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

A Comprehensive Performance Evaluation of Deformable Face Tracking "In-the-Wild"

Recently, technologies such as face detection, facial landmark localisation and face recognition and verification have matured enough to provide effective and efficient solutions for imagery captured under arbitrary conditions (referred to as "in-the-wild"). This is partially attributed to the fact that comprehensive "in-the-wild" benchmarks have been developed for face detection, landmark localisation and recognition/verification. A very important technology that has not been thoroughly evaluated yet is deformable face tracking "in-the-wild". Until now, the performance has mainly been assessed qualitatively by visually assessing the result of a deformable face tracking technology on short videos. In this paper, we perform the first, to the best of our knowledge, thorough evaluation of state-of-the-art deformable face tracking pipelines using the recently introduced 300VW benchmark. We evaluate many different architectures focusing mainly on the task of on-line deformable face tracking. In particular, we compare the following general strategies: (a) generic face detection plus generic facial landmark localisation, (b) generic model free tracking plus generic facial landmark localisation, as well as (c) hybrid approaches using state-of-the-art face detection, model free tracking and facial landmark localisation technologies. Our evaluation reveals future avenues for further research on the topic.Comment: E. Antonakos and P. Snape contributed equally and have joint second authorshi

A Comparative Study: Globality versus Locality for Graph Construction in Discriminant Analysis

Local graph based discriminant analysis (DA) algorithms recently have attracted increasing attention to mitigate the limitations of global (graph) DA algorithms. However, there are few particular concerns on the following important issues: whether the local construction is better than the global one for intraclass and interclass graphs, which (intraclass or interclass) graph should locally or globally be constructed? and, further how they should be effectively jointed for good discriminant performances. In this paper, pursuing our previous studies on the graph construction and DA, we firstly address the issues involved above, and then by jointly utilizing both the globality and the locality, we develop, respectively, a Globally marginal and Locally compact Discriminant Analysis (GmLcDA) algorithm based on so-introduced global interclass and local intraclass graphs and a Locally marginal and Globally compact Discriminant Analysis (LmGcDA) based on so-introduced local interclass and global intraclass graphs, the purpose of which is not to show how novel the algorithms are but to illustrate the analyses in theory. Further, by comprehensively comparing the Locally marginal and Locally compact DA (LmLcDA) based on locality alone, the Globally marginal and Globally compact Discriminant Analysis (GmGcDA) just based on globality alone, GmLcDA, and LmGcDA, we suggest that the joint of locally constructed intraclass and globally constructed interclass graphs is more discriminant

Optimization in semi-supervised classification of multivariate time series

Abstract. In this thesis, I study methods that classify time series in a semi-supervised manner. I compare the performance of models that assume independent and identically distributed observations against models that assume nearby observations to be dependent of each other. These models are evaluated on three real world time series data sets. In addition, I carefully go through the theory of mathematical optimization behind two successful algorithms used in this thesis: Support Vector Data Description and Dynamic Time Warping. For the algorithm Dynamic Time Warping, I provide a novel proof that is based on dynamic optimization. The experiments in this thesis suggest that the assumption of observations in time series to be independent and identically distributed may deteriorate the results of semi-supervised classification. The novel self-training method presented in this thesis called Peak Evaluation using Perceptually Important Points shows great performance on multivariate time series compared to the methods currently existing in literature. The feature subset selection of multivariate time series may improve classification performance, but finding a reliable unsupervised feature subset selection method remains an open question

Euler principal component analysis

Principal Component Analysis (PCA) is perhaps the most prominent learning tool for dimensionality reduction in pattern recognition and computer vision. However, the 2-norm employed by standard PCA is not robust to outliers. In this paper, we propose a kernel PCA method for fast and robust PCA, which we call Euler-PCA (e-PCA). In particular, our algorithm utilizes a robust dissimilarity measure based on the Euler representation of complex numbers. We show that Euler-PCA retains PCA’s desirable properties while suppressing outliers. Moreover, we formulate Euler-PCA in an incremental learning framework which allows for efficient computation. In our experiments we apply Euler-PCA to three different computer vision applications for which our method performs comparably with other stateof- the-art approaches