Amanda K. Ziemann

Spatially Adaptive Hyperspectral Unmixing

Spectral unmixing is a common task in hyperspectral data analysis. In order to sufficiently spectrally unmix the data, three key steps must be accomplished: Estimate the number of endmembers (EMs), identify the EMs, and then unmix the data. Several different statistical and geometrical approaches have been developed for all steps of the unmixing process. However, many of these methods rely on using the full image to estimate the number and extract the EMs from the background data. In this paper, spectral unmixing is accomplished using a spatially adaptive approach. Linear unmixing is performed per pixel with EMs identified at the local level, but global abundance maps are created by clustering the locally determined EMs into common groups. Results show that the unmixing residual error of each pixels spectrum from real data, estimated from the spatially adaptive methodology, is reduced when compared to a global scale EM estimation and linear unmixing methodology. The component algorithms of the new spatially adaptive approach, which complete the three key unmixing steps, can be interchanged while maintaining spatial information, making this new methodology modular. A final advantage of the spatially adaptive spectral unmixing methodology is the user-defined spatial scale size.

Iterative convex hull volume estimation in hyperspectral imagery for change detection

Historically in change detection, statistically based methods have been used. However, as the spatial resolution of spectral images improves, the data no longer maintain a Gaussian distribution, and some assumptions about the data - and subsequently all algorithms based upon those statistical assumptions - fail. Here we present the Simplex Volume Estimation algorithm (SVE), which avoids these potential hindrances by taking a geometrical approach. In particular, we employ the linear mixture model to approximate the convex hull enclosing the data through identification of the simplex vertices (known as endmembers). SVE begins by processing an image and tiling it into squares. Next, SVE iterates through the tiles and for each set of pixels it identifies the number of corners (as vectors) that define the simplex of that set of data. For each tile, it then iterates through the increasing dimensionality, or number of endmembers, while every time calculating the volume of the simplex that is defined by that number of endmembers. When the volume is calculated in a dimension that is higher than that of the inherent dimensionality of the data, the volume will theoretically drop to zero. This value is indicative of the inherent dimensionality of the data as represented by the convex hull. Further, the volume of the simplex will fluctuate when a new material is introduced to the dataset, indicating a change in the image. The algorithm then analyzes the volume function associated with each tile and assigns the tile a metric value based on that function. The values of these metrics will be compared by using hyperspectral imagery collected from different platforms over experimental setups with known changes between flights. Results from these tests will be presented along with a path forward for future research.

Spectral image complexity estimated through local convex hull volume

Most spectral image processing schemes develop models of the data in the hyperspace by using first and second order statistics or linear subspace geometries applied to the image globally. However, it is simple to show that the data are typically not multivariate Gaussian or are not well defined by linear geometries when considering the entire image, particularly as the spatial resolution improves and the scene becomes more cluttered. Here, we use the concept of a convex hull that encloses the data to rank local regions within an image by an estimate of their complexity. The complexity as defined here is directly related to the volume of the hull in n dimensions that encloses the data under the assumptions that less complex data will have fewer distinct materials and more complex data will have more materials. They will also be more widely separated in the hyperspace. The method uses the Gram Matrix approach to estimate the volume of the hull and is applied to an image that has been tiled. The complexity of each tile is then estimated showing the relative changes in complexity over a large area spectral image. Results will be shown for reflective hyperspectral imagery over different scene contents with resolutions of ≈2–3 m. Ultimately this methodology can be used to develop localized models of an image and may provide insight into the large area search problem.

Hyperspectral target detection using manifold learning and multiple target spectra

Imagery collected from satellites and airborne platforms provides an important tool for remotely analyzing the content of a scene. In particular, the ability to remotely detect a specific material within a scene is of critical importance in nonproliferation and other applications. The sensor systems that process hyperspectral images collect the high-dimensional spectral information necessary to perform these detection analyses. For a d-dimensional hyperspectral image, however, where d is the number of spectral bands, it is common for the data to inherently occupy an m-dimensional space with m ≪ d. In the remote sensing community, this has led to recent interest in the use of manifold learning, which seeks to characterize the embedded lower-dimensional, nonlinear manifold that the data discretely approximate. The research presented here focuses on a graph theory and manifold learning approach to target detection, using an adaptive version of locally linear embedding that is biased to separate target pixels from background pixels. This approach incorporates multiple target signatures for a particular material, accounting for the spectral variability that is often present within a solid material of interest.

An adaptive locally linear embedding manifold learning approach for hyperspectral target detection

Algorithms for spectral analysis commonly use parametric or linear models of the data. Research has shown, however, that hyperspectral data -- particularly in materially cluttered scenes -- are not always well-modeled by statistical or linear methods. Here, we propose an approach to hyperspectral target detection that is based on a graph theory model of the data and a manifold learning transformation. An adaptive nearest neighbor (ANN) 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, transformed manifold coordinates. Then, target detection is performed in the manifold space using Spectral Angle Mapper. This methodology is an improvement over previous iterations of this approach due to the incorporation of ANN, the artificial target manifold, and the choice of detector in the transformed space. We implement our approach in a spatially local way: the image is delineated into square tiles, and the detection maps are normalized across the entire image. Target detection results will be shown using laboratory-measured and scene-derived target data from the SHARE 2012 collect.

Target detection using the background model from the topological anomaly detection algorithm

The Topological Anomaly Detection (TAD) algorithm has been used as an anomaly detector in hyperspectral and multispectral images. TAD is an algorithm based on graph theory that constructs a topological model of the background in a scene, and computes an anomalousness ranking for all of the pixels in the image with respect to the background in order to identify pixels with uncommon or strange spectral signatures. The pixels that are modeled as background are clustered into groups or connected components, which could be representative of spectral signatures of materials present in the background. Therefore, the idea of using the background components given by TAD in target detection is explored in this paper. In this way, these connected components are characterized in three different approaches, where the mean signature and endmembers for each component are calculated and used as background basis vectors in Orthogonal Subspace Projection (OSP) and Adaptive Subspace Detector (ASD). Likewise, the covariance matrix of those connected components is estimated and used in detectors: Constrained Energy Minimization (CEM) and Adaptive Coherence Estimator (ACE). The performance of these approaches and the different detectors is compared with a global approach, where the background characterization is derived directly from the image. Experiments and results using self-test data set provided as part of the RIT blind test target detection project are shown.

Manifold representations of single and multiple material classes in high resolution HSI

Hyperspectral image data are traditionally analyzed using statistical models. However, as the spatial and spectral resolutions of the images improve as a result of advances in sensor technology, the data no longer maintain a Gaussian distribution; this is due to increased material diversity in the scene, i.e., clutter. This causes many statistical assumptions about the data — and subsequently, the algorithms based on those assumptions — to be flawed. In high dimensional data, manifold learning seeks to recover the embedded non-linear, lower-dimensional manifold upon which the data inherently lie. By recovering the lower-dimensional manifold, intrinsic structures and relationships within the data may be identified and exploited. Here, we consider the impacts of increasing material spectral clutter on the low dimensional manifolds recovered from high spatial resolution hyperspectral scenes for both single and multiple material classes. The Locally Linear Embedding manifold learning method is modified to use an adaptive graph, and is used to extract low dimensional manifolds from hyperspectral image data collected during the SHARE 2012 campaign.

Assessing the impact of background spectral graph construction techniques on the topological anomaly detection algorithm

Anomaly detection algorithms have historically been applied to hyperspectral imagery in order to identify pixels whose material content is incongruous with the background material in the scene. Typically, the application involves extracting man-made objects from natural and agricultural surroundings. A large challenge in designing these algorithms is determining which pixels initially constitute the background material within an image. The topological anomaly detection (TAD) algorithm constructs a graph theory-based, fully non-parametric topological model of the background in the image scene, and uses codensity to measure deviation from this background. In TAD, the initial graph theory structure of the image data is created by connecting an edge between any two pixel vertices x and y if the Euclidean distance between them is less than some resolution r. While this type of proximity graph is among the most well-known approaches to building a geometric graph based on a given set of data, there is a wide variety of dierent geometrically-based techniques. In this paper, we present a comparative test of the performance of TAD across four dierent constructs of the initial graph: mutual k-nearest neighbor graph, sigma-local graph for two different values of σ > 1, and the proximity graph originally implemented in TAD.

An adaptive k-nearest neighbor graph building technique with applications to hyperspectral imagery

The analysis of remotely sensed spectral imagery has a variety of applications in both the public and private sectors, including tracking urban development, monitoring the spread of diseased crops, and mapping environmental disasters. The high spatial and spectral resolutions in hyperspectral imagery (HSI) make it particularly desirable for these types of analyses, as HSI sensors capture “color” information beyond what the human eye can see; this allows for greater differentiation between materials. However, those same properties can make HSI more difficult to analyze: traditional statistical or linear data models are not always able to well-model the high-dimensional HSI data for materially cluttered scenes. In recent years, the literature has shown an increase in the use of graph theory-based models for HSI analysis. These models are often used as the foundation for data transformations and manifold learning algorithms including Locally Linear Embedding, Commute Time Distance, and ISOMAP. A challenge associated with the graph building techniques used in these transformations is that they are typically k-nearest neighbor (kNN) graphs, which requires the user to designate a universal k value for the dataset. There is a need for an adaptive approach to building a kNN graph for HSI analysis so as to handle the particular characteristics of hyperspectral data in the spectral space, such as the sparse regions of data due to anomalies or rare targets in the scene, and the dense regions of data due to background clusters. Here, we present adaptive nearest neighbors, or ANN, which identifies a different k value for each pixel, so that pixels in denser regions have a higher k value and pixels in sparser regions have a lower k value. The resulting ANN graphs will be compared against kNN, and will be shown for synthetic data as well as hyperspectral data. While the focus here is on HSI, the ANN technique is applicable to any type of data analysis using a graph-based model.

Target detection performed on manifold approximations recovered from hyperspectral data

In high dimensional data, manifold learning seeks to identify the embedded lower-dimensional, non-linear mani- fold upon which the data lie. This is particularly useful in hyperspectral imagery where inherently m-dimensional data is often sparsely distributed throughout the d-dimensional spectral space, with m << d. By recovering the manifold, inherent structures and relationships within the data – which are not typically apparent otherwise – may be identified and exploited. The sparsity of data within the spectral space can prove challenging for many types of analysis, and in particular with target detection. In this paper, we propose using manifold recovery as a preprocessing step for spectral target detection algorithms. A graph structure is first built upon the data and the transformation into the manifold space is based upon that graph structure. Then, the Adaptive Co- sine/Coherence Estimator (ACE) algorithm is applied. We present an analysis of target detection performance in the manifold space using scene-derived target spectra from two different hyperspectral images.