Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches

Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, ill-posed inverse problem because of model inaccuracies, observation noise, environmental conditions, endmember variability, and data set size. Researchers have devised and investigated many models searching for robust, stable, tractable, and accurate unmixing algorithms. This paper presents an overview of unmixing methods from the time of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models are first discussed. Signal-subspace, geometrical, statistical, sparsity-based, and spatial-contextual unmixing algorithms are described. Mathematical problems and potential solutions are described. Algorithm characteristics are illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensin

Efficient Human Activity Recognition in Large Image and Video Databases

Vision-based human action recognition has attracted considerable interest in recent research for its applications to video surveillance, content-based search, healthcare, and interactive games. Most existing research deals with building informative feature descriptors, designing efficient and robust algorithms, proposing versatile and challenging datasets, and fusing multiple modalities. Often, these approaches build on certain conventions such as the use of motion cues to determine video descriptors, application of off-the-shelf classifiers, and single-factor classification of videos. In this thesis, we deal with important but overlooked issues such as efficiency, simplicity, and scalability of human activity recognition in different application scenarios: controlled video environment (e.g.~indoor surveillance), unconstrained videos (e.g.~YouTube), depth or skeletal data (e.g.~captured by Kinect), and person images (e.g.~Flicker). In particular, we are interested in answering questions like (a) is it possible to efficiently recognize human actions in controlled videos without temporal cues? (b) given that the large-scale unconstrained video data are often of high dimension low sample size (HDLSS) nature, how to efficiently recognize human actions in such data? (c) considering the rich 3D motion information available from depth or motion capture sensors, is it possible to recognize both the actions and the actors using only the motion dynamics of underlying activities? and (d) can motion information from monocular videos be used for automatically determining saliency regions for recognizing actions in still images

Statistical and Dynamical Modeling of Riemannian Trajectories with Application to Human Movement Analysis

abstract: The data explosion in the past decade is in part due to the widespread use of rich sensors that measure various physical phenomenon -- gyroscopes that measure orientation in phones and fitness devices, the Microsoft Kinect which measures depth information, etc. A typical application requires inferring the underlying physical phenomenon from data, which is done using machine learning. A fundamental assumption in training models is that the data is Euclidean, i.e. the metric is the standard Euclidean distance governed by the L-2 norm. However in many cases this assumption is violated, when the data lies on non Euclidean spaces such as Riemannian manifolds. While the underlying geometry accounts for the non-linearity, accurate analysis of human activity also requires temporal information to be taken into account. Human movement has a natural interpretation as a trajectory on the underlying feature manifold, as it evolves smoothly in time. A commonly occurring theme in many emerging problems is the need to \emph{represent, compare, and manipulate} such trajectories in a manner that respects the geometric constraints. This dissertation is a comprehensive treatise on modeling Riemannian trajectories to understand and exploit their statistical and dynamical properties. Such properties allow us to formulate novel representations for Riemannian trajectories. For example, the physical constraints on human movement are rarely considered, which results in an unnecessarily large space of features, making search, classification and other applications more complicated. Exploiting statistical properties can help us understand the \emph{true} space of such trajectories. In applications such as stroke rehabilitation where there is a need to differentiate between very similar kinds of movement, dynamical properties can be much more effective. In this regard, we propose a generalization to the Lyapunov exponent to Riemannian manifolds and show its effectiveness for human activity analysis. The theory developed in this thesis naturally leads to several benefits in areas such as data mining, compression, dimensionality reduction, classification, and regression.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201

Learning with Algebraic Invariances, and the Invariant Kernel Trick

When solving data analysis problems it is important to integrate prior knowledge and/or structural invariances. This paper contributes by a novel framework for incorporating algebraic invariance structure into kernels. In particular, we show that algebraic properties such as sign symmetries in data, phase independence, scaling etc. can be included easily by essentially performing the kernel trick twice. We demonstrate the usefulness of our theory in simulations on selected applications such as sign-invariant spectral clustering and underdetermined ICA

DISCRIMINATIVE LEARNING AND RECOGNITION USING DICTIONARIES

In recent years, the theory of sparse representation has emerged as a powerful tool for efficient processing of data in non-traditional ways. This is mainly due to the fact that most signals and images of interest tend to be sparse or compressible in some dictionary. In other words, they can be well approximated by a linear combination of a few elements (also known as atoms) of a dictionary. This dictionary can either be an analytic dictionary composed of wavelets or Fourier basis or it can be directly trained from data. It has been observed that dictionaries learned directly from data provide better representation and hence can improve the performance of many practical applications such as restoration and classification. In this dissertation, we study dictionary learning and recognition under supervised, unsupervised, and semi-supervised settings. In the supervised case, we propose an approach to recognize humans in unconstrained videos, where the main challenge is exploiting the identity information in multiple frames and the accompanying dynamic signature. These identity cues include face, body, and motion. Our approach is based on video-dictionaries for face and body. We design video-dictionaries to implicitly encode temporal, pose, and illumination information. Next, we propose a novel multivariate sparse representation method that jointly represents all the video data by a sparse linear combination of training data. To increase the ability of our algorithm to learn nonlinearities, we apply kernel methods to learn the dictionaries. Next, we address the problem of matching faces across changes in pose in unconstrained videos. Our approach consists of two methods based on 3D rotation and sparse representation that compensate for changes in pose. We demonstrate the superior performance of our approach over several state-of-the-art algorithms through extensive experiments on unconstrained video datasets. In the unsupervised case, we present an approach that simultaneously clusters images and learns dictionaries from the clusters. The method learns dictionaries in the Radon transform domain. The main feature of the proposed approach is that it provides in-plane rotation and scale invariant clustering, which is useful in many applications such as Content Based Image Retrieval (CBIR). We demonstrate through experiments that the proposed rotation and scale invariant clustering provides not only good retrieval performances but also substantial improvements and robustness compared to traditional Gabor-based and several state-of-the-art shape-based methods. We then extend the dictionary learning problem to a generalized semi-supervised formulation, where each training sample is provided with a set of possible labels and only one label among them is the true one. Such applications can be found in image and video collections where one often has only partially labeled data. For instance, given an image with multiple faces and a caption specifying the names, we can be sure that each of the faces belong to one of the names specified, while the exact identity of each face is not known. Labeling involves significant amount of human effort and is expensive. This has motivated researchers to develop learning algorithms from partially labeled training data. In this work, we develop dictionary learning algorithms that utilize such partially labeled data. The proposed method aims to solve the problem of ambiguously labeled multiclass-classification using an iterative algorithm. The dictionaries are updated using either soft (EM-based) or hard decision rules. Extensive evaluations on existing datasets demonstrate that the proposed method performs significantly better than state-of-the-art approaches for learning from ambiguously labeled data. As sparsity plays a major role in our research, we further present a sparse representation-based approach to find the salient views of 3D objects. The salient views are categorized into two groups. The first are boundary representative views that have several visible sides and object surfaces that may be attractive to humans. The second are side representative views that best represent side views of the approximating convex shape. The side representative views are class-specific views and possess the most representative power compared to other within-class views. Using the concept of characteristic view class, we first present a sparse representation-based approach for estimating the boundary representative views. With the estimated boundaries, we determine the side representative views based on a minimum reconstruction error criterion. Furthermore, to evaluate our method, we introduce the notion of geometric dictionaries built from salient views for applications in 3D object recognition, retrieval and sparse-to-full reconstruction. By a series of experiments on four publicly available 3D object datasets, we demonstrate the effectiveness of our approach over state-of-the-art algorithms and baseline methods

Unsupervised Representative Selection and Signal Unmixing

This thesis presents unsupervised machine learning algorithms to tackle two related problems: selecting representatives in a dataset and identifying constituent components in mixture data. In both problems, we aim to reveal a few key hidden features that sufficiently explain the data. The main intuition behind our algorithms is that, in an appropriately constructed dictionary, a sparse representation of the data corresponds to selecting these unknown features. Our goal is to efficiently seek such sparse representations under suitable conditions. In the representative selection problem, our objective is to pick a few representative data points that capture distinguished characteristics of a dataset. This corresponds to identifying the vertices of the polytope generated by the data. To do so, we start by modeling each data point as a convex combination of the polytope vertices. Then, in the dictionary formed by the dataset itself, we look for sparse representations of the data which subsequently imply the vertices. To seek such sparse representations, we proposed a greedy pursuit algorithm and a non-convex entropy minimization algorithm. We theoretically justify our proposed algorithms and demonstrate their vertex recovery performance on both synthetic and real data. In the unmixing problem, we assume that each data point is a mixture of a few unknown components, and we wish to decompose data into these underlying constituents. We consider a highly under-sampled regime in which the number of measurements is far less than the data dimension. Furthermore, we solve an even more challenging unmixing problem in which the under-sampled mixture are indirectly observed via a nonlinear operator such as Sigmoid and Relu. To find the unknown constituents, we form a dictionaries with atoms resembling the constituents and seek the sparse representations corresponding to them. We proposed a fast and robust greedy algorithm, called UnmixMP, to find such sparse representations. We prove its robust unmixing performance and support our theoretical analysis by various experiments on both synthetic and real image data. Our algorithms are fast and robust, and supported by rigorous theoretical analysis. Our experimental results shows that the proposed are significantly more robust than state-of-the-art representative selection and unmixing algorithms in the aforementioned settings

Sparse Modeling for Image and Vision Processing

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is, automatically selecting a simple model among a large collection of them. In signal processing, sparse coding consists of representing data with linear combinations of a few dictionary elements. Subsequently, the corresponding tools have been widely adopted by several scientific communities such as neuroscience, bioinformatics, or computer vision. The goal of this monograph is to offer a self-contained view of sparse modeling for visual recognition and image processing. More specifically, we focus on applications where the dictionary is learned and adapted to data, yielding a compact representation that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics and Visio