The detection of subpixel targets in hyperspectral images is complicated by interference arising from other background materials. This paper describes three target detection algorithms implemented in Data Fusion Corporation's HYPERTOOLS, a suite of hyperspectral image analysis tools. The matched subspace filter (MSF) is a generalized likelihood ratio test designed to detect target signatures while suppressing known interference signatures in a hyperspectral image. The fill-factor matched subspace filter (FFMSF) and the mixture-modeled matched subspace filter (MMMSF) extend the MSF by fusing geometrical (i.e., material abundance) and statistical (i.e., an assessment of the applicability of a linear replacement mixture model) information with the MSF output. The MSF, FFMSF, and MMMSF require one, two, and three thresholds, respectively. Automated means of determining these thresholds are proposed and justified.
The MSF is further designed to allow the processing of multirank target and interference spectral matrices. As more information about a target or targets is included in the MSF, the detection performance of the MSF is expected to improve. If the target and/or interference matrices are singular or nearly singular, however, the performance of the MSF may instead be degraded. Singular value decomposition (SVD) may be employed to prepare spectral data matrices for optimal performance of the MSF. Although the use of singular value decomposition for preprocessing data matrices is well-known in signal processing, the determination of thresholds for the selection of left-singular vectors spanning the data space remains more of “an art.” An automated method for determining the number of useful left-singular vectors is proposed based on an interpretation of the singular values and on the analysis of the dimensions of the measurement space.
The problem of constructing a single classifier when multiple phenomenologies are measured by different sensor types is made more difficult because features take diversified forms, and classifiers built from them have variable performance. For example, features can be continuous or binary valued (as in discrete labels), or be composed of incompatible structural primitives. Therefore, it is difficult to lump all of these features together into a single classifier for decision making. This realization leads to the combined use of multiple classifiers.
The solution presented in this paper describes the formulation and development of:
A computational procedure for computing approximate hyperplane decision boundaries to achieve a balanced classifier.
Achieving a minimum Bayes-risk balanced classifier as a convex combination of balanced classifiers. This is done for both independent and correlated cases.
Convex combinations of balanced classifiers are balanced. However, our research has further generalized this concept by computing optimal convex combinations of classifiers so as to also attain the property of being minimum Bayes-risk for the combined classifier. The principle exploited was to incorporate either the decisions or the decision statistics of the individual classifiers within a combined confusion matrix considering both the correlated and independent cases. This was posed as an optimization problem to be approached via Markov-Chain Monte Carlo methods. Some preliminary results are shown.
The matched subspace filter (MSF) is a target detection algorithm implemented in Data Fusion Corporation's <i>HYPER-TOOLS</i>, a suite of hyperspectral image analysis tools. This generalized likelihood ratio test is designed to detect target signatures while suppressing known interference signatures in a hyperspectral image. The importance of interference suppression is illustrated in detection performance experiments in which spectral taggant panels are located in hyperspectral reflectance images. The MSF may also be successfully applied to data in which the spectra's continua have been removed in order to isolate spectral absorption features. A connection is established between the detection performance of the MSF and the subspace angle between the target and interference subspaces.
The problem of tracking of a group of targets is considered in this paper. We will present an overview of an investigation into this problem by first using the targets velocity state vectors covariance matrix to establish target grouping and then by exploiting concepts derived from game theory, in particular the leader-follower techniques, and graph theory to represent and establish relationships that influence the tracking of objects that belong to a group formation.
In this paper we evaluate the ability of the Matched Subspace Detector (MSD), Matched Filter Detector (MFD) and Orthogonal Subspace Projection (OSP) to discriminate material types in laboratory samples of intimately mixed bidirectional reflectance data. The analysis consists of a series of experiments where bidirectional reflectance spectra of intimate mixtures of enstatite-olivine and anorthite-olivine in various proportions are converted to single scattering albedo (SSA) using Hapke's model for bidirectional reflectance. The linearized SSA spectra are used as inputs to the various detectors and the output for each is evaluated as a function of the proportion of target- to-interference. Results are presented as a series of figures that show overall the MSD has a higher target-to- background separation (i.e., better class separation) than either the MFD or OSP. This target-to-background separation results in fewer false alarms for the MSD than either of the other two detectors.
We describe a geometric model of high-resolution radar (HRR), where objects being imaged by the sensor are assumed to consists of a collection of isotropic scattering centers distributed in three dimensions. Three, four, five and six point pure HRR invariant quantities for non-coplanar reflecting centers are presented. New work showing invariants combining HRR and SAR measurements are then presented. All these techniques require matching corresponding features in multiple HRR and/or SAR views. These features are represented using analytic scattering models. Multiple features within the same HRR resolution cell can be individually detected and separated using interference-suppression filters. These features can then be individually tracked to maintain correspondence as the object poise changes. We validate our HRR/SAR invariants using the XPATCH simulation system. Finally, a view-based method for 3D model reconstruction is developed and demonstrated.
This paper presents a linear system approximation for automated analysis of passive, long-wave infrared (LWIR) imagery. The approach is based on the premise that for a time varying ambient temperature field, the ratio of object surface temperature to ambient temperature is independent of amplitude and is a function only of frequency. Thus, for any given material, it is possible to compute a complex transfer function in the frequency domain with real and imaginary parts that are indicative of the material type. Transfer functions for a finite set of ordered points on a hypothesized object create an invariant set for that object. This set of variates is then concatenated with another set of variates (obtained either from the same object or a different object) to form two random complex vectors. Statistical tests of affine independence between the two random vectors is facilitated by decomposing the generalized correlation matrix into canonical form and testing the hypothesis that the sample canonical correlations are all zero for a fixed probability of false alarm (PFA). In the case of joint Gaussian distributions, the statistical test is a maximum likelihood. Results are presented using real images.
In this paper we address the problem of detecting targets in hyperspectral images when the target signature is buried in random noise and interference (from other materials in the same pixel). We assume that the hyperspectral pixel measurement is a linear combination of the target and interference signatures observed in additive noise. The linear mixing assumption leads to a linear vector space interpretation of the measurement vector, which can be decomposed into a noise-only subspace and a target-plus- interference subspace. While it is true that the target and interference subspaces are orthogonal to the noise-only subspace, the target subspace and interference subspace are, in general, not orthogonal. The non-orthogonality between the target and interference subspaces results in leakage of interference signals into the output of matched filters resulting in false detections (i.e., higher false alarm rates). In this paper, we replace the Matched Filer Detector (MFD), which is based on orthogonal projections, with a Matched Subspace Detector (MSD), which is built on non- orthogonal or oblique projections. The advantage of oblique projections is that they eliminate the leakage of interference signals into the detector, thereby making detectors based on oblique projections invariant to the amount of interference. Furthermore, under Gaussian assumptions for the additive noise, it has been shown that the MSD is Uniformly Most Powerful (higher probability of detect for a fixed probability of false alarm) among all detectors that share this invariance to interference power. In this paper we evaluate the ability of two versions of the MSD to detect targets in HYDICE data collected over sites A and B located at the U.S. Army Yuma proving grounds. We compute data derived receiver operating characteristics (ROC) curves and show that the MSD out- performs the MFD.
Dental medicine needs to observe the motion of the jaw with respect to the skull in three dimensions. This represents, therefore, a problem domain in which one has to observe, in real-time, the motion of one three- dimensional body in 3-D space (the jaw) with respect to another three-dimensional body in 3-D space (the skull) which both may move independently. This paper discusses an innovative solution to this requirement. The solution is implemented on a personal computer and is based on light-emitting diodes that are attached to the two moving 3-D objects. The innovation has been granted patent protection2. An element of the solution is the hand-held 3-D cursor whose position is also trackable as a separate three-dimensional body in 3-D space and allows the user to identify the XYZ coordinates of any point by a free-hand pointing action. Applications of this real-time 3-D measurement system are not only in dental medicine but may extend to mechanical engineering, medical gait analysis and other applications where 3-D motions need to be tracked in real time.