope of this Special Issue encompasses investigations into techniques and ICT approaches and, in particular, the study and application of signal- and image-based methods and, in turn, exploration of the advantages of their application in the previously mentioned areas

Enhanced Deep Network Designs Using Mitochondrial DNA Based Genetic Algorithm And Importance Sampling

Machine learning (ML) is playing an increasingly important role in our lives. It has already made huge impact in areas such as cancer diagnosis, precision medicine, self-driving cars, natural disasters predictions, speech recognition, etc. The painstakingly handcrafted feature extractors used in the traditional learning, classification and pattern recognition systems are not scalable for large-sized datasets or adaptable to different classes of problems or domains. Machine learning resurgence in the form of Deep Learning (DL) in the last decade after multiple AI (artificial intelligence) winters and hype cycles is a result of the convergence of advancements in training algorithms, availability of massive data (big data) and innovation in compute resources (GPUs and cloud). If we want to solve more complex problems with machine learning, we need to optimize all three of these areas, i.e., algorithms, dataset and compute. Our dissertation research work presents the original application of nature-inspired idea of mitochondrial DNA (mtDNA) to improve deep learning network design. Additional fine-tuning is provided with Monte Carlo based method called importance sampling (IS). The primary performance indicators for machine learning are model accuracy, loss and training time. The goal of our dissertation is to provide a framework to address all these areas by optimizing network designs (in the form of hyperparameter optimization) and dataset using enhanced Genetic Algorithm (GA) and importance sampling. Algorithms are by far the most important aspect of machine learning. We demonstrate the application of mitochondrial DNA to complement the standard genetic algorithm for architecture optimization of deep Convolution Neural Network (CNN). We use importance sampling to reduce the dataset variance and sample more often from the instances that add greater value from the training outcome perspective. And finally, we leverage massive parallel and distributed processing of GPUs in the cloud to speed up training. Thus, our multi-approach method for enhancing deep learning combines architecture optimization, dataset optimization and the power of the cloud to drive better model accuracy and reduce training time

Vertical Take-Off and Landing Control via Dual-Quaternions and Sliding Mode

The landing and reusability of space vehicles is one of the driving forces into renewed interest in space utilization. For missions to planetary surfaces, this soft landing has been most commonly accomplished with parachutes. However, in spite of their simplicity, they are susceptible to parachute drift. This parachute drift makes it very difficult to predict where the vehicle will land, especially in a dense and windy atmosphere such as Earth. Instead, recent focus has been put into developing a powered landing through gimbaled thrust. This gimbaled thrust output is dependent on robust path planning and controls algorithms. Being able to have a powered landing with on-board real-time control algorithms is absolutely essential to exploring the solar system as it is the only effective way to bring heavy equipment or people to a planetary surface. A robust, efficient, and easy-to-use controls algorithm will be formulated to solve this controls problem known as the \emph{soft landing problem}. Through representing rigid body motion with dual-quaternions, translation and rotation can be represented in a single compact form that is free of singularities and provides the shortest path interpolation compared to any other formulation. These rigid bodies will be shown to follow a desired time-dependent orientation and position through one of the most powerful methods of modern control known for its accuracy, robustness, and easy tuning and implementation -- sliding mode control

Proceedings of the Workshop on Change of Representation and Problem Reformulation

The proceedings of the third Workshop on Change of representation and Problem Reformulation is presented. In contrast to the first two workshops, this workshop was focused on analytic or knowledge-based approaches, as opposed to statistical or empirical approaches called 'constructive induction'. The organizing committee believes that there is a potential for combining analytic and inductive approaches at a future date. However, it became apparent at the previous two workshops that the communities pursuing these different approaches are currently interested in largely non-overlapping issues. The constructive induction community has been holding its own workshops, principally in conjunction with the machine learning conference. While this workshop is more focused on analytic approaches, the organizing committee has made an effort to include more application domains. We have greatly expanded from the origins in the machine learning community. Participants in this workshop come from the full spectrum of AI application domains including planning, qualitative physics, software engineering, knowledge representation, and machine learning