Bags of Affine Subspaces for Robust Object Tracking

We propose an adaptive tracking algorithm where the object is modelled as a continuously updated bag of affine subspaces, with each subspace constructed from the object's appearance over several consecutive frames. In contrast to linear subspaces, affine subspaces explicitly model the origin of subspaces. Furthermore, instead of using a brittle point-to-subspace distance during the search for the object in a new frame, we propose to use a subspace-to-subspace distance by representing candidate image areas also as affine subspaces. Distances between subspaces are then obtained by exploiting the non-Euclidean geometry of Grassmann manifolds. Experiments on challenging videos (containing object occlusions, deformations, as well as variations in pose and illumination) indicate that the proposed method achieves higher tracking accuracy than several recent discriminative trackers.Comment: in International Conference on Digital Image Computing: Techniques and Applications, 201

The Role of Riemannian Manifolds in Computer Vision: From Coding to Deep Metric Learning

A diverse number of tasks in computer vision and machine learning enjoy from representations of data that are compact yet discriminative, informative and robust to critical measurements. Two notable representations are offered by Region Covariance Descriptors (RCovD) and linear subspaces which are naturally analyzed through the manifold of Symmetric Positive Definite (SPD) matrices and the Grassmann manifold, respectively, two widely used types of Riemannian manifolds in computer vision. As our first objective, we examine image and video-based recognition applications where the local descriptors have the aforementioned Riemannian structures, namely the SPD or linear subspace structure. Initially, we provide a solution to compute Riemannian version of the conventional Vector of Locally aggregated Descriptors (VLAD), using geodesic distance of the underlying manifold as the nearness measure. Next, by having a closer look at the resulting codes, we formulate a new concept which we name Local Difference Vectors (LDV). LDVs enable us to elegantly expand our Riemannian coding techniques to any arbitrary metric as well as provide intrinsic solutions to Riemannian sparse coding and its variants when local structured descriptors are considered. We then turn our attention to two special types of covariance descriptors namely infinite-dimensional RCovDs and rank-deficient covariance matrices for which the underlying Riemannian structure, i.e. the manifold of SPD matrices is out of reach to great extent. %Generally speaking, infinite-dimensional RCovDs offer better discriminatory power over their low-dimensional counterparts. To overcome this difficulty, we propose to approximate the infinite-dimensional RCovDs by making use of two feature mappings, namely random Fourier features and the Nystrom method. As for the rank-deficient covariance matrices, unlike most existing approaches that employ inference tools by predefined regularizers, we derive positive definite kernels that can be decomposed into the kernels on the cone of SPD matrices and kernels on the Grassmann manifolds and show their effectiveness for image set classification task. Furthermore, inspired by attractive properties of Riemannian optimization techniques, we extend the recently introduced Keep It Simple and Straightforward MEtric learning (KISSME) method to the scenarios where input data is non-linearly distributed. To this end, we make use of the infinite dimensional covariance matrices and propose techniques towards projecting on the positive cone in a Reproducing Kernel Hilbert Space (RKHS). We also address the sensitivity issue of the KISSME to the input dimensionality. The KISSME algorithm is greatly dependent on Principal Component Analysis (PCA) as a preprocessing step which can lead to difficulties, especially when the dimensionality is not meticulously set. To address this issue, based on the KISSME algorithm, we develop a Riemannian framework to jointly learn a mapping performing dimensionality reduction and a metric in the induced space. Lastly, in line with the recent trend in metric learning, we devise end-to-end learning of a generic deep network for metric learning using our derivation

SEGMENTATION, RECOGNITION, AND ALIGNMENT OF COLLABORATIVE GROUP MOTION

Modeling and recognition of human motion in videos has broad applications in behavioral biometrics, content-based visual data analysis, security and surveillance, as well as designing interactive environments. Significant progress has been made in the past two decades by way of new models, methods, and implementations. In this dissertation, we focus our attention on a relatively less investigated sub-area called collaborative group motion analysis. Collaborative group motions are those that typically involve multiple objects, wherein the motion patterns of individual objects may vary significantly in both space and time, but the collective motion pattern of the ensemble allows characterization in terms of geometry and statistics. Therefore, the motions or activities of an individual object constitute local information. A framework to synthesize all local information into a holistic view, and to explicitly characterize interactions among objects, involves large scale global reasoning, and is of significant complexity. In this dissertation, we first review relevant previous contributions on human motion/activity modeling and recognition, and then propose several approaches to answer a sequence of traditional vision questions including 1) which of the motion elements among all are the ones relevant to a group motion pattern of interest (Segmentation); 2) what is the underlying motion pattern (Recognition); and 3) how two motion ensembles are similar and how we can 'optimally' transform one to match the other (Alignment). Our primary practical scenario is American football play, where the corresponding problems are 1) who are offensive players; 2) what are the offensive strategy they are using; and 3) whether two plays are using the same strategy and how we can remove the spatio-temporal misalignment between them due to internal or external factors. The proposed approaches discard traditional modeling paradigm but explore either concise descriptors, hierarchies, stochastic mechanism, or compact generative model to achieve both effectiveness and efficiency. In particular, the intrinsic geometry of the spaces of the involved features/descriptors/quantities is exploited and statistical tools are established on these nonlinear manifolds. These initial attempts have identified new challenging problems in complex motion analysis, as well as in more general tasks in video dynamics. The insights gained from nonlinear geometric modeling and analysis in this dissertation may hopefully be useful toward a broader class of computer vision applications

Geometric deep learning: going beyond Euclidean data

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field

A Survey on Knowledge Graphs: Representation, Acquisition and Applications

Human knowledge provides a formal understanding of the world. Knowledge graphs that represent structural relations between entities have become an increasingly popular research direction towards cognition and human-level intelligence. In this survey, we provide a comprehensive review of knowledge graph covering overall research topics about 1) knowledge graph representation learning, 2) knowledge acquisition and completion, 3) temporal knowledge graph, and 4) knowledge-aware applications, and summarize recent breakthroughs and perspective directions to facilitate future research. We propose a full-view categorization and new taxonomies on these topics. Knowledge graph embedding is organized from four aspects of representation space, scoring function, encoding models, and auxiliary information. For knowledge acquisition, especially knowledge graph completion, embedding methods, path inference, and logical rule reasoning, are reviewed. We further explore several emerging topics, including meta relational learning, commonsense reasoning, and temporal knowledge graphs. To facilitate future research on knowledge graphs, we also provide a curated collection of datasets and open-source libraries on different tasks. In the end, we have a thorough outlook on several promising research directions

Graph-based Semi-supervised Learning: Algorithms and Applications.

114 p.Graph-based semi-supervised learning have attracted large numbers of researchers and it is an important part of semi-supervised learning. Graph construction and semi-supervised embedding are two main steps in graph-based semi-supervised learning algorithms. In this thesis, we proposed two graph construction algorithms and two semi-supervised embedding algorithms. The main work of this thesis is summarized as follows:1. A new graph construction algorithm named Graph construction based on self-representativeness and Laplacian smoothness (SRLS) and several variants are proposed. Researches show that the coefficients obtained by data representation algorithms reflect the similarity between data samples and can be considered as a measurement of the similarity. This kind of measurement can be used for the weights of the edges between data samples in graph construction. Each column of the coefficient matrix obtained by data self-representation algorithms can be regarded as a new representation of original data. The new representations should have common features as the original data samples. Thus, if two data samples are close to each other in the original space, the corresponding representations should be highly similar. This constraint is called Laplacian smoothness.SRLS graph is based on l2-norm minimized data self-representation and Laplacian smoothness. Since the representation matrix obtained by l2 minimization is dense, a two phrase SRLS method (TPSRLS) is proposed to increase the sparsity of graph matrix. By extending the linear space to Hilbert space, two kernelized versions of SRLS are proposed. Besides, a direct solution to kernelized SRLS algorithm is also introduced.2. A new sparse graph construction algorithm named Sparse graph with Laplacian smoothness (SGLS) and several variants are proposed. SGLS graph algorithm is based on sparse representation and use Laplacian smoothness as a constraint (SGLS). A kernelized version of the SGLS algorithm and a direct solution to kernelized SGLS algorithm are also proposed. 3. SPP is a successful unsupervised learning method. To extend SPP to a semi-supervised embedding method, we introduce the idea of in-class constraints in CGE into SPP and propose a new semi-supervised method for data embedding named Constrained Sparsity Preserving Embedding (CSPE).4. The weakness of CSPE is that it cannot handle the new coming samples which means a cascade regression should be performed after the non-linear mapping is obtained by CSPE over the whole training samples. Inspired by FME, we add a regression term in the objective function to obtain an approximate linear projection simultaneously when non-linear embedding is estimated and proposed Flexible Constrained Sparsity Preserving Embedding (FCSPE).Extensive experiments on several datasets (including facial images, handwriting digits images and objects images) prove that the proposed algorithms can improve the state-of-the-art results

Graph-based Data Modeling and Analysis for Data Fusion in Remote Sensing

Hyperspectral imaging provides the capability of increased sensitivity and discrimination over traditional imaging methods by combining standard digital imaging with spectroscopic methods. For each individual pixel in a hyperspectral image (HSI), a continuous spectrum is sampled as the spectral reflectance/radiance signature to facilitate identification of ground cover and surface material. The abundant spectrum knowledge allows all available information from the data to be mined. The superior qualities within hyperspectral imaging allow wide applications such as mineral exploration, agriculture monitoring, and ecological surveillance, etc. The processing of massive high-dimensional HSI datasets is a challenge since many data processing techniques have a computational complexity that grows exponentially with the dimension. Besides, a HSI dataset may contain a limited number of degrees of freedom due to the high correlations between data points and among the spectra. On the other hand, merely taking advantage of the sampled spectrum of individual HSI data point may produce inaccurate results due to the mixed nature of raw HSI data, such as mixed pixels, optical interferences and etc. Fusion strategies are widely adopted in data processing to achieve better performance, especially in the field of classification and clustering. There are mainly three types of fusion strategies, namely low-level data fusion, intermediate-level feature fusion, and high-level decision fusion. Low-level data fusion combines multi-source data that is expected to be complementary or cooperative. Intermediate-level feature fusion aims at selection and combination of features to remove redundant information. Decision level fusion exploits a set of classifiers to provide more accurate results. The fusion strategies have wide applications including HSI data processing. With the fast development of multiple remote sensing modalities, e.g. Very High Resolution (VHR) optical sensors, LiDAR, etc., fusion of multi-source data can in principal produce more detailed information than each single source. On the other hand, besides the abundant spectral information contained in HSI data, features such as texture and shape may be employed to represent data points from a spatial perspective. Furthermore, feature fusion also includes the strategy of removing redundant and noisy features in the dataset. One of the major problems in machine learning and pattern recognition is to develop appropriate representations for complex nonlinear data. In HSI processing, a particular data point is usually described as a vector with coordinates corresponding to the intensities measured in the spectral bands. This vector representation permits the application of linear and nonlinear transformations with linear algebra to find an alternative representation of the data. More generally, HSI is multi-dimensional in nature and the vector representation may lose the contextual correlations. Tensor representation provides a more sophisticated modeling technique and a higher-order generalization to linear subspace analysis. In graph theory, data points can be generalized as nodes with connectivities measured from the proximity of a local neighborhood. The graph-based framework efficiently characterizes the relationships among the data and allows for convenient mathematical manipulation in many applications, such as data clustering, feature extraction, feature selection and data alignment. In this thesis, graph-based approaches applied in the field of multi-source feature and data fusion in remote sensing area are explored. We will mainly investigate the fusion of spatial, spectral and LiDAR information with linear and multilinear algebra under graph-based framework for data clustering and classification problems