Harmonic Analysis Inspired Data Fusion for Applications in Remote Sensing

This thesis will address the fusion of multiple data sources arising in remote sensing, such as hyperspectral and LIDAR. Fusing of multiple data sources provides better data representation and classification results than any of the independent data sources would alone. We begin our investigation with the well-studied Laplacian Eigenmap (LE) algorithm. This algorithm offers a rich template to which fusion concepts can be added. For each phase of the LE algorithm (graph, operator, and feature space) we develop and test different data fusion techniques. We also investigate how partially labeled data and approximate LE preimages can used to achieve data fusion. Lastly, we study several numerical acceleration techniques that can be used to augment the developed algorithms, namely the Nystrom extension, Random Projections, and Approximate Neighborhood constructions. The Nystrom extension is studied in detail and the application of Frame Theory and Sigma-Delta Quantization is proposed to enrich the Nystrom extension

Robust online subspace learning

In this thesis, I aim to advance the theories of online non-linear subspace learning through the development of strategies which are both efficient and robust. The use of subspace learning methods is very popular in computer vision and they have been employed to numerous tasks. With the increasing need for real-time applications, the formulation of online (i.e. incremental and real-time) learning methods is a vibrant research field and has received much attention from the research community. A major advantage of incremental systems is that they update the hypothesis during execution, thus allowing for the incorporation of the real data seen in the testing phase. Tracking acts as an attractive and popular evaluation tool for incremental systems, and thus, the connection between online learning and adaptive tracking is seen commonly in the literature. The proposed system in this thesis facilitates learning from noisy input data, e.g. caused by occlusions, casted shadows and pose variations, that are challenging problems in general tracking frameworks. First, a fast and robust alternative to standard L2-norm principal component analysis (PCA) is introduced, which I coin Euler PCA (e-PCA). The formulation of e-PCA is based on robust, non-linear kernel PCA (KPCA) with a cosine-based kernel function that is expressed via an explicit feature space. When applied to tracking, face reconstruction and background modeling, promising results are achieved. In the second part, the problem of matching vectors of 3D rotations is explicitly targeted. A novel distance which is robust for 3D rotations is introduced, and formulated as a kernel function. The kernel leads to a new representation of 3D rotations, the full-angle quaternion (FAQ) representation. Finally, I propose 3D object recognition from point clouds, and object tracking with color values using FAQs. A domain-specific kernel function designed for visual data is then presented. KPCA with Krein space kernels is introduced, as this kernel is indefinite, and an exact incremental learning framework for the new kernel is developed. In a tracker framework, the presented online learning outperforms the competitors in nine popular and challenging video sequences. In the final part, the generalized eigenvalue problem is studied. Specifically, incremental slow feature analysis (SFA) with indefinite kernels is proposed, and applied to temporal video segmentation and tracking with change detection. As online SFA allows for drift detection, further improvements are achieved in the evaluation of the tracking task.Open Acces

Automatic age progression and estimation from faces

Recently, automatic age progression has gained popularity due to its numerous applications. Among these is the frequent search for missing people, in the UK alone up to 300,000 people are reported missing every year. Although many algorithms have been proposed, most of the methods are affected by image noise, illumination variations, and facial expressions. Furthermore, most of the algorithms use a pattern caricaturing approach which infers ages by manipulating the target image and a template face formed by averaging faces at the intended age. To this end, this thesis investigates the problem with a view to tackling the most prominent issues associated with the existing algorithms. Initially using active appearance models (AAM), facial features are extracted and mapped to people’s ages, afterward a formula is derived which allows the convenient generation of age progressed images irrespective of whether the intended age exists in the training database or not. In order to handle image noise as well as varying facial expressions, a nonlinear appearance model called kernel appearance model (KAM) is derived. To illustrate the real application of automatic age progression, both AAM and KAM based algorithms are then used to synthesise faces of two popular long missing British and Irish kids; Ben Needham and Mary Boyle. However, both statistical techniques exhibit image rendering artefacts such as low-resolution output and the generation of inconsistent skin tone. To circumvent this problem, a hybrid texture enhancement pipeline is developed. To further ensure that the progressed images preserve people’s identities while at the same time attaining the intended age, rigorous human and machine based tests are conducted; part of this tests resulted to the development of a robust age estimation algorithm. Eventually, the results of the rigorous assessment reveal that the hybrid technique is able to handle all existing problems of age progression with minimal error.National Information Technology Development Agency of Nigeria (NITDA

Nonlinear unmixing of hyperspectral images: Models and algorithms

When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas relies on the widely used linear mixing model (LMM). However, the LMM may be not valid, and other nonlinear models need to be considered, for instance, when there are multiscattering effects or intimate interactions. Consequently, over the last few years, several significant contributions have been proposed to overcome the limitations inherent in the LMM. In this article, we present an overview of recent advances in nonlinear unmixing modeling