ROC Analysis of ATR from SAR images using a Model-Based. Recognizer Incorporating Pose Information

Size: px

Start display at page:

Download "ROC Analysis of ATR from SAR images using a Model-Based. Recognizer Incorporating Pose Information"

Noreen Phillips
6 years ago
Views:

1 ROC Analysis of ATR from SAR images using a Model-Based Recognizer Incorporating Pose Information David Cyganski, Brian King, Richard F. Vaz, and John A. Orr Machine Vision Laboratory Electrical and Computer Engineering Department Worcester Polytechnic Institute Worcester, MA ABSTRACT An automatic target recognition (ATR) technique developed by the authors features analytically derived object models which are formed from entire image suites, yet are compact and allow a direct target recognition and pose determination procedure. In contrast to the pose-invariant information used to form the models in conventional approaches, view-dependent information is retained in the formation of the compact models for this new approach. All model-based ATR systems are confronted with the problem of image variation as a function of viewing angle. This problem can be addressed by use of an exhaustive library of views, at the expense of a large suite of literal images and a computationally intensive search-based recognition process. Means for overcoming these storage and processing obstacles have traditionally involved some type of view-independent target representation, often developed from some composite view of the target over the viewing angles of interest. This results in a much more compact target model, and a more direct recognition process. Unfortunately, the gains in storage and computational requirements of these invariant algorithms come at the price of diminished target discrimination capability. The new algorithm incorporates pose as a fundamental parameter which is solved for as part of the recognition process, and does not discard the pose-related information which is relevant to target recognition. In this paper, the newly-developed technique is applied to synthetic aperture radar (SAR) images to develop receiver operating characteristic (ROC) curves in the presence of both multiplicative noise (speckle) and clutter. Comparative curves are also developed for a conventional Generalized Quadratic Classier ATR system. Keywords: automatic target recognition, detection, SAR 1 Introduction and Overview 1.1 WPI LSD/DOA ATD&R Algorithm One of the fundamental challenges of model-based automatic target recognition (ATR) is that targets manifest themselves in quite dierent ways in an image, depending upon the location and orientation of the target with

2 respect to the sensing device(s). Consequently, target models must account for this, typically either by comprising an exhaustive set of target views, or by relying on properties of the imaged target which are invariant to target pose. When the exhaustive approach is taken, the models require a great deal of storage space, and the recognition process involves a search through this space which may preclude real-time application, especially if the target library is large. Approaches to ameliorate these computational costs can involve averaging or blurring over subsets of views, 1 on-the-y template generation, 2 or ordered search strategies, 3 but these approaches still follow the expensive search-based paradigm to some extent. Another class of ATR algorithms exploits properties of the target images which are invariant under target rotations and/or translations. These approaches do not suer from the storage and computational demands of the exhaustive search-based techniques, and are eective to the extent to which the invariant properties of the imaged target are distinctive and unique to that target. These approaches include methods which rely on geometric invariance properties, 4 as well as methods which are based on generalizations of the matched spatial lter concept, 5 which includes synthetic discriminant function (SDF) lters. 6 A notable example of the invariant model approach is the minimum average correlation energy (MACE) lter, 7 in which a model template designed to suppress false alarms is created for the target suite. All of these techniques develop a target model which in some sense represents common or \averaged" target data. Thus, if objects may be imaged from any perspective (e.g., airborne targets), then targets of similar size may well have similar \averaged" model representations, as the many dissimilar views combine to produce a relatively featureless model, resulting in poor performance as compared with exhaustive matching systems like those described above. 8 A recently developed technique known as the Linear Signal Decomposition/Direction of Arrival (LSD/DOA) approach 9 also provides means for model-based ATR of targets which may be viewed from unknown perspectives. Similarly to the invariance-based techniques, the LSD/DOA approach does not require large target models, and the recognition process is direct rather than search-based. However, the models used in the LSD/DOA technique do not represent information which is invariant to target pose, but rather encode and exploit the relationship between target pose and signature so that the detection process simultaneously provides both pose estimates and target identity information. That is, these compact models incorporate the variation in target signature as a function of target pose; they exploit the information which is variant under changes in target orientation and position. This is quite distinct from the approaches described above, which rely on models consisting of invariant information. The LSD/DOA algorithm 9 eects a partitioning of the ATR problem into two stages: model construction and pose estimation/recognition. The model construction process involves solution of a large (usually overdetermined) set of equations to determine the elements of a particular basis for the image suite. This Reciprocal Basis Set (RBS) is developed such that the pose estimation/recognition stage can be performed directly and eciently, with no searching or iteration. That is, the computational burden associated with the ATR problem is largely shifted to the model-building process in this algorithm. Generation of the RBS target models involves a great reduction in data, as a complete suite of object views is reduced to a small set of RBS elements. The number of basis elements used, and hence the size of the target model, can be chosen according to cost/performance considerations, but is in any event very modest compared to the the data from which the model is derived. The basis elements are generated such that linear projection of target images onto the basis elements will result in a set of inner product measures which simultaneously provide a sucient statistic for target matching and represent the data from which target pose parameter estimates can be determined. This is due to the fact that the RBS elements are chosen to encode the target pose into these inner product results, which are called Synthetic Wavefront Samples (SWS). These are so named because, for a given target image, the SWS will be samples of a multidimensional complex exponential wave, the directional cosines of which reveal the pose parameters of the imaged target. A Direction of Arrival (DOA) algorithm then uses the SWS to solve for the target pose parameter estimates. If more RBS functions are used, then this larger target model allows generation of more SWS, which in turn can provide better pose estimates and more reliable target

3 θ θ Reciprocal Basis Set Figure 1: LSD/DOA Block Diagram Acquired Image Direct Linear Signal Projection D.O.A. Estimated ^ Pose, θ Signal Model Generalized Likelihood Ratio Test Selected Hypothesis Figure 2: LSD/DOA Implementation detection. The reader is referred to Cyganski 9 for mathematical and implementational details of the LSD/DOA algorithm; a block diagram depicting the algorithm is given in Figure 1. Viewed from a detection theoretic perspective, the LSD/DOA algorithm comprises a composite hypothesis decision system; that is, the hypothesis for the detection decision is parameterized by the (unknown) target pose parameters. Given statistics which describe the noise eects on the SWS, a decision rule in the form of a generalized likelihood ratio test (GLRT) can be developed. In general, the noise corrupting the SWS is correlated, and the optimal GLRT does not yield itself to analytic solution. However, under simplifying assumptions Gaussian image noise and a perfect DOA estimation, a useful GLRT which incorporates the pose parameter estimates from the DOA algorithm can be developed. Furthermore, tests which incorporate knowledge of the correct pose parameters can be used to develop a uniformly most powerful (UMP) test to provide a performance bound for this composite hypothesis decision process. The complete LSD/DOA implementation is shown in Figure 2.

4 2 LSD/DOA versus Generalized Quadratic Classier 2.1 ATR via a Generalized Quadratic Classier For the purpose of comparison with the behavior of the new LSD/DOA system described above, an ATR system in which the target model is developed from information common to the target suite was implemented. As was mentioned in Section 1.1, there is a broad family of such approaches. In order to investigate, in a straightforward fashion, the implications of using LSD/DOA, a pose-dependent classier, as opposed to exhaustive or reduced-size exhaustive systems, the performance of a generalized quadratic classier (GQC) was compared with that of the LSD/DOA classier. Given an image of a target in a particular pose as hypothesis-1 and a known alternative hypothesis-0 image, the linear detector which maximizes the postdetection SNR when the target is present in additive white Gaussian noise is the well-known matched lter. Now given an unknown hypothesis-0 image, an appropriate model for the case of background clutter that undergoes large variation, the optimal detector becomes a quadratic classier. That is, the decision metric amounts to the Euclidean distance of the given image from the hypothesis-1 image. Some authors also refer to quadratic classier as a matched lter as it can be implemented by summing a linear matched lter output with terms representing weighted measures of image and lter energy. As target pose varies over some number of viewing parameters, the target image undergoes an excursion in image space. A reasonable (and asymptotically optimal with increasing numbers of lters) approach to developing a detector for the suite of target instantiations is to use a bank of lters, each matched to the average of the target image suite over a small range of pose variation. The output of this \composite lter" is taken to be the output of the single lter that achieves the minimum quadratic measure. This system may be called a generalized quadratic classier, GQC, in the sense that the resulting output is a sucient statistic for a generalized likelihood ratio test with the hypotheses stated above. When the number of lters equals that of the target suite, the GQC implements the fully exhaustive and optimal (given only those exemplars) classier. We have implemented a exible system for evaluation of the GQC results as the the number of lters in the bank is varied from one up to the number of images in the target suite. 2.2 SAR Target and Background Images The LSD/DOA ATR algorithm applies a non-linear estimation technique to data obtained by applying several linear lters to the test images. These linear lters, called reciprocal basis functions (RBFs) are obtained by processing a suite of target exemplars. These exemplars should comprise a set of object images nely spaced in pose parameters. As explained above, the same such set of exemplars is also required for construction of the GQC. To conduct this test with SAR images thus requires such a suite or means to construct such a suite for a given target. The basis for our target exemplar generation was a set of spotlight SAR phase history les provided by Wright Laboratories. The tests described in the following are based upon use of T72 tank data obtained in the L band with 10 degree elevation and (HH) only polarization. From this data a sequence of 318 images was generated, representative of a xed direction of monostatic illumination and 318 uniformly spaced viewpoint orientations over 360 degrees of the azimuthal orientation. The SAR target images that were reconstructed were downsampled so as to achieve approximately a 1 ft. by 1 ft.

5 range and cross-range resolution. For background and null hypothesis (H0) images, we used SAR clutter images obtained from Lincoln Labs (Stockbridge, NY). The LL clutter images depict strip maps with a 1 ft. by 1 ft. resolution. Again, only the HH reconstructions were used for the tests. Images representing the target present hypothesis (H1) were obtained by masking out a region of a clutter image corresponding to the convex hull of the brightest target pixels and inserting the target image into this masked region. 2.3 Speckle noise corruption and example results To complete the generation of realistic test cases, each target image was corrupted by the addition of specklelike noise. As these images are logarithmic intensity SAR images, the originally multiplicative SAR speckle noise process can be introduced to the processed images as an additive noise process. The noise process in this case must have a log-gamma probability density. Thus our test instance generator synthesizes independent log-gamma noise samples that are summed with the logarithmic intensity images. The following gures will serve to both show: an example of the application of the combined synthetic scene generator in which synthetic SAR target images are corrupted with speckle noise and then merged with existing SAR clutter images; an example of the application of the LSD/DOA algorithm as a non-linear matched lter system; an example of the output of the LSD/DOA algorithm as a pose estimator as it might be used in a model driven recognition system. Figure 3 shows the sampling of 53 target images used in the construction of a set of eight LSD/DOA RBS lters. These target images were rendered from SAR phase histories of a T-72 tank (as described above). Six of these target images were corrupted by speckle noise and then superimposed upon the SAR clutter images described above. The background clutter image was chosen so as to obtain a low contrast target to background ratio, exemplifying a reduced signature target recognition problem. The resulting image is seen in Figure 4. With the low image to background contrast and the realistic, random, speckle corruption of the targets, only two of the six targets are typically identiable by most people in this man-made-discrete rich image. An eight lter LSD/DOA algorithm was then applied to the scene to obtain a match metric image. This image, in which darker shades of gray are used to distinguish regions of high match, is shown in Figure 5. As can be seen six targets were identied in the image. In fact, these targets are correctly identied. In Figure 6 we see the same match metric image with two sets of silhouettes of the tanks (one dark and one light gray) superimposed. One silhouette is that of the actual tank image from which the test image was constructed. The second silhouette is that of a tank with the pose angle that was identied by the LSD/DOA pose angle estimation process. As can be seen, the pose angle error is less than a few degrees for each of these cases.

6 Figure 3: Fifty-three samples (6.8 spacing) from the T-72 SAR target suite. Figure 4: Six T-72 speckle contaminated targets are located in this SAR image.

7 Figure 5: The six dark points identify high match values in the LSD/DOA output. Figure 6: The six true target silhouettes are shown superimposed on the match value image.

8 3 Receiver Operating Characteristic Results The LSD/DOA and GQC ATR systems were compared using a receiver operating characteristic (ROC) generation system. An ROC curve shows the performance of a detector across the range of possible threshold values; therefore to generate a ROC curve statistics must be generated to estimate the detection and false alarm probabilities for every possible threshold. From those thresholds an ROC curve can be constructed for any ATR system that asymptotically approaches the actual continuous ROC curve as the number of trials increases. 3.1 Comparison Results We used 53 of the above 318 target images (generated as above) to create a SAR target model suite for generating the RBS (Reciprocal Basis Set) images which constitute the linear lters in the LSD/DOA ATR. The LSD/DOA algorithm implementation used our recently developed optimum Generalized Likelihood Ratio Test (GLRT) decision system that is specically optimized for the target lters being applied. It also uses the non-stationary noise optimized Kay-Estimator DOA algorithm we recently developed. We also incorporated a pixel-usage weighting scheme to tailor the distribution of energy in the RBS functions so as to reduce inuence of target pixels on the periphery of the target. The GQC ATR was constructed from all 318 images by averaging groups of approximately 318/n images to form the n lters in the case of an n lter GQC (as is done in the Lincoln Labs baseline system 8 ). In gure 7 and gure 8 we present a set of ROC curves (that is, P d, probability of detection, versus P f a, probability of false alarm,) that depict the performance of the LSD/DOA algorithm and that of the GQC Bank for various numbers of linear lters in each. The gures only dier in that one is plotted on a linear scale while the other is plotted on a logarithmic scale. The image to background contrast ratio was made quite small in order to produce several well populated ROC curves for these tests. This is required in order to produce such curves in a timely fashion, however the resulting false alarm rates are articially high. For that reason, these curves should only be used to judge the performance of the LSD/DOA algorithm versus that of the GQC bank within the context of these tests and not for comparison with other ROC curves obtained for dierent target/background scenarios. Note that for the test scenario described here, for SAR images varying over 318 poses, impressed upon SAR clutter with 1 degree of freedom (DOF) and degraded by random speckle noise, we found that an LSD/DOA algorithm operating with 8 linear lters (reciprocal basis images) trained with 53 sample images from the 318 possible images, produced an ROC curve that outperformed a GQC bank with 106 lters (constructed from all 318 possible poses in the test set). 4 Conclusions In general it appears that the LSD/DOA method is able to obtain the same performance in the 1-DOF test cases as a GQC bank while using only about 1/10 as many linear lters. As the number of lters required in an N-DOF case should increase in both cases as the Nth power of that in the 1-DOF case, this is a very signicant improvement in processing \speed" and lter storage space in the case of several degrees of freedom.

9 1.00 ROC Comparison on Speckled Field Scene 0.99 Probability of Detect LSD/DOA - 8 SWS CMF - 79 Filters CMF Filters CMF Filters Probabilty of False Alarm Figure 7: ROC curves for SAR tests comparing LSD/DOA and GQC for various number of linear lters (LIN scale). The image to background contrast ratio was made quite small in order to produce several well populated ROC curves for these tests. This is required in order to produce such curves in a timely fashion, however the resulting false alarm rates are articially high. For that reason, these curves should only be used to judge the performance of the LSD/DOA algorithm versus that of the GQC bank within the context of these tests and not for comparison with other ROC curves obtained for dierent target/background scenarios.

10 ROC Comparison on Speckled Field Scene Probability of Detection LSD/DOA - 8 SWS CMF - 79 Filters CMF Filters CMF Filters Probability of False Alarm Figure 8: ROC curves for SAR tests comparing LSD/DOA and GQC for various numbers of linear lters (LOG scale). The image to background contrast ratio was made quite small in order to produce several well populated ROC curves for these tests. This is required in order to produce such curves in a timely fashion, however the resulting false alarm rates are articially high. For that reason, these curves should only be used to judge the performance of the LSD/DOA algorithm versus that of the GQC bank within the context of these tests and not for comparison with other ROC curves obtained for dierent target/background scenarios.

11 5 REFERENCES [1] Dyer, C.R., and S.B. Ho, \Medial-Axis-Based Shape Smoothing," Proc. Seventh ICPR, pp , July 30, [2] Verbout, S.H., W.W. Irving, A.S. Hanes, \Improving a Template-Based Classier in a SAR Automatic Target Recognition System by Using 3-D Target Information," MIT Lincoln Laboratory Journal, vol. 6, No. 1, pp Spring [3] Ben-Arie, J., and Z.A. Meiri, \3-D Object Recognition by Optimal Matching Search of Multinary Relations Graphs," Computer Vision, Graphics, Image Processing, vol. 37, pp , March [4] Reeves, A.P., R.J. Prokop, S.E. Andrews, and F.P. Kuhl, \Three-Dimensional Shape Analysis Using Moments and Fourier Descriptors," IEEE Trans. on PAMI, vol. PAMI-10, pp , [5] VanderLugt, A.B., \Signal Detection by Complex Matched Spatial Filtering," IEEE Trans. Inf. Theory, vol. IT-10, p. 139, [6] Chang, W.T., D. Casasent, and D. Fetterly, \SDF Control of Correlation Plane Structure for 3-D Object Representation and Recognition," SPIE Vol. 507, Processing and Display of Three-Dimensional Data II, [7] Mahalanobis, A., B.V. Kumar, and D. Casasent, \Minimum Average Correlation Energy Filters," Applied Optics, vol. 26, no. 17, pp , [8] Novak, L.M., G.J. Owirka, C.M. Netishen, \Radar Target Identication using Spatial Matched Filters," Pattern Recognition, Vol. 27, No. 4, pp , [9] Cyganski, D., R.F. Vaz, and C.R. Wright, \Model-Based 3-D Object Pose Estimation from linear image decomposition and direction of arrival techniques," Proc. SPIE Proceedings, Conference on Model-Based Vision, vol. 1827, November 1992, Boston. Viewable on the WWW,

On-Line Process F(x, y) Direct Linear Signal Projection

On-Line Process F(x, y) Direct Linear Signal Projection Multi-Target Discrimination with Linear Signal Decomposition/Direction of Arrival Based ATR Barry K. Hill, David Cyganski, and Richard F. Vaz Machine Vision Laboratory Electrical and Computer Engineering