Michael D. DeVore

SAR ATR performance using a conditionally Gaussian model

A family of conditionally Gaussian signal models for synthetic aperture radar (SAR) imagery is presented, extending a related class of models developed for high resolution radar range profiles. This signal model is robust with respect to the variations of the complex-valued radar signals due to the coherent combination of returns from scatterers as those scatterers move through relative distances on the order of a wavelength of the transmitted signal (target speckle). The target type and the relative orientations of the sensor, target, and ground plane parameterize the conditionally Gaussian model. Based upon this model, algorithms to jointly estimate both the target type and pose are developed. Performance results for both target pose estimation and target recognition are presented for publicly released data from the MSTAR program.

ATR performance of a Rician model for SAR images

Radar targets often have both specular and diffuse scatterers. A conditionally Rician model for the amplitudes of pixels in Synthetic Aperture Radar (SAR) images quantitatively accounts for both types of scatterers. Conditionally Rician models generalize conditionally Gaussian models by including means with uniformly distributed phases in the complex imagery. Qualitatively, the values of the two parameters in the Rician model bring out different aspects of the images. For automatic target recognition (ATR), log-likelihoods are computed using parameters estimated from training data. Using MSTAR data, the resulting performance for a number of four class ATR problems representing both standard and extended operating conditions is studied and compared to the performance of corresponding conditionally Gaussian models. Performance is measured quantitatively using the Hilbert-Schmidt squared error for orientation estimation and the probability of error for recognition. For the MSTAR dataset used, the results indicate that algorithms based on conditionally Rician and conditionally Gaussian models yield similar results when a rich set of training data is available, but the performance under the Rician model suffers with smaller training sets. Due to the smaller number of distribution parameters, the conditionally Gaussian approach is able to yield a better performance for any fixed complexity.

Quantitative statistical assessment of conditional models for synthetic aperture radar

Many applications of object recognition in the presence of pose uncertainty rely on statistical models-conditioned on pose-for observations. The image statistics of three-dimensional (3-D) objects are often assumed to belong to a family of distributions with unknown model parameters that vary with one or more continuous-valued pose parameters. Many methods for statistical model assessment, for example the tests of Kolmogorov-Smirnov and K. Pearson, require that all model parameters be fully specified or that sample sizes be large. Assessing pose-dependent models from a finite number of observations over a variety of poses can violate these requirements. However, a large number of small samples, corresponding to unique combinations of object, pose, and pixel location, are often available. We develop methods for model testing which assume a large number of small samples and apply them to the comparison of three models for synthetic aperture radar images of 3-D objects with varying pose. Each model is directly related to the Gaussian distribution and is assessed both in terms of goodness-of-fit and underlying model assumptions, such as independence, known mean, and homoscedasticity. Test results are presented in terms of the functional relationship between a given significance level and the percentage of samples that wold fail a test at that level.

Statistical analysis-based error models for the Microsoft Kinect(TM) depth sensor.

The stochastic error characteristics of the Kinect sensing device are presented for each axis direction. Depth (z) directional error is measured using a flat surface, and horizontal (x) and vertical (y) errors are measured using a novel 3D checkerboard. Results show that the stochastic nature of the Kinect measurement error is affected mostly by the depth at which the object being sensed is located, though radial factors must be considered, as well. Measurement and statistics-based models are presented for the stochastic error in each axis direction, which are based on the location and depth value of empirical data measured for each pixel across the entire field of view. The resulting models are compared against existing Kinect error models, and through these comparisons, the proposed model is shown to be a more sophisticated and precise characterization of the Kinect error distributions.

Performance-complexity tradeoffs for several approaches to ATR from SAR images

The performance of an automatic target recognition (ATR) system for synthetic aperture radar (SAR) images is generally dependent upon a set of parameters which captures the assumptions made approximations made in the implementation of the system. This set of parameters implicitly or explicitly determines a level of database complexity for the system. A comprehensive analysis of the empirical tradeoffs between ATR performance and database complexity is presented for variations of several algorithms including a likelihood approach under a conditionally Gaussian model for pixel distribution, a mean squared error classifier on pixel dB values, and a mean squared error classifier on pixel quarter power values. These algorithms are applied under a common framework to identical training and testing sets of SAR images for a wide range of system parameters. Their performance is characterized both in terms of the percentage of correctly classified test images and the average squared Hilbert-Schmidt distance between the estimated and true target orientations across all test images. Performance boundary curves are presented and compared, and algorithm performance is detailed at key complexity values. For the range of complexity considered, it is shown that in terms of target orientation estimation the likelihood based approach under a conditionally Gaussian model yields superior performance for any given database complexity than any of the other approaches tested. It is also shown that some variant of each of the approaches tested delivers superior target classification performance over some range of complexity.

Engineering trade study: extract, transform, load tools for data migration

The widespread need within corporate information systems (IS) divisions to migrate large quantities of data between data stores has spawned a family of commercial products, which are commonly referred to as extract-transform-load (ETL) tools. The focus of this paper is the development of engineering trade studies to be used for ETL tool evaluation. This approach: (1) Identifies selection criteria that are essential in the evaluation of an ETL tool, (2) Develops scenarios that examine each criterion, and (3) Develops quantitative measures useful for evaluating the various aspects of ETL usage. This approach generates replicable evaluation methods that can be used and modified by companies to address their own ETL product needs. With the results generated through such evaluations, companies will be able to make informed decisions and choose the best ETL tool for their purposes.

Probabilistic approach to model extraction from training data

Many of the approaches to automatic target recognition (ATR) for synthetic aperture radar (SAR) images that have been proposed in the literature fall into one of two broad classes, those based on prediction of images from models (CAD or otherwise) of the targets and those based on templates describing typical received images which are often estimated from sample data. Systems utilizing model-based prediction typically synthesize an expected SAR image given some target class and pose and then search for the combination of class and pose which maximizes some match metric between the synthesized and observed images. This approach has the advantage of being robust with respect to target pose and articulation not previously encountered but does require detailed models of the targets of interest. On the other hand, template-based systems typically do not require detailed target models but instead store expected images for a range of targets and poses based on previous observations (training data) and then search for the template which most closely represents the observed image. We consider the design and use of probabilistic models for targets developed from training data which do not require CAD models of the targets but which can be used in a hypothesize-and-predict manner similar to other model-based approaches. The construction of such models requires the extraction from training data of functions which characterize the target radar cross section in terms of target class, pose, articulation, and other sources of variability. We demonstrate this approach using a conditionally Gaussian model for SAR image data and under that model develop the tools required to determine target models and to use those models to solve inference problems from an image of an unknown target. The conditionally Gaussian model is applied in a target-centered reference frame resulting in a probabilistic model on the surface of the target. The model is segmented based on the information content in regions of the target space. Modeling radar power variability and target positional uncertainty results in improved accuracy. Performance results are presented for both target classification and orientation estimation using the publicly available MSTAR dataset.

Target-Centered Models and Information-Theoretic Segmentation for Automatic Target Recognition

We present an approach to automatic target recognition (ATR) from synthetic aperture radar (SAR) imagery which combines advantages of both model-based and template-based approaches. Prior observations are used to estimate the statistical properties of reflectance over regions in the training scene. These target-centered statistical models can then be used to estimate the statistical properties of sensor output for arbitrary pose. Two-sided hypothesis tests which are maximally powerful at the most likely alternative are developed in a information-theoretic framework to address target model segmentation and confuser rejection. Segmentation of target from clutter is performed in the target-centered coordinate system using all prior observations to produce a consistent segmentation over all poses. We present performance and computation complexity results as a function of segmentation threshold, confuser-rejection threshold, and operating conditions for publicly available SAR data.

Relationships between computational system performance and recognition system performance

The implementation of computational systems to perform intensive operations often involves balancing the performance specification, system throughput, and available system resources. For problems of automatic target recognition (ATR), these three quantities of interest are the probability of classification error, the rate at which regions of interest are processed, and the computational power of the underlying hardware. An understanding of the inter-relationships between these factors can be an aid in making informed choices while exploring competing design possibilities. To model these relationships we have combined characterizations of ATR performance, which yield probability of classification error as a function of target model complexity, with analytical models of computational performance, which yield throughput as a function of target model complexity. Together, these constitute a parametric curve that is parameterized by target model complexity for any given recognition problem and hardware implementation. We demonstrate this approach on the problem of ATR from synthetic aperture radar imagery using a subset of the publicly released MSTAR dataset. We use this approach to characterize the achievable classification rate as a function of required throughput for various hardware configurations.

Analytical and experimental performance-complexity tradeoffs in ATR

Many automatic target recognition systems are designed based on training data. In model-based approaches, parameters are estimated from the training data and used in the actual implementation of the system. Often for a fixed-size training set, as the complexity of the model increases, the performance gets better initially then worsens. While this phenomenon is well-known in the statistics community, its importance in the design of target recognition systems is often neglected. For target recognition systems with decisions based on likelihood ratios using estimated parameters, we present complementary analytical and experimental results on this phenomenon. Analytical results assume independent samples for training and assume the existence of an underlying true distribution on the data that is not known. For several model classes, an optimal model complexity can be derived. Experimentally, these results are used to guide the design of target recognition systems for synthetic aperture radar data collected in the MSTAR program using probability of error for performance.