Graph Laplacian for Image Anomaly Detection

Reed-Xiaoli detector (RXD) is recognized as the benchmark algorithm for image anomaly detection; however, it presents known limitations, namely the dependence over the image following a multivariate Gaussian model, the estimation and inversion of a high-dimensional covariance matrix, and the inability to effectively include spatial awareness in its evaluation. In this work, a novel graph-based solution to the image anomaly detection problem is proposed; leveraging the graph Fourier transform, we are able to overcome some of RXD's limitations while reducing computational cost at the same time. Tests over both hyperspectral and medical images, using both synthetic and real anomalies, prove the proposed technique is able to obtain significant gains over performance by other algorithms in the state of the art.Comment: Published in Machine Vision and Applications (Springer

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

Spectral Target Detecting Using Schroedinger Eigenmaps

Applications of optical remote sensing processes include environmental monitoring, military monitoring, meteorology, mapping, surveillance, etc. Many of these tasks include the detection of specific objects or materials, usually few or small, which are surrounded by other materials that clutter the scene and hide the relevant information. This target detection process has been boosted lately by the use of hyperspectral imagery (HSI) since its high spectral dimension provides more detailed spectral information that is desirable in data exploitation. Typical spectral target detectors rely on statistical or geometric models to characterize the spectral variability of the data. However, in many cases these parametric models do not fit well HSI data that impacts the detection performance. On the other hand, non-linear transformation methods, mainly based on manifold learning algorithms, have shown a potential use in HSI transformation, dimensionality reduction and classification. In target detection, non-linear transformation algorithms are used as preprocessing techniques that transform the data to a more suitable lower dimensional space, where the statistical or geometric detectors are applied. One of these non-linear manifold methods is the Schroedinger Eigenmaps (SE) algorithm that has been introduced as a technique for semi-supervised classification. The core tool of the SE algorithm is the Schroedinger operator that includes a potential term that encodes prior information about the materials present in a scene, and enables the embedding to be steered in some convenient directions in order to cluster similar pixels together. A completely novel target detection methodology based on SE algorithm is proposed for the first time in this thesis. The proposed methodology does not just include the transformation of the data to a lower dimensional space but also includes the definition of a detector that capitalizes on the theory behind SE. The fact that target pixels and those similar pixels are clustered in a predictable region of the low-dimensional representation is used to define a decision rule that allows one to identify target pixels over the rest of pixels in a given image. In addition, a knowledge propagation scheme is used to combine spectral and spatial information as a means to propagate the \potential constraints to nearby points. The propagation scheme is introduced to reinforce weak connections and improve the separability between most of the target pixels and the background. Experiments using different HSI data sets are carried out in order to test the proposed methodology. The assessment is performed from a quantitative and qualitative point of view, and by comparing the SE-based methodology against two other detection methodologies that use linear/non-linear algorithms as transformations and the well-known Adaptive Coherence/Cosine Estimator (ACE) detector. Overall results show that the SE-based detector outperforms the other two detection methodologies, which indicates the usefulness of the SE transformation in spectral target detection problems

Efficient Nonlinear Dimensionality Reduction for Pixel-wise Classification of Hyperspectral Imagery

Classification, target detection, and compression are all important tasks in analyzing hyperspectral imagery (HSI). Because of the high dimensionality of HSI, it is often useful to identify low-dimensional representations of HSI data that can be used to make analysis tasks tractable. Traditional linear dimensionality reduction (DR) methods are not adequate due to the nonlinear distribution of HSI data. Many nonlinear DR methods, which are successful in the general data processing domain, such as Local Linear Embedding (LLE) [1], Isometric Feature Mapping (ISOMAP) [2] and Kernel Principal Components Analysis (KPCA) [3], run very slowly and require large amounts of memory when applied to HSI. For example, applying KPCA to the 512×217 pixel, 204-band Salinas image using a modern desktop computer (AMD FX-6300 Six-Core Processor, 32 GB memory) requires more than 5 days of computing time and 28GB memory! In this thesis, we propose two different algorithms for significantly improving the computational efficiency of nonlinear DR without adversely affecting the performance of classification task: Simple Linear Iterative Clustering (SLIC) superpixels and semi-supervised deep autoencoder networks (SSDAN). SLIC is a very popular algorithm developed for computing superpixels in RGB images that can easily be extended to HSI. Each superpixel includes hundreds or thousands of pixels based on spatial and spectral similarities and is represented by the mean spectrum and spatial position of all of its component pixels. Since the number of superpixels is much smaller than the number of pixels in the image, they can be used as input for nonlinearDR, which significantly reduces the required computation time and memory versus providing all of the original pixels as input. After nonlinear DR is performed using superpixels as input, an interpolation step can be used to obtain the embedding of each original image pixel in the low dimensional space. To illustrate the power of using superpixels in an HSI classification pipeline,we conduct experiments on three widely used and publicly available hyperspectral images: Indian Pines, Salinas and Pavia. The experimental results for all three images demonstrate that for moderately sized superpixels, the overall accuracy of classification using superpixel-based nonlinear DR matches and sometimes exceeds the overall accuracy of classification using pixel-based nonlinear DR, with a computational speed that is two-three orders of magnitude faster. Even though superpixel-based nonlinear DR shows promise for HSI classification, it does have disadvantages. First, it is costly to perform out-of-sample extensions. Second, it does not generalize to handle other types of data that might not have spatial information. Third, the original input pixels cannot approximately be recovered, as is possible in many DR algorithms.In order to overcome these difficulties, a new autoencoder network - SSDAN is proposed. It is a fully-connected semi-supervised autoencoder network that performs nonlinear DR in a manner that enables class information to be integrated. Features learned from SSDAN will be similar to those computed via traditional nonlinear DR, and features from the same class will be close to each other. Once the network is trained well with training data, test data can be easily mapped to the low dimensional embedding. Any kind of data can be used to train a SSDAN,and the decoder portion of the SSDAN can easily recover the initial input with reasonable loss.Experimental results on pixel-based classification in the Indian Pines, Salinas and Pavia images show that SSDANs can approximate the overall accuracy of nonlinear DR while significantly improving computational efficiency. We also show that transfer learning can be use to finetune features of a trained SSDAN for a new HSI dataset. Finally, experimental results on HSI compression show a trade-off between Overall Accuracy (OA) of extracted features and PeakSignal to Noise Ratio (PSNR) of the reconstructed image

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