Detection of Buried Objects using GPR Change Detection in Polarimetric Huynen Spaces

Transcription

1 Detection of Buried Objects using GPR Change Detection in Polarimetric Huynen Spaces Firooz Sadjadi Lockheed Martin Corporation Saint Anthony, Minnesota USA Anders Sullivan Army Research Laboratory Adelphi, Maryland, USA Guillermo Gaunaurd Army Research Laboratory Adelphi, Maryland, USA Abstract Change detection is a useful method for detecting new events in a scene such as the placement of mines, and/or the movement of people, vehicles and structures. The basis of the approach is to examine an area via radar several times. Once, before there were targets planted there, and the other (or others) after. The change detection algorithm will notice if there are any changes after the first view was made. False alarm, that is a critical issue in this approach, can be reduced in a number of ways: exploiting additional information such as phase and polarization, and 2) exploiting critical attributes by computing changes in focused subspaces. In this paper we present a new approach for polarimetric change detection, whereby the target is represented not in terms of the complex scattering elements but in terms of phenomenologically-based Huynen parameters. Each element of the Huynen parameter set conveys useful physical and geometrical attributes about the scatterers thus augmenting the potential for significant false alarm mitigation. Results of the application of this approach on fully polarimetric signatures of simulated buried targets are provided. These results indicate that Huynen parameters are more effective for change detection than the scattering matrix elements in generating higher unambiguous autocorrelation peaks and less prominent cross-correlation peaks. 1. Introduction Change detection (CD) has been shown to be a useful method for detecting new events in a scene such as the placement of mines, and/or the movement of people, vehicles and structures. The basis of the approach is to examine an area via usually radar several times. Once, before there were targets planted there, and the other (or others) after. The change detection algorithm will notice if there are any changes after the first view was made. If there are, one then has to determine the rate of false alarms to insure that the change is due to a real threat. Since it is almost certain that there will be changes noticeable, the key to the approach is to reduce / eliminate the false alarms. To reduce false alarms and improve detection probabilities, the process of change detection in radar that includes both imaging and non-imaging systems, has gone through a number of evolutionary stages: 1) Noncoherent change detection, whereby only the radar cross sections are used in the change estimation; this approach has very limited use. 2) Coherent nonpolarimetric change detection [1], whereby both the phase and amplitude of a single polarization scattering matrix are used for change estimation. This approach is the most common, but suffers from high numbers of false alarms. 3) Polarimetric vector coherent change detection, whereby three complex scattering elements for vertical, horizontal and cross polarizations are used for the change detection. In this paper we present a new approach for polarimetric change detection using ground penetrating radar (GPR) signatures, whereby the target is represented not in terms of three complex scattering elements but in terms of phenomenologically-based Huynen parameters. Each element of the Huynen parameter set conveys useful physical and geometrical attributes about the scatterers thus augmenting the potential for significant false alarm mitigation. Results of the application of this approach on fully polarimetric signatures of simulated buried targets are provided. These results indicate that Huynen parameters are more effective for change detection than the scattering matrix elements in generating higher unambiguous autocorrelation peaks and more non-dominating cross-correlation curves. 2. Stokes and Huynen-fork parameters relationships From a Sinclair matrix S [2], the product S*S has eigenvalues obtained from the eigenvalue equation: S S γ 2 I =0 (1) /08/$ IEEE

2 where I is the identity matrix and the eigenvalues γ i 2 (for i=1, 2) are real since S*S is Hermitian. The eigenvalue equation can be written as: where B and C are γ 4 B γ 2 C =0 (2) B = S xx 2 +2 S xy 2 + S yy 2 (3a) C = S xx S yy 2 + Sxy 4 2SxyRe(S 2 xx S yy ) (3b) in terms of Sinclair matrix elements [2, 3]. The eigenvalues are the roots of (2), which are: γ 1 2 = 1 2 [B + B 2 4C] (4a) γ 2 2 = 1 2 [B B 2 4C] (4b) which correspond to the states of maximum received power. From (3) one of the polarization ratios P is: P = S xxsxy + S xy Syy S xy 2 + S yy 2 γ 2 (5) and for cases in which only the relative phase is important (i.e., when is real) then the polarization ratio for maximum received power and, analogously, from the second eigenvalue one finds: S xx + Syy P 1 = S xy S xy 2 + S yy 2 γ 2 (6a) P 2 = 1 S xy S xy 2 + S xx 2 γ 2 S xx + S yy from which it follows that P 1 = 1 P 2 (6b) and then the minimum backscattered power, in one case, is found from, (7) S yy P 2 +2S xy P + S xx =0, (8) and in the other case, using the same equation, but replacing P by 1/P, the results are: Sxy 2 S xx S yy S xy P 3 = (9a) S yy Sxy 2 S xx S yy + S xy P 4 = (9b) S yy The Huynen polarization fork [4] is a pattern that appears when the standard Stokes parameters G 1,G 2,G 3,G corresponding to the above four polarization ratios, are plotted on the Poincare sphere. If a wave has polarization states represented by spherical coordinates G 1,G 2,G 3, then its amplitude is G. Any monochromatic wave can be represented by a point on the surface of the Poincare sphere. If 2ɛ is the elevation (or latitude) angle and 2τ is the azimuth (or longitude) angle of the point on the sphere, then the Stokes parameters can be expressed as: G G 1 G 2 G 3 = E x 2 + E y 2 G cos2ɛcos2τ G cos2ɛsin2τ G sin2ɛ (10) from which it follows that the square of the amplitude is: G 2 = G G G 3 3 (11) The Stokes parameters corresponding to same polarization state P are given by: G 1 1 P 2 = G 1+ P 2 G 2 = 2ReP G 1+ P 2 G 3 = 2ImP G 1+ P 2 (12a) (12b) (12c) where P is any one of the four ratios P 1,P 2,P 3,P 4. These relations follow from the identities: G G 1 E y = (13a) 2 G + G 1 E x = (13b) 2 G 3 = 2 E x 2 ImP (13c) G 2 = 2 E x 2 ReP (13d) Combining (10 and (13) yields, G 2 = tan2τ G 1 G 3 = sin2ɛ (14) G where the Stokes parameter ratios are found from (12). The ratio of the two eigenvalues in (4) is: γ 1 γ 2 = B B 2 4C B + B 2 4C = γ 2 2 tan 2 β (15) C which defines the polarizability angle β. This is half the angle made by the tines of the Huynen fork. Polarizability is the target characteristic causing the target to scatter an unpolarized incident wave as one with a higher degree of polarization. Clearly β is related to the eigenvalue ratio yielding the maximum received power.

3 3. Numerical results and interpretation For any combination of Stokes parameters and any of the four polarization states considered, one can generate graphs of their frequency dependence in the range 0 f 6 GHz. This is only possible because all the elements of the S-matrix can be numerically evaluated by the method of moment(mom) [5, 6, 7, 8], and the computer code that was implemented from it. This was analyzed for the case of either one or two buried cylinders. The frequency range for the generated signatures were from 300 MHz to 6 GHz. The targets consisted of cylinders of diameters 20 cm and heights of 15 cm. The targets were buried 10 cm underground. The soil had a relative permitivity of 4 and a conductivity of 0.01 S/m. The cylinders were placed such that their axis of rotation were perpendicular to the air/ground interface. The angle of incidence for the radar was 45 degrees with respect to the air-ground surface normal. The cylinders were considered to be perfect conductors placed in a lossy soil. Two scenarios were considered: 1) The scene consisted of a single cylinder that is viewed at time t 1 (first pass), and 2) the scene consisted of two identical cylinders placed 10 cm apart observed at time t 2 (second pass). For each case the complete S matrix was obtained and used to generate plots of Huynen-fork parameters as functions of frequency Polarimetric change detection in Huynen-space Change detection has been used extensively in the past several years for detecting small changes that can occur in a scene by comparing the geometrically-registered signatures of that scene at different time-intervals. In a typical change detection scenario an aircraft equipped with a radar is flown over a scene on a regular flight path and then the scene signatures at different time intervals are registered and then correlated, and normalized to detect regions where a change in the radar signature has taken place. With coherent radar in which phase and amplitude of the radar signatures are used, correlation is performed in complex spaces, very minute changes can be detected that can be an indication of random or planned activities. In the work being presented here we have extended this to polarimetric Huynen-space. In this space, as described in the previous sections, Huynen-fork signatures are used to represent the same scene signatures at different time intervals. Thus, correlation is performed in the Huynen fork space. Among the several available Huynen-fork parameters, we specifically concentrate on τ,ɛ, and β. In this study we find an answer to the question that if in a scene, a mine-like object is buried, and then at a later stage a second mine-like object is added to it, then the change detection technique can help to better detect this new object Change detection in one-dimensional data In applications where information resides at a pixel rather than at an area or array of pixels, the one dimensional change detection can play a role similar to that of the 2-D signals. Examples include GPR and hyperspectral data that are somewhat similar to each other in that at the pixel or point of study we have access to a set of data points corresponding to physical characteristics of the object at the location (pixel) at different frequencies or depths (ranges). In these cases the problem being considered is exploring the quality of the correlation between the two sets under consideration. In this paper we look at a number of quality metrics applied on the same data sets considered in both Huynen parameter-space and scattering matrix-space. By a Huynen parameter-space we imply attributes derived from Huynen parameters such as ɛ, τ, and β Quality metrics for one-dimensional change detection Assessment of correlation performance is important in the selection of attributes and domains used for computing correlation functions [9, 10]. Two metrics for assessing the quality of an autocorrelation are defined and used: 1) The ratio of the height of the highest peak (main-lobe height) to the width of this main-lobe, described as the distance between abscissas of the zero crossings of the main-lobe: M 1 highest peak height highest peak width, (16) and 2) the ratio of the height of the main-lobe to the height of the highest side-lobe: M 2 highest peak height highest side-lobe peak height. (17) These two metrics measure the desired quality of the main lobe to be a thumb-tack-like peak as high as possible, and have as small a width as possible on one hand and have side lobes that have as small height as possible compared to the height of the main lobe. Table 1 shows the results of computing these two metrics for the polarimetric GPR data used in our study. As can be seen τ 1,τ 3, and τ 4 when used as way of representing GPR signatures of buried targets generate the best autocorrelation peaks. They have more than up to 10 times higher height-to-width and have more than twice main to side-lobe height ratios as compared to the results obtainable with the complex scattering parameters S vv,s hh, and S hv. It can be seen that other Huynen fork parameters also generate higher M 1 quality metric values than those of the scattering matrix parameters. The values for main to side-lobe height ratios (M 2 ) for other Huynenfork parameters are also generally higher than those of the scattering matrix parameters with the exceptions of ɛ 3, and

4 ɛ 4 that have almost similar values with those of scattering matrix elements. The above results can also be seen visually in Figures 1, 2, and 3 that show the normalized autocorrelations for Huynen parameters τ 1,τ 2,ɛ 1,ɛ 2, and scattering matrix parameters S vv,s hh for the one-cylinder target case. Table 1. Quality metric values for autocorrelation (one-cylinder target case) for Huynen-fork parameters and scattering matrix elements (parameters)-m 1 is in 10 4 units parameters M 1 M 2 ɛ ɛ ɛ ɛ τ τ τ τ β a S vv S hh S hv a no secondary peaks Table 2. Quality metric values for cross-correlation results for Huynen-fork parameters and scattering matrix parameters (elements)-m 1 is in 10 4 units parameters M 1 M 2 maximum peak height ɛ ɛ ɛ ɛ τ τ τ τ β b S vv S hh S hv b no secondary peaks These results indicate that using Huynen-fork parameters as a means of representing polarimetric GPR data can help in reducing ambiguities in detecting true changes by generating better autocorrelation signatures. This will lead to potentially lower false alarms (false changes detected). Figure 1. Autocorrelation plots of τ 1 and τ 2 as functions of frequency for one-cylinder target 3.4. Cross correlation results Table 2 shows the results of computing the above two quality metrics when signatures of buried one and two cylinders are cross-correlated. It is desirable that both metrics show smaller values as compared with their corresponding autocorrelation cases, indicative of changes from oneto two-cylinder targets. As can be seen from this Table the largest drop in values for highest peak heights to highest peak widths are associated with all Huynen parameters as compared to those of the scattering matrix elements that remain almost unchanged. For the ratios of highest peak height to 2nd highest peaks, the Huynen parameters have an average value of 1.39 compared with an average value of 4.28 from the corresponding value for autocorrelations.

5 Figure 2. Autocorrelation plots of ɛ 1 and ɛ 2 as functions of frequency for one-cylinder target Figure 3. Autocorrelation plots of S vv and S hh as functions of frequency for one-cylinder target Whereas for the scattering matrix elements, the average value for this metric is 1.42 for cross-correlation and 2.23 for autocorrelation functions. This shows that Huynen parameters decrease twice as much as compared with those from the scattering matrix elements. The right column in Table 2 shows the values of the highest peaks. Since all auto and cross correlations are normalized, the maximum allowable value for each entry is 1. As can be seen for the case of scattering matrix values the highest peaks are around 0.5, whereas for τ 1 to τ 4, they are around These results are also observed visually in Figure 4 that compares the crosscorrelation between one and two cylinder target signatures using the Huynen parameter τ 1 and the scattering matrix parameter S vv. 4. Summary and conclusions In this paper we presented a new method for change detection in terms of phenomenologically-based Huynen parameters. Each element of the Huynen parameter set conveys useful physical and geometrical attributes about the scatterers thus augmenting the potential for significant false alarm mitigation. Results of the application of this approach on fully polarimetric signatures of simulated buried targets are provided. These results indicate that Huynen parameters are more suitable for change detection than the scattering matrix elements in generating higher unambiguous autocorrelation peaks and more cross-correlation curves of lowheight and lower quality peaks (peaks with lower height to width ratios and lower main-peak-height to side-lobe-height

6 [4] J. R. Huynen, Phenomenological Theory of Radar Targets, PhD Dissertation, Technical University, Delft, the Netherlands, (1970). Also, an article of the same title in: Electromagnetic Scattering, P.L.E. Uslenghi, Editor, Ch. 11, Academic Press, N.Y. pp , [5] R. F. Harrington, Field Computation by Moment Methods, Macmillan Co., NY (1968). [6] N. Geng, and L. Carin, Wideband electromagnetic scattering from a dielectric body of revolution buried in a layered lossy, dispersive medium, IEEE Transactions on Antennas and Propagation, AP-47, pp , (1999). [7] S. Vitebskiy, K. Sturgess and L. Carin, Short-pulse plane wave scattering from buried perfectly conducting bodies of revolution, IEEE Transactions on Antennas and Propagation, AP-44, pp , (1996). [8] A. Sullivan, J. Sichina, and L. Nguyen, Identification of mine and UXO target features using computational electromagnetics, Proceedings of SPIE, Detection and Remediation Technologies for Mines and Mine-like Targets VI, Vol. 4394, pp , April [9] P. D. Gianino, c. L. Woods, and j. L. Horner, Analysis of spatial light modulator contrast ratios and optical correlation, Applied Optics, vol. 34, no. 29, pp , October Figure 4. Cross-correlation plots of S vv and τ 1 as functions of frequency for one and two-cylinder targets [10] F. A. Sadjadi, Performance Evaluations of correlations of digital images using different separability measures, IEEE Transaction on Pattern Analysis and Machine Intelligence, PAMI-4, No. 4, July ratios). References [1] D. G. Corr, Coherent change detection for urban development monitoring, Digest of IEE Colloquium on Radar Interferometry, pp. 6.1 to 6.6, April [2] G. Sinclair, The transmission and reception of elliptically polarized waves, Proceeding of the IRE, 38 (2), , Feb [3] H. Mott, Antenna for Radar and Communications: A polarimetric Approach, J. Wiley and Sons, Inc., NY, (1992).