Jason C. Isaacs

Optimizing coverage of three-dimensional wireless sensor networks by means of photon mapping

As wireless sensor networks applied to 3D spaces gain in prominence, it becomes necessary to develop means of understanding how to optimize 3D sensor coverage while taking into account the environmental conditions in which they operate. To accomplish this goal, this paper presents the Sensor Placement Optimization via Queries (SPOQ) simulation algorithm. It determines where to place the minimal number of simulated bistatic sensors such that they cover as much of the single-source-illuminated virtual environment as possible. SPOQ performs virtual sensor placement optimization by means of making queries to the photon map generated by the photon mapping algorithm and uses this query output as input to a prevailing modified sensor placement algorithm. Since SPOQ uses photon mapping, SPOQ can take into account static or dynamic simulated environmental conditions and can use exploratory or precomputed sensing. The SPOQ method is computationally efficient, requiring less memory than other sensor placement solutions.

Diffusion features for target specific recognition with synthetic aperture sonar raw signals and acoustic color

Given a high dimensional dataset, one would like to be able to represent this data using fewer parameters while preserving relevant signal information. If we assume the original data actually exists on a lower dimensional manifold embedded in a high dimensional feature space, then recently popularized approaches based in graph-theory and differential geometry allow us to learn the underlying manifold that generates the data. One such technique, called Diffusion Maps, is said to preserve the local proximity between data points by first constructing a representation for the underlying manifold. This work examines target specific classification problems using Diffusion Maps to embed inverse imaged synthetic aperture sonar signal data for automatic target recognition. The data set contains six target types. Results demonstrate that the diffusion features capture suitable discriminating information from the raw signals and acoustic color to improve target specific recognition with a lower false alarm rate. However, fusion performance is degraded.

Geodesic shape distance and integral invariant shape features for automatic target recognition

Scale, rotational, and translational invariance is important in shape classification problems for automatic target recognition. In this work, we employ integral invariant shape metrics and geodesic shape distance features for shape analysis of closed curves extracted from 2-D synthetic aperture sonar imagery. Results demonstrate that both metrics allow for good class separation over multiple target shapes whether through pair-wise comparison or with a small library of shape templates.

Metrics of the Laplace-Beltrami eigenfunctions for 2D shape matching

Assuming that a 1D curve can be represented as a graph embedded in a 2D-space, the metrics of the eigenfunctions of the weighted graph-Laplacian and diffusion operator of that graph are then a representation of the shape of that curve with invariance to rotation, scale, and translation. The diffusion operator is said to preserve the local proximity between data points by constructing a representation for the underlying manifold by an approximation of the Laplace-Beltrami operator acting on the graph of this curve. This work examines 2D shape clustering problems using a spectral metric of the Laplace-Betrami eigenfunctions for shape analysis of closed curves. Results demonstrate that the spectral metrics allow for good class separation over multiple targets with noise.

Signal diffusion features for automatic target recognition in synthetic aperture sonar

Given a high dimensional dataset, one would like to be able to represent this data using fewer parameters while preserving relevant signal information, previously this was done with principal component analysis, factor analysis, or basis pursuit. However, if we assume the original data actually exists on a lower dimensional manifold embedded in a high dimensional feature space, then recently popularized approaches based in graph-theory and differential geometry allow us to learn the underlying manifold that generates the data. One such manifold-learning technique, called Diffusion Maps, is said to preserve the local proximity between data points by first constructing a representation for the underlying manifold. This work examines binary target classification problems using Diffusion Maps to embed inverse imaged synthetic aperture sonar signal data with various diffusion kernel representations for automatic target recognition. Results over three sonar datasets demonstrate that the resulting diffusion maps capture suitable discriminating information from the signals to improve target recognition and drastically lower the false alarm rate.

Laplace-Beltrami eigenfunction metrics and geodesic shape distance features for shape matching in synthetic aperture sonar

Assuming that a 1D curve is a representation of a manifold embedded in a 2D-space, the metrics of the eigenfunctions of the weighted graph-Laplacian and diffusion operator of that manifold are then a representation of the shape of that manifold with invariance to rotation, scale, and translation. In this work, we employ spectral metrics of the eigenfunctions of the Laplace-Beltrami operator compared with geodesic shape distance features for shape analysis of closed curves extracted from 2-D synthetic aperture sonar imagery. Results demonstrate that the spectral eigenfunction diffusion metric and the geodesic distance allow for good class separation over multiple noisy target shapes with a computational advantage to the eigenfunction method.

Discriminative sparsity for Sonar ATR

Advancements in Sonar image capture have enabled researchers to apply sophisticated object identification algorithms in order to locate targets of interest in images such as mines. Despite progress in this field, modern sonar automatic target recognition (ATR) approaches lack robustness to the amount of noise one would expect in real-world scenarios, the capability to handle blurring incurred from the physics of image capture, and the ability to excel with relatively few training samples. We address these challenges by adapting modern sparsity-based techniques with dictionaries comprising of training from each class. We develop new discriminative (as opposed to generative) sparse representations which can help automatically classify targets in Sonar imaging. Using a simulated SAS data set from the Naval Surface Warfare Center (NSWC), we obtained compelling classification rates for multi-class problems even in cases with considerable noise and sparsity in training samples.

Sonar automatic target recognition for underwater UXO remediation

Automatic target recognition (ATR) for unexploded ordnance (UXO) detection and classification using sonar data of opportunity from open oceans survey sites is an open research area. The goal here is to develop ATR spanning real-aperture and synthetic aperture sonar imagery. The classical paradigm of anomaly detection in images breaks down in cluttered and noisy environments. In this work we present an upgraded and ultimately more robust approach to object detection and classification in image sensor data. In this approach, object detection is performed using an in-situ weighted highlight-shadow detector; features are generated on geometric moments in the imaging domain; and finally, classification is performed using an Ada-boosted decision tree classifier. These techniques are demonstrated on simulated real aperture sonar data with varying noise levels.

Automated cable tracking in sonar imagery

The classical paradigm of line and curve detection in images, as prescribed by the Hough transform, breaks down in cluttered and noisy imagery. In this paper we present an “upgraded” and ultimately more robust approach to line detection in images. The classical approach to line detection in imagery is low-pass filtering, followed by edge detection, followed by the application of the Hough transform. Peaks in the Hough transform correspond to straight line segments in the image. In our approach we replace low pass filtering by anisotropic diffusion; we replace edge detection by phase analysis of frequency components; and finally, lines corresponding to peaks in the Hough transform are statistically analyzed to reveal the most prominent and likely line segments (especially if the line thickness is known a priori) in the context of sampling distributions. The technique is demonstrated on real and synthetic aperture sonar (SAS) imagery.

Constructions of equiangular tight frames with Genetic Algorithms

Equiangular tight frames have applications in communications, signal processing, and coding theory. Previous work demonstrates that few real equiangular tight frames exist for most pairs (n,d), where the frame Φn d is a d × n matrix with d ≤ n. This work proposes a genetic algorithm as a solution to the frame design problem. Specifically, the problem of designing real equiangular tight frames by minimizing the subspace minor angle sum-squared error. Numerical experiments show that the proposed method is successful for pairs (n,d) with d less than nine.