Topological & network theoretic approaches in hyperspectral remote sensing

Hyperspectral remote sensing is a valuable new technology that has numerous com- mercial and scientific applications. For example, it has been used to study crop health, mineral and soil composition, and pollution levels. Hyperspectral imaging also has im- portant military and intelligence applications such as the identification of man-made materials, and detection of chemical and biological plumes. The key mathematical challenges of hyperspectral imaging include image classification, anomaly detection, and target detection. Image classification is the process of grouping pixels into spec- trally similar clusters. This thesis describes a new topological and network-theoretic approach for classifying pixels in hyperspectral image data. Pixels in hyperspectral image data sets are thought of as constituting a point cloud in a high dimensional topological space, and a network structure is imposed on the data by considering the spectral distance between pairs of pixels. We use the tools of persistent homology to argue that the resulting network effectively models the com- plex nonlinear structures in the data. We then perform data clustering by applying a network based community detection algorithm called the method of maximum modu- larity. The method of maximum modularity is an unsupervised, deterministic method for detecting communities in networks where neither the number of communities nor their sizes needs to be specified in advance. Examples of real hyperspectral images that have been classified using the method of maximum modularity are provided in order to demonstrate the feasibility of the approach

Spectral Target Detection using Physics-Based Modeling and a Manifold Learning Technique

Identification of materials from calibrated radiance data collected by an airborne imaging spectrometer depends strongly on the atmospheric and illumination conditions at the time of collection. This thesis demonstrates a methodology for identifying material spectra using the assumption that each unique material class forms a lower-dimensional manifold (surface) in the higher-dimensional spectral radiance space and that all image spectra reside on, or near, these theoretic manifolds. Using a physical model, a manifold characteristic of the target material exposed to varying illumination and atmospheric conditions is formed. A graph-based model is then applied to the radiance data to capture the intricate structure of each material manifold, followed by the application of the commute time distance (CTD) transformation to separate the target manifold from the background. Detection algorithms are then applied in the CTD subspace. This nonlinear transformation is based on a random walk on a graph and is derived from an eigendecomposition of the pseudoinverse of the graph Laplacian matrix. This work provides a geometric interpretation of the CTD transformation, its algebraic properties, the atmospheric and illumination parameters varied in the physics-based model, and the influence the target manifold samples have on the orientation of the coordinate axes in the transformed space. This thesis concludes by demonstrating improved detection results in the CTD subspace as compared to detection in the original spectral radiance space

Object Detection in High Resolution Aerial Images and Hyperspectral Remote Sensing Images

With rapid developments in satellite and sensor technologies, there has been a dramatic increase in the availability of remotely sensed images. However, the exploration of these images still involves a tremendous amount of human interventions, which are tedious, time-consuming, and inefficient. To help imaging experts gain a complete understanding of the images and locate the objects of interest in a more accurate and efficient way, there is always an urgent need for developing automatic detection algorithms. In this work, we delve into the object detection problems in remote sensing applications, exploring the detection algorithms for both hyperspectral images (HSIs) and high resolution aerial images. In the first part, we focus on the subpixel target detection problem in HSIs with low spatial resolutions, where the objects of interest are much smaller than the image pixel spatial resolution. To this end, we explore the detection frameworks that integrate image segmentation techniques in designing the matched filters (MFs). In particular, we propose a novel image segmentation algorithm to identify the spatial-spectral coherent image regions, from which the background statistics were estimated for deriving the MFs. Extensive experimental studies were carried out to demonstrate the advantages of the proposed subpixel target detection framework. Our studies show the superiority of the approach when comparing to state-of-the-art methods. The second part of the thesis explores the object based image analysis (OBIA) framework for geospatial object detection in high resolution aerial images. Specifically, we generate a tree representation of the aerial images from the output of hierarchical image segmentation algorithms and reformulate the object detection problem into a tree matching task. We then proposed two tree-matching algorithms for the object detection framework. We demonstrate the efficiency and effectiveness of the proposed tree-matching based object detection framework. In the third part, we study object detection in high resolution aerial images from a machine learning perspective. We investigate both traditional machine learning based framework and end-to-end convolutional neural network (CNN) based approach for various object detection tasks. In the traditional detection framework, we propose to apply the Gaussian process classifier (GPC) to train an object detector and demonstrate the advantages of the probabilistic classification algorithm. In the CNN based approach, we proposed a novel scale transfer module that generates enhanced feature maps for object detection. Our results show the efficiency and competitiveness of the proposed algorithms when compared to state-of-the-art counterparts

A manifold learning approach to target detection in high-resolution hyperspectral imagery

Imagery collected from airborne platforms and satellites provide an important medium for remotely analyzing the content in a scene. In particular, the ability to detect a specific material within a scene is of high importance to both civilian and defense applications. This may include identifying targets such as vehicles, buildings, or boats. Sensors that process hyperspectral images provide the high-dimensional spectral information necessary to perform such analyses. However, for a d-dimensional hyperspectral image, it is typical for the data to inherently occupy an m-dimensional space, with m \u3c\u3c d. In the remote sensing community, this has led to a recent increase in the use of manifold learning, which aims to characterize the embedded lower-dimensional, non-linear manifold upon which the hyperspectral data inherently lie. Classic hyperspectral data models include statistical, linear subspace, and linear mixture models, but these can place restrictive assumptions on the distribution of the data; this is particularly true when implementing traditional target detection approaches, and the limitations of these models are well-documented. With manifold learning based approaches, the only assumption is that the data reside on an underlying manifold that can be discretely modeled by a graph. The research presented here focuses on the use of graph theory and manifold learning in hyperspectral imagery. Early work explored various graph-building techniques with application to the background model of the Topological Anomaly Detection (TAD) algorithm, which is a graph theory based approach to anomaly detection. This led towards a focus on target detection, and in the development of a specific graph-based model of the data and subsequent dimensionality reduction using manifold learning. An adaptive graph is built on the data, and then used to implement an adaptive version of locally linear embedding (LLE). We artificially induce a target manifold and incorporate it into the adaptive LLE transformation; the artificial target manifold helps to guide the separation of the target data from the background data in the new, lower-dimensional manifold coordinates. Then, target detection is performed in the manifold space

Collaborative sparse regression using spatially correlated supports - Application to hyperspectral unmixing

This paper presents a new Bayesian collaborative sparse regression method for linear unmixing of hyperspectral images. Our contribution is twofold; first, we propose a new Bayesian model for structured sparse regression in which the supports of the sparse abundance vectors are a priori spatially correlated across pixels (i.e., materials are spatially organised rather than randomly distributed at a pixel level). This prior information is encoded in the model through a truncated multivariate Ising Markov random field, which also takes into consideration the facts that pixels cannot be empty (i.e, there is at least one material present in each pixel), and that different materials may exhibit different degrees of spatial regularity. Secondly, we propose an advanced Markov chain Monte Carlo algorithm to estimate the posterior probabilities that materials are present or absent in each pixel, and, conditionally to the maximum marginal a posteriori configuration of the support, compute the MMSE estimates of the abundance vectors. A remarkable property of this algorithm is that it self-adjusts the values of the parameters of the Markov random field, thus relieving practitioners from setting regularisation parameters by cross-validation. The performance of the proposed methodology is finally demonstrated through a series of experiments with synthetic and real data and comparisons with other algorithms from the literature

A Comprehensive Survey of Deep Learning in Remote Sensing: Theories, Tools and Challenges for the Community

In recent years, deep learning (DL), a re-branding of neural networks (NNs), has risen to the top in numerous areas, namely computer vision (CV), speech recognition, natural language processing, etc. Whereas remote sensing (RS) possesses a number of unique challenges, primarily related to sensors and applications, inevitably RS draws from many of the same theories as CV; e.g., statistics, fusion, and machine learning, to name a few. This means that the RS community should be aware of, if not at the leading edge of, of advancements like DL. Herein, we provide the most comprehensive survey of state-of-the-art RS DL research. We also review recent new developments in the DL field that can be used in DL for RS. Namely, we focus on theories, tools and challenges for the RS community. Specifically, we focus on unsolved challenges and opportunities as it relates to (i) inadequate data sets, (ii) human-understandable solutions for modelling physical phenomena, (iii) Big Data, (iv) non-traditional heterogeneous data sources, (v) DL architectures and learning algorithms for spectral, spatial and temporal data, (vi) transfer learning, (vii) an improved theoretical understanding of DL systems, (viii) high barriers to entry, and (ix) training and optimizing the DL.Comment: 64 pages, 411 references. To appear in Journal of Applied Remote Sensin

Characterization of the spectral distribution of hyperspectral imagery for improved exploitation

Widely used methods of target, anomaly, and change detection when applied to spectral imagery provide less than desirable results due to the complex nature of the data. In the case of hyperspectral data, dimension reduction techniques are employed to reduce the amount of data used in the detection algorithms in order to produce better results and/or decreased computation time. This essentially ignores a significant amount of the data collected in k unique spectral bands. Methods presented in this work explore using the distribution of the collected data in the full k dimensions in order to identify regions of interest contained in spatial tiles of the scene. Here, interest is defined as small and large scale manmade activity. The algorithms developed in this research are primarily data driven with a limited number of assumptions. These algorithms will individually be applied to spatial subsets or tiles of the full scene to indicate the amount of interest contained. Each tile is put through a series of tests using the algorithms based on the full distribution of the data in the hyperspace. The scores from each test will be combined in such a way that each tile is labeled as either interesting or not interesting. This provides a cueing mechanism for image analysts to visually inspect locations within a hyperspectral scene with a high likelihood of containing manmade activity