The development of a more unified theory of automatic target recognition (ATR) has received considerable attention over
the last several years from individual researchers, working groups, and workshops. One of the major benefits expected
to accrue from such a theory is an ability to analytically derive performance metrics that accurately predict real-world
behavior. Numerous sources of uncertainty affect the actual performance of an ATR system, so direct calculation has been
limited in practice to a few special cases because of the practical difficulties of manipulating arbitrary probability distributions
over high dimensional spaces. This paper introduces an alternative approach for evaluating ATR performance based
on a generalization of NorbertWiener's polynomial chaos theory. Through this theory, random quantities are expressed not
in terms of joint distribution functions but as convergent orthogonal series over a shared random basis. This form can be
used to represent any finite-variance distribution and can greatly simplify the propagation of uncertainties through complex
systems and algorithms. The paper presents an overview of the relevant theory and, as an example application, a discussion
of how it can be applied to model the distribution of position errors from target tracking algorithms.
KEYWORDS: Detection and tracking algorithms, Data processing, Target recognition, Data modeling, Automatic target recognition, Clouds, Sensors, LIDAR, 3D modeling, 3D metrology
This paper illustrates an approach to sequential hypothesis testing designed not to minimize the amount of data collected
but to reduce the overall amount of processing required, while still guaranteeing pre-specified conditional probabilities
of error. The approach is potentially useful when sensor data are plentiful but time and processing capability are
constrained. The approach gradually reduces the number of target hypotheses under consideration as more sensor data
are processed, proportionally allocating time and processing resources to the most likely target classes. The approach is
demonstrated on a multi-class ladar-based target recognition problem and compared with uniform-computation tests.
This paper illustrates a statistical model-based approach to the problem of target detection in a cluttered scene from
long-wave infrared images, accommodating both unknown range to the target, unknown target location in the image,
and unknown gain control settings on the imaging device. The philosophical perspective adopted emphasizes an
iterative process of model creation and refinement and subsequent evaluation. The overarching theme is on the clear
statement of all assumptions regarding the relationships between ground truth and corresponding imagery, the
assurance that each admits quantifiable refutation, and the opportunity costs associated with their adoption for a
particular problem.
KEYWORDS: Data modeling, Imaging systems, 3D metrology, Detection and tracking algorithms, 3D acquisition, LIDAR, 3D modeling, Target recognition, Radar imaging, Object recognition
Shape measurements form powerful features for recognizing objects, and many imaging modalities produce three-dimensional shape information. Stereo-photogrammetric techniques have been extensively developed, and many researchers have looked at related techniques such as shape from motion, shape from accommodation, and shape from shading. Recently, considerable attention has focused on laser radar systems for imaging distant objects, such as automobiles from an airborne platform, and on laser-based active stereo imaging for close-range objects, such as part scanners for automated inspection. Each use of these laser imagers generally results in a range image, an array of distance measurements as a function of direction. For multi-look data or data fused from multiple sensors, we may more generally treat the data as a 3D point-cloud, an unordered collection of 3D points measured from the surface of the scene. This paper presents a general approach to object recognition in the presence of significant clutter, that is suitable for application to a wide range of 3D imaging systems. The approach relies on a probabilistic framework relating 3D point-cloud data and the objects from which they are measured. Through this framework a minimum probability of error recognition algorithm is derived that accounts for both obscuring and nonobscuring clutter, and that accommodates arbitrary (range and cross-range) measurement errors. The algorithm is applied to a problem of target recognition from actual 3D point-cloud data measured in the laboratory from scale models of civilian automobiles. Noisy 3D measurements are used to train models of the automobiles, and these models are used to classify the automobiles when present in a scene containing natural and man-made clutter.
KEYWORDS: Optical spheres, Detection and tracking algorithms, Error analysis, 3D modeling, Optical engineering, Algorithm development, Data modeling, Monte Carlo methods, Shape analysis, LIDAR
We derive a pair of algorithms, one optimal and the other approximate, for recognizing three-dimensional objects from a collection of points chosen from their surface according to some probabilistic mechanism. The measurements are assumed to be noisy, and the measured location of a given point is translated according to a noise probability distribution. Distributions governing surface point selection and measurement noise can take a variety of forms depending upon the particular measurement scenario. At one extreme, each measurement is assumed to yield values restricted to a one-dimensional ray, a special case commonly adopted in the literature. At the other extreme, measured points are chosen uniformly from the object's surface, and the noise distribution is spherically symmetric, a worst-case scenario that involves no prior information about the measurements. We apply these two algorithms to shape recognition problems involving simple geometrical objects, and examine their relative behavior using a combination of analytical derivation and Monte Carlo simulation. We show that the approximate algorithm can be far simpler to compute, and its performance is competitive with the optimal algorithm when noise levels are relatively low. We show the existence of a critical noise level, beyond which the approximate algorithm exhibits catastrophic failure.
Hypothesis testing algorithms for automatic target recognition (ATR) are often formulated in terms of some assumed distribution family. The parameter values corresponding to a particular target class together with the distribution family constitute a model for the target's signature. In practice such models exhibit inaccuracy because of incorrect assumptions about the distribution family and/or because of errors in the assumed parameter values, which are often determined experimentally. Model inaccuracy can have a significant impact on performance predictions for target recognition systems. Such inaccuracy often causes model-based predictions that ignore the difference between assumed and actual distributions to be overly optimistic. This paper reports on research to quantify the effect of inaccurate models on performance prediction and to estimate the effect using only trained parameters. We demonstrate that for large observation vectors the class-conditional probabilities of error can be expressed as a simple function of the difference between two relative entropies. These relative entropies quantify the discrepancies between the actual and assumed distributions and can be used to express the difference between actual and predicted error rates. Focusing on the problem of ATR from synthetic aperture radar (SAR) imagery, we present estimators of the probabilities of error in both ideal and plug-in tests expressed in terms of the trained model parameters. These estimators are defined in terms of unbiased estimates for the first two moments of the sample statistic. We present an analytical treatment of these results and include demonstrations from simulated radar data.
Many applications which process radar data, including automatic target recognition and synthetic aperture radar image formation, are based on probabilistic models for the raw or processed data. Often, data collected from distinct directions are assumed to represent independent observations. This assumption is not valid for all data collection scenarios. A range of models can be developed that allow for successively more complex dependencies between measured data, up to deterministic computational electromagnetic models, in which observations from different orientations have a known relationship. We consider models for the autocovariance functions of nonstationary processes defined on a circular domain that fall between these two extremes. We adopt a model of covariance as a linear combination of periodic basis functions and address maximum-likelihood estimation of the coefficients by the method of expectation-maximization (EM). Finally, we apply these estimation methods to SAR image data and demonstrate the results as they apply to target recognition.
Model-based approaches to automatic target recognition (ATR) generally infer the class and pose of objects in imagery by exploiting theoretical models of the formed images. Recently, we have performed an evaluation of several statistical models for synthetic aperture radar (SAR) and have conducted experiments with ATR algorithms derived from these models. In particular, a one-parameter complex Gaussian model, classically used to model diffuse scattering, was shown to deliver higher recognition rates than a one-parameter quarter-power normal model on actual SAR data. However an extended, two-parameter quarter-power model was consistently a better fit to the data than a corresponding two-parameter Gaussian model. In this paper, we apply Rician, gamma, and K distribution models, which are two-parameter extensions of the complex Gaussian and quarter-power normal models, to ATR from SAR magnitude imagery. We consider maximum-likelihood estimation of unknown model parameters and apply the resulting training and testing algorithms to actual SAR data. We show that the K distribution model performs better than the Rician and gamma models for both large and small sample sizes. The one-parameter complex Gaussian model performed slightly better than the K model overall. For small sample sizes, this is likely due to the relative stability in estimating only one model parameter. For large sample sizes this is likely due to a lack of persistence in specular reflections over the large angular intervals required to obtain large samples.
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.
Parametric approaches to problems of inference from observed data often rely on assumed probabilistic models for the data which may be based on knowledge of the physics of the data acquisition. Given a rich enough collection of sample data, the validity of those assumed models can be assessed in a statistical hypothesis testing framework using any of a number of goodness-of-fit tests developed over the last hundred years for this purpose. Such assessments can be used both to compare alternate models for observed data and to help determine the conditions under which a given model breaks down. We apply three such methods, the (chi) 2 test of Karl Pearson, Kolmogorov's goodness-of-fit test, and the D'Agostino-Pearson test for normality, to quantify how well the data fit various models for synthetic aperture radar (SAR) images. The results of these tests are used to compare a conditionally Gaussian model for complex-valued SAR pixel values, a conditionally log-normal model for SAR pixel magnitudes, and a conditionally normal model for SAR pixel quarter-power values. Sample data for these tests are drawn from the publicly released MSTAR dataset.
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.
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.
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.
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