The Schroedinger eigenmaps (SE) algorithm using spatial and spectral information has been applied to supervised classification of hyperspectral imagery (HSI). We have previously introduced the use of SE in spectral target detection problems. The original SE-based target detector was built on the spectral information encoded in the Laplacian and Schroedinger operators. The original SE-based detector is extended such that spatial connectivity of target-like pixels is explored and encoded into the Schroedinger operator using a “knowledge propagation” scheme. The modified SE-based detector is applied to two HSI data sets that share similar target materials. Receiver operating characteristic curves and rates of detection and false alarm at object level are used as quantitative metrics to assess the detector. In addition, the Schroedinger embedding performance in target detection is compared against the performances of principal component embedding and the Laplacian embedding. Results show that the SE-based detector with spatial–spectral features outperforms the other considered approaches.
Spectral target detection refers to the process of searching for a specific material with a known spectrum over a large area containing materials with different spectral signatures. Traditional target detection methods in hyperspectral imagery (HSI) require assuming the data fit some statistical or geometric models and based on the model, to estimate parameters for defining a hypothesis test, where one class (i.e., target class) is chosen over the other classes (i.e., background class). Nonlinear manifold learning methods such as Laplacian eigenmaps (LE) have extensively shown their potential use in HSI processing, specifically in classification or segmentation. Recently, Schroedinger eigenmaps (SE), which is built upon LE, has been introduced as a semisupervised classification method. In SE, the former Laplacian operator is replaced by the Schroedinger operator. The Schroedinger operator includes by definition, a potential term V that steers the transformation in certain directions improving the separability between classes. In this regard, we propose a methodology for target detection that is not based on the traditional schemes and that does not need the estimation of statistical or geometric parameters. This method is based on SE, where the potential term V is taken into consideration to include the prior knowledge about the target class and use it to steer the transformation in directions where the target location in the new space is known and the separability between target and background is augmented. An initial study of how SE can be used in a target detection scheme for HSI is shown here. In-scene pixel and spectral signature detection approaches are presented. The HSI data used comprise various target panels for testing simultaneous detection of multiple objects with different complexities.
The applicability of Laplacian Eigenmaps (LE) and Schroedinger Eigenmaps (SE) has been widely shown in the processing of hyperspectral imagery. Speciﬁcally, we have previously shown that SE has a promising performance in spectral target detection. SE, unlike LE, could include prior information or labeled data points into a barrier potential term that steers the transformation in certain directions making the labeled points and the similar points pulled toward the origin in the new space. We have also noticed that the barrier potentials generated from a few labeled points may aﬀect in a brittle manner the dimensionality in the Schroedinger space and in turn, the target detection performance. In this paper, we show that the number of SE used in the detection could be increased without aﬀecting the detection performance by adding spatial and spectral constraints on the individual labeled points and propagating this knowledge to nearby points through a modiﬁed Schroedinger matrix. We apply our algorithm to hyperspectral data sets with several target panels and diﬀerent complexity in order to have a wide framework of assessment.
Proc. SPIE. 9840, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XXII
KEYWORDS: Target detection, Hyperspectral imaging, Principal component analysis, Detection and tracking algorithms, Image segmentation, Silver, Control systems, Algorithm development, Hyperspectral target detection, RGB color model
The Biased Normalized Cuts (BNC) algorithm is a useful technique for detecting targets or objects in RGB imagery. In this paper, we propose modifying BNC for the purpose of target detection in hyperspectral imagery. As opposed to other target detection algorithms that typically encode target information prior to dimensionality reduction, our proposed algorithm encodes target information after dimensionality reduction, enabling a user to detect different targets in interactive mode. To assess the proposed BNC algorithm, we utilize hyperspectral imagery (HSI) from the SHARE 2012 data campaign, and we explore the relationship between the number and the position of expert-provided target labels and the precision/recall of the remaining targets in the scene.
Spectral imagery such as multispectral and hyperspectral data could be seen as a set of panchromatic images stacked as a 3d cube, with two spatial dimensions and one spectral. For hyperspectral imagery, the spectral dimension is highly sampled, which implies redundant information and a high spectral dimensionality. Therefore, it is necessary to use transformations on the data not only to reduce processing costs, but also to reveal some features or characteristics of the data that were hidden in the original space. Schrodinger Eigenmaps (SE) is a novel mathematical method for non-linear representation of a data set that attempts to preserve the local structure while the spectral dimension is reduced. SE could be seen as an extension of Laplacian Eigenmaps (LE), where the diffusion process could be steered in certain directions determined by a potential term. SE was initially introduced as a semi supervised classification technique and most recently, it has been applied to target detection showing promising performance. In target detection, only the barrier potential has been used, so different forms to define barrier potentials and its influence on the data embedding are studied here. In this way, an experiment to assess the target detection vs. how strong the influence of potentials is and how many eigenmaps are used in the detection, is proposed. The target detection is performed using a hyperspectral data set, where several targets with different complexity are presented in the same scene.
Non-linear dimensionality reduction methods have been widely applied to hyperspectral imagery due to its structure as the information can be represented in a lower dimension without losing information, and because the non-linear methods preserve the local geometry of the data while the dimension is reduced. One of these methods is Laplacian Eigenmaps (LE), which assumes that the data lies on a low dimensional manifold embedded in a high dimensional space. LE builds a nearest neighbor graph, computes its Laplacian and performs the eigendecomposition of the Laplacian. These eigenfunctions constitute a basis for the lower dimensional space in which the geometry of the manifold is preserved. In addition to the reduction problem, LE has been widely used in tasks such as segmentation, clustering, and classification. In this regard, a new Schrodinger Eigenmaps (SE) method was developed and presented as a semi-supervised classification scheme in order to improve the classification performance and take advantage of the labeled data. SE is an algorithm built upon LE, where the former Laplacian operator is replaced by the Schrodinger operator. The Schrodinger operator includes a potential term V, that, taking advantage of the additional information such as labeled data, allows clustering of similar points. In this paper, we explore the idea of using SE in target detection. In this way, we present a framework where the potential term V is defined as a barrier potential: a diagonal matrix encoding the spatial position of the target, and the detection performance is evaluated by using different targets and different hyperspectral scenes.
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.
Understanding the capabilities of satellite sensors with spatial and spectral characteristics similar to those of MODIS for
Maritime Domain Awareness (MDA) is of importance because of the upcoming NPOES with 100 minutes revisit time
carrying the MODIS-like VIIRS multispectral imaging sensor. This paper presents an experimental study of ship
detection using MODIS imagery. We study the use of ship signatures such as contaminant plumes in clouds and the
spectral contrast between the ship and the sea background for detection. Results show the potential and challenges for
such approach in MDA.
This paper presents an algorithm for automated extraction of interest points (IPs)in multispectral and hyperspectral
images. Interest points are features of the image that capture information from its neighbours and they
are distinctive and stable under transformations such as translation and rotation. Interest-point operators for
monochromatic images were proposed more than a decade ago and have since been studied extensively. IPs have
been applied to diverse problems in computer vision, including image matching, recognition, registration, 3D
reconstruction, change detection, and content-based image retrieval. Interest points are helpful in data reduction,
and reduce the computational burden of various algorithms (like registration, object detection, 3D reconstruction
etc) by replacing an exhaustive search over the entire image domain by a probe into a concise set of highly
informative points. An interest operator seeks out points in an image that are structurally distinct, invariant to
imaging conditions, stable under geometric transformation, and interpretable which are good candidates for interest
points. Our approach extends ideas from Lowe's keypoint operator that uses local extrema of Difference of
Gaussian (DoG) operator at multiple scales to detect interest point in gray level images. The proposed approach
extends Lowe's method by direct conversion of scalar operations such as scale-space generation, and extreme
point detection into operations that take the vector nature of the image into consideration. Experimental results
with RGB and hyperspectral images which demonstrate the potential of the method for this application and the
potential improvements of a fully vectorial approach over band-by-band approaches described in the literature.