non-gaussian cfar techniques for target detection ... - Semantic Scholar
NON-GAUSSIAN CFAR TECHNIQUES FOR TARGET DETECTION IN HIGH RESOLUTION SAR IMAGES Shyam Kuttikkad and Rama Chellappa
Department of Electrical Engineering and Center for Automation Research University of Maryland at College Park College Park, Maryland 20742 USA
ABSTRACT
Constant False Alarm Rate (CFAR) processing of Synthetic Aperture Radar (SAR) images facilitates target detection in spatially varying background clutter. The traditional Rayleigh distribution does not appear to be a good choice for modeling the natural terrain backscatter in high resolution SAR. We use the Weibull and K distributions to model clutter since they seem to t observed data better and also include the Rayleigh distribution as a special case. The Cell Averaged CFAR technique works well in situations where a single, small target is present in locally homogeneous clutter. The Order Statistic CFAR is more useful for larger targets and in multiple target situations. Comparisons are made between the various CFAR techniques by applying them to real, high-resolution SAR images, obtained from the MIT Lincoln Laboratory.
1. INTRODUCTION Target detection in SAR images can be done by comparing the received backscatter magnitude to a xed threshold, if only thermal noise is present. But if the target is embedded in spatially varying background clutter, as is common in SAR images of terrain, an adaptive threshold has to be used to keep the probability of false alarm, a constant. Thus a CFAR detector is useful for making target-in-clutter decisions in high resolution SAR images of natural regions. The adaptive threshold, with which the output of each pixel is compared, is generated using a weighted combination of the outputs obtained from a moving window of reference cells from the background. The background clutter is assumed to have an underlying statistical distribution. The traditional circular Gaussian assumption for complex backscatter, which results in a Rayleigh magnitude distribution, is This work is supported by the Air Force Oce of Scienti c Research under the contract F49620-92-J0130.
not a good t for data obtained at low grazing angles and from high resolution radars [1]. Distributions with larger tails and larger standard deviation-tomean ratio, than Rayleigh, seem to match the empirical distribution better. The Lognormal, Weibull and K-distributions satisfy these conditions, but the Lognormal distribution tends to overestimate the range of variation obtained from real clutter. Thus, the Weibull and K-distributions are of interest for clutter modeling, because they lie between the two extremes of Rayleigh and Lognormal, and they include the Rayleigh distribution as a special case. Several types of CFAR techniques have been suggested in the literature [2]-[5], based on the method of obtaining the adaptive threshold from the reference window. The Cell Averaged CFAR (CACFAR) is the simplest of these, where all cells in the reference window are used to compute the clutter parameters, and hence, the adaptive threshold. The CACFAR detector does not perform very well when parts of the target overlap with the reference window, interfering with the computation of the threshold. The Order Statistic CFAR (OSCFAR) technique works better in such situations. An ordered statistic of the reference cells is used to compute the threshold in an OSCFAR detector. Two-parameter CFAR detectors for multi-polarization data are considered in [6] and [7]. CFAR techniques can be used as a rst step in a feature extraction scheme for SAR imagery. In this paper, we demonstrate the application of CACFAR and OSCFAR techniques to detect targets in high resolution SAR terrain images. Other techniques like, GreatestOf CFAR and Censored CFAR, do not o er any significant advantage over the OSCFAR technique, for the images we have experimented with, and hence are not discussed in this paper. The Weibull and K distributions are chosen as models for the clutter distribution. Comparisons are made between the di erent choices of clutter distribution, CFAR techniques, and reference windows used to obtain the adaptive threshold.
2. ADAPTIVE THRESHOLD COMPUTATION 2.1. Weibull Clutter
The Weibull probability density function (PDF) has been suggested as a model for sea and ground clutter at low grazing angles and at high resolutions. The output of the magnitude envelope detector is assumed to have the Weibull PDF: x C C x C ?1 0 (1) pX (x) = 0;B ( B ) exp ?( B ) ; xx < 0 where B is the scale parameter and C is the shape parameter. With C = 2, this reduces to the Rayleigh model. In general, both B and C are not known a priori and have to be estimated from the observed data. Several techniques exist for the simultaneous estimation of these two parameters [8]-[10]. Since the non-iterative techniques of estimating the Weibull parameters [8, 10] are based on ordered statistics of the reference cells, we use the iterative maximum likelihood method of [9] for our CACFAR detector. The following set of equations are used to estimate B and C (the estimates are denoted as B^ and C^ respectively): PM C^ mP=1 xm ln xm M xC^ m=1 m
? M1
M X
lnxm = 1^ C m=1
(2)
!1=C^
M X B^ = M1 xCm^ (3) m=1 where M is the number of reference cells considered for estimation and xm is the output of the mth reference cell. The resulting adaptive threshold, Tca , and the probability of false alarm, PFA , are related by [11] "
#
C^ T ca (4) PFA = exp ? ^ B The OSCFAR threshold is derived from two ranked background samples, xi and xj , such that x1 xi xj xM . This technique was considered in [12] and modi ed slightly in [13]. It has been shown in [10], that the optimum choice of i and j are given by pi = 0:1673 and pj = 0:9737, where pk = k=(M + 1). The adaptive OSCFAR threshold, Tos , is then given by
Tos = x1i ? x j
where
(5)
i = ln[? ln(1 ? p )]ln ? ln[? ln(1 ? p )] j
i
(6)
PFA M for CACFAR for OSCFAR 0.01 3.358 2.528 0.001 4.697 3.546 0.0001 6.012 4.552 0.00001 7.318 5.556 0.000001 8.604 6.564 Table 1: K-Distribution Threshold Multiplier for = 3=2 and M = 120 i is related to PFA by [5] M!( i + M ? i)! PFA = (M ? i)!( i + M)!
2.2. K-Distributed Clutter
(7)
A Rayleigh voltage uctuation, whose variance changes in space and time according to the gamma distribution, leads to the K-distribution model for clutter. The Kdistributed clutter is given by the PDF 4C (Cx) K (2Cx) pX (x) = ?() (8) ?1 where K (y) is the modi ed Bessel function with degrees of freedom, is the shape parameter which e ects the spikiness of the clutter, ?() is the Gammafunction of , and C is the power parameter, such that the mean clutter power is P0 = =C 2. There is no robust method available for estimating the parameter , although empirical relations have been derived for sea clutter [14]. Lower values of result in more spikiness and = 1 corresponds to the Rayleigh density. Analysis can be simpli ed by assuming that = m + 1=2, where m is a nonnegative integer. In general, given the PDF, pW (w), of the test statistic W, the probability of false alarm is given by [15] Z 1 2C PFA = ?() (Tw) K (2CTw) pW (w)dw (9) 0 For the CACFAR detector, the test statistic is the sum of M correlated reference cell outputs, each of which is a K-distributed random variable. Closed form expressions (for speci c values of ) for pW (w) are given in [15]. The resulting PDF for = 3=2 is reproduced here as an example 2M 2M ?1e?2Cw (10) pW (w) = (2C) ?(2M) w The test statistic for the OSCFAR detector is the kth ordered reference cell output, whose PDF is then given
(a) Bridge (HH Polarization)
(b) Powerline Tower (HV Polarization)
Figure 1: Original SAR Images by
2(Cw) M ?k+1 K M ?k (2Cw) ?() k?1 (11) K (2Cw) K ?1(2Cw) 1 ? 2(Cw) ?() In general, these equations have to be solved numerically to obtain the appropriate threshold. Table 1 shows the test statistic multiplier, , for di erent values of PFA , with = 3=2 and M = 120. pW (w) = 2Ck Mk
3. EXPERIMENTAL RESULTS We work with a single polarization channel of the high resolution (1ft x 1ft), fully polarimetric, SAR data obtained from Lincoln Laboratory (We thank Dr. Les Novak for providing the data). The particular polarization channel which yields the best detection results depends on various factors like the geometric and material properties of the target, target orientation with respect to the radar etc. For detecting point targets using CFAR, a single polarization channel seems to suf ce. Both a solid reference window, around the cell under test, and a hollow window, suitably separated from the test cell [6], were used to estimate the clutter parameters. The results of applying the various CFAR techniques to two test images (Figure 1) are shown in Figures 2-5. Figure 1 (a) is an image of a road bridge, where the metal guard rail on the bridge and other strong re ectors serve as targets. Figure 1 (b) shows a couple of powerline towers amidst vegetation. In both cases, a hollow window, with M = 120, was used to compute the adaptive threshold. In general, the OSCFAR technique resolves nearby targets better than the CACFAR technique, because, although the mean of the reference cell voltages is a ected by the presence of additional targets, the ordered statistic is not. But the
two-sample Weibull OSCFAR did not perform as well as the maximum likelihood method based CACFAR, although the latter is more computationally intensive. In all cases, threshold selection based on the hollow reference window was better at detecting targets than the one based on the solid window, with the same number of cells. This was true because in the latter case, parts of the target overlap with the reference window, interfering with the threshold computation. For comparison purposes, the OSCFAR outputs of the HV and VV polarizations of the Bridge image are given in Figures 6 and 7 respectively, for K-distributed clutter assumption. Figure 8 shows the result when a solid reference window, as opposed to a hollow stencil, is used for clutter parameter estimation. Figures 6-8 are to be compared with the result shown in Figure 5 (a). No conclusions can be made regarding the superiority of Weibull clutter model over K distributed clutter model or vice versa. The fact that the two distributions are very similar for clutter which is not very spiky, could account for this phenomenon. More work needs to be done to come up with a good technique for estimating the shape parameter for K-distributed ground clutter.
4. REFERENCES [1] M. I. Skolnik, Introduction to Radar Systems, 2nd ed., McGraw-Hill, New York, 1980. [2] H. M. Finn and R. S. Johnson, \Adaptive detection mode with threshold control as a function of spatially sampled clutter-level estimates," RCA Review, vol. 29, pp. 414-464, Sept. 1968. [3] V. G. Hansen, \Constant false alarm rate processing in search radars," Proc. of IEE 1973 Intl. Radar Conf., London, pp. 325-332, 1973. [4] M. Weiss, \Analysis of some modi ed cellaveraging CFAR processors in multiple-target sit-
[5] [6]
[7]
[8] [9]
[10] [11]
[12]
[13]
[14]
[15]
uations," IEEE Trans. on AES, vol. 18, pp. 102114, Jan. 1982. H. Rohling, \Radar CFAR thresholding in clutter and multiple target situations," IEEE Trans. on AES, vol. 19, pp. 608-621, July 1983. L. M. Novak, M. C. Burl, W. W. Irving and G. J. Owirka, \Optimal polarimetric processing for enhanced target detection," IEEE National Telesystems Conf. Proceedings, pp. 69-75, 1991. L. M. Novak and S. R. Hesse, \On the performance of order-statistics CFAR detectors," 25th Asilomar Conf. on Sig., Sys. and Computers, pp. 835840, 1991. M. V. Menon, \Estimation of the shape and scale parameters of the Weibull distribution," Technometrics, vol. 5, pp. 175-182, May 1963. A. C. Cohen, \Maximum likelihood estimation in the Weibull distribution based on complete and censored samples," Technometrics, vol. 7, pp. 579588, Nov.1965. S. D. Dubey, \Some percentile estimators for Weibull parameters," Technometrics, vol. 9, pp. 119-129, Feb. 1967. R. Ravid and N. Levanon, \Maximum likelihood CFAR for Weibull background," IEE Proc.-F, Commun. Radar and Sig. Proc., vol. 139, pp. 256264, June 1992. P. Weber and S. Haykin, \Ordered statistics CFAR for two-parameter distributions with variable skewness," IEEE Trans. on AES, vol. 21, pp. 819-821, 1983. N. Levanon and M. Shor, \Order statistic CFAR for Weibull background," IEE Proc.-F, Commun. Radar and Sig. Proc., vol. 137, pp. 157-162, June 1990. K. D. Ward, C. J. Baker and S. Watts, \Maritime surveillance radar, Part 1: Radar scattering from the ocean surface," IEE Proc.-F, Commun. Radar and Sig. Proc., vol. 137, pp. 51-62, April 1990. B. C. Armstrong and H. D. Griths, \CFAR detection of uctuating targets in spatially correlated K-distributed clutter," IEE Proc.-F, Commun. Radar and Sig. Proc., vol. 138, pp. 139-152, April 1990.
Figure 6: HV Polarization; K-distributed Clutter with = 1:5; OSCFAR; PFA = 10?3
Figure 7: VV Polarization; K-distributed Clutter with = 1:5; OSCFAR; PFA = 10?3
Figure 8: Solid Reference Window; K-distributed Clutter with = 1:5; OSCFAR; PFA = 10?3
(a)
(b) Figure 2: Weibull Clutter; CACFAR; PFA = 10?3
(a)
(b) Figure 3: Weibull Clutter; OSCFAR; PFA = 10?3
(a)
(b)
Figure 4: K-Distributed Clutter with = 1:5; CACFAR; PFA = 10?3
(a)
(b)
Figure 5: K-Distributed Clutter with = 1:5; OSCFAR; PFA = 10?3
Department of Electrical Engineering and Center for Automation Research University of Maryland at College Park College Park, Maryland 20742 USA
ABSTRACT
Constant False Alarm Rate (CFAR) processing of Synthetic Aperture Radar (SAR) images facilitates target detection in spatially varying background clutter. The traditional Rayleigh distribution does not appear to be a good choice for modeling the natural terrain backscatter in high resolution SAR. We use the Weibull and K distributions to model clutter since they seem to t observed data better and also include the Rayleigh distribution as a special case. The Cell Averaged CFAR technique works well in situations where a single, small target is present in locally homogeneous clutter. The Order Statistic CFAR is more useful for larger targets and in multiple target situations. Comparisons are made between the various CFAR techniques by applying them to real, high-resolution SAR images, obtained from the MIT Lincoln Laboratory.
1. INTRODUCTION Target detection in SAR images can be done by comparing the received backscatter magnitude to a xed threshold, if only thermal noise is present. But if the target is embedded in spatially varying background clutter, as is common in SAR images of terrain, an adaptive threshold has to be used to keep the probability of false alarm, a constant. Thus a CFAR detector is useful for making target-in-clutter decisions in high resolution SAR images of natural regions. The adaptive threshold, with which the output of each pixel is compared, is generated using a weighted combination of the outputs obtained from a moving window of reference cells from the background. The background clutter is assumed to have an underlying statistical distribution. The traditional circular Gaussian assumption for complex backscatter, which results in a Rayleigh magnitude distribution, is This work is supported by the Air Force Oce of Scienti c Research under the contract F49620-92-J0130.
not a good t for data obtained at low grazing angles and from high resolution radars [1]. Distributions with larger tails and larger standard deviation-tomean ratio, than Rayleigh, seem to match the empirical distribution better. The Lognormal, Weibull and K-distributions satisfy these conditions, but the Lognormal distribution tends to overestimate the range of variation obtained from real clutter. Thus, the Weibull and K-distributions are of interest for clutter modeling, because they lie between the two extremes of Rayleigh and Lognormal, and they include the Rayleigh distribution as a special case. Several types of CFAR techniques have been suggested in the literature [2]-[5], based on the method of obtaining the adaptive threshold from the reference window. The Cell Averaged CFAR (CACFAR) is the simplest of these, where all cells in the reference window are used to compute the clutter parameters, and hence, the adaptive threshold. The CACFAR detector does not perform very well when parts of the target overlap with the reference window, interfering with the computation of the threshold. The Order Statistic CFAR (OSCFAR) technique works better in such situations. An ordered statistic of the reference cells is used to compute the threshold in an OSCFAR detector. Two-parameter CFAR detectors for multi-polarization data are considered in [6] and [7]. CFAR techniques can be used as a rst step in a feature extraction scheme for SAR imagery. In this paper, we demonstrate the application of CACFAR and OSCFAR techniques to detect targets in high resolution SAR terrain images. Other techniques like, GreatestOf CFAR and Censored CFAR, do not o er any significant advantage over the OSCFAR technique, for the images we have experimented with, and hence are not discussed in this paper. The Weibull and K distributions are chosen as models for the clutter distribution. Comparisons are made between the di erent choices of clutter distribution, CFAR techniques, and reference windows used to obtain the adaptive threshold.
2. ADAPTIVE THRESHOLD COMPUTATION 2.1. Weibull Clutter
The Weibull probability density function (PDF) has been suggested as a model for sea and ground clutter at low grazing angles and at high resolutions. The output of the magnitude envelope detector is assumed to have the Weibull PDF: x C C x C ?1 0 (1) pX (x) = 0;B ( B ) exp ?( B ) ; xx < 0 where B is the scale parameter and C is the shape parameter. With C = 2, this reduces to the Rayleigh model. In general, both B and C are not known a priori and have to be estimated from the observed data. Several techniques exist for the simultaneous estimation of these two parameters [8]-[10]. Since the non-iterative techniques of estimating the Weibull parameters [8, 10] are based on ordered statistics of the reference cells, we use the iterative maximum likelihood method of [9] for our CACFAR detector. The following set of equations are used to estimate B and C (the estimates are denoted as B^ and C^ respectively): PM C^ mP=1 xm ln xm M xC^ m=1 m
? M1
M X
lnxm = 1^ C m=1
(2)
!1=C^
M X B^ = M1 xCm^ (3) m=1 where M is the number of reference cells considered for estimation and xm is the output of the mth reference cell. The resulting adaptive threshold, Tca , and the probability of false alarm, PFA , are related by [11] "
#
C^ T ca (4) PFA = exp ? ^ B The OSCFAR threshold is derived from two ranked background samples, xi and xj , such that x1 xi xj xM . This technique was considered in [12] and modi ed slightly in [13]. It has been shown in [10], that the optimum choice of i and j are given by pi = 0:1673 and pj = 0:9737, where pk = k=(M + 1). The adaptive OSCFAR threshold, Tos , is then given by
Tos = x1i ? x j
where
(5)
i = ln[? ln(1 ? p )]ln ? ln[? ln(1 ? p )] j
i
(6)
PFA M for CACFAR for OSCFAR 0.01 3.358 2.528 0.001 4.697 3.546 0.0001 6.012 4.552 0.00001 7.318 5.556 0.000001 8.604 6.564 Table 1: K-Distribution Threshold Multiplier for = 3=2 and M = 120 i is related to PFA by [5] M!( i + M ? i)! PFA = (M ? i)!( i + M)!
2.2. K-Distributed Clutter
(7)
A Rayleigh voltage uctuation, whose variance changes in space and time according to the gamma distribution, leads to the K-distribution model for clutter. The Kdistributed clutter is given by the PDF 4C (Cx) K (2Cx) pX (x) = ?() (8) ?1 where K (y) is the modi ed Bessel function with degrees of freedom, is the shape parameter which e ects the spikiness of the clutter, ?() is the Gammafunction of , and C is the power parameter, such that the mean clutter power is P0 = =C 2. There is no robust method available for estimating the parameter , although empirical relations have been derived for sea clutter [14]. Lower values of result in more spikiness and = 1 corresponds to the Rayleigh density. Analysis can be simpli ed by assuming that = m + 1=2, where m is a nonnegative integer. In general, given the PDF, pW (w), of the test statistic W, the probability of false alarm is given by [15] Z 1 2C PFA = ?() (Tw) K (2CTw) pW (w)dw (9) 0 For the CACFAR detector, the test statistic is the sum of M correlated reference cell outputs, each of which is a K-distributed random variable. Closed form expressions (for speci c values of ) for pW (w) are given in [15]. The resulting PDF for = 3=2 is reproduced here as an example 2M 2M ?1e?2Cw (10) pW (w) = (2C) ?(2M) w The test statistic for the OSCFAR detector is the kth ordered reference cell output, whose PDF is then given
(a) Bridge (HH Polarization)
(b) Powerline Tower (HV Polarization)
Figure 1: Original SAR Images by
2(Cw) M ?k+1 K M ?k (2Cw) ?() k?1 (11) K (2Cw) K ?1(2Cw) 1 ? 2(Cw) ?() In general, these equations have to be solved numerically to obtain the appropriate threshold. Table 1 shows the test statistic multiplier, , for di erent values of PFA , with = 3=2 and M = 120. pW (w) = 2Ck Mk
3. EXPERIMENTAL RESULTS We work with a single polarization channel of the high resolution (1ft x 1ft), fully polarimetric, SAR data obtained from Lincoln Laboratory (We thank Dr. Les Novak for providing the data). The particular polarization channel which yields the best detection results depends on various factors like the geometric and material properties of the target, target orientation with respect to the radar etc. For detecting point targets using CFAR, a single polarization channel seems to suf ce. Both a solid reference window, around the cell under test, and a hollow window, suitably separated from the test cell [6], were used to estimate the clutter parameters. The results of applying the various CFAR techniques to two test images (Figure 1) are shown in Figures 2-5. Figure 1 (a) is an image of a road bridge, where the metal guard rail on the bridge and other strong re ectors serve as targets. Figure 1 (b) shows a couple of powerline towers amidst vegetation. In both cases, a hollow window, with M = 120, was used to compute the adaptive threshold. In general, the OSCFAR technique resolves nearby targets better than the CACFAR technique, because, although the mean of the reference cell voltages is a ected by the presence of additional targets, the ordered statistic is not. But the
two-sample Weibull OSCFAR did not perform as well as the maximum likelihood method based CACFAR, although the latter is more computationally intensive. In all cases, threshold selection based on the hollow reference window was better at detecting targets than the one based on the solid window, with the same number of cells. This was true because in the latter case, parts of the target overlap with the reference window, interfering with the threshold computation. For comparison purposes, the OSCFAR outputs of the HV and VV polarizations of the Bridge image are given in Figures 6 and 7 respectively, for K-distributed clutter assumption. Figure 8 shows the result when a solid reference window, as opposed to a hollow stencil, is used for clutter parameter estimation. Figures 6-8 are to be compared with the result shown in Figure 5 (a). No conclusions can be made regarding the superiority of Weibull clutter model over K distributed clutter model or vice versa. The fact that the two distributions are very similar for clutter which is not very spiky, could account for this phenomenon. More work needs to be done to come up with a good technique for estimating the shape parameter for K-distributed ground clutter.
4. REFERENCES [1] M. I. Skolnik, Introduction to Radar Systems, 2nd ed., McGraw-Hill, New York, 1980. [2] H. M. Finn and R. S. Johnson, \Adaptive detection mode with threshold control as a function of spatially sampled clutter-level estimates," RCA Review, vol. 29, pp. 414-464, Sept. 1968. [3] V. G. Hansen, \Constant false alarm rate processing in search radars," Proc. of IEE 1973 Intl. Radar Conf., London, pp. 325-332, 1973. [4] M. Weiss, \Analysis of some modi ed cellaveraging CFAR processors in multiple-target sit-
[5] [6]
[7]
[8] [9]
[10] [11]
[12]
[13]
[14]
[15]
uations," IEEE Trans. on AES, vol. 18, pp. 102114, Jan. 1982. H. Rohling, \Radar CFAR thresholding in clutter and multiple target situations," IEEE Trans. on AES, vol. 19, pp. 608-621, July 1983. L. M. Novak, M. C. Burl, W. W. Irving and G. J. Owirka, \Optimal polarimetric processing for enhanced target detection," IEEE National Telesystems Conf. Proceedings, pp. 69-75, 1991. L. M. Novak and S. R. Hesse, \On the performance of order-statistics CFAR detectors," 25th Asilomar Conf. on Sig., Sys. and Computers, pp. 835840, 1991. M. V. Menon, \Estimation of the shape and scale parameters of the Weibull distribution," Technometrics, vol. 5, pp. 175-182, May 1963. A. C. Cohen, \Maximum likelihood estimation in the Weibull distribution based on complete and censored samples," Technometrics, vol. 7, pp. 579588, Nov.1965. S. D. Dubey, \Some percentile estimators for Weibull parameters," Technometrics, vol. 9, pp. 119-129, Feb. 1967. R. Ravid and N. Levanon, \Maximum likelihood CFAR for Weibull background," IEE Proc.-F, Commun. Radar and Sig. Proc., vol. 139, pp. 256264, June 1992. P. Weber and S. Haykin, \Ordered statistics CFAR for two-parameter distributions with variable skewness," IEEE Trans. on AES, vol. 21, pp. 819-821, 1983. N. Levanon and M. Shor, \Order statistic CFAR for Weibull background," IEE Proc.-F, Commun. Radar and Sig. Proc., vol. 137, pp. 157-162, June 1990. K. D. Ward, C. J. Baker and S. Watts, \Maritime surveillance radar, Part 1: Radar scattering from the ocean surface," IEE Proc.-F, Commun. Radar and Sig. Proc., vol. 137, pp. 51-62, April 1990. B. C. Armstrong and H. D. Griths, \CFAR detection of uctuating targets in spatially correlated K-distributed clutter," IEE Proc.-F, Commun. Radar and Sig. Proc., vol. 138, pp. 139-152, April 1990.
Figure 6: HV Polarization; K-distributed Clutter with = 1:5; OSCFAR; PFA = 10?3
Figure 7: VV Polarization; K-distributed Clutter with = 1:5; OSCFAR; PFA = 10?3
Figure 8: Solid Reference Window; K-distributed Clutter with = 1:5; OSCFAR; PFA = 10?3
(a)
(b) Figure 2: Weibull Clutter; CACFAR; PFA = 10?3
(a)
(b) Figure 3: Weibull Clutter; OSCFAR; PFA = 10?3
(a)
(b)
Figure 4: K-Distributed Clutter with = 1:5; CACFAR; PFA = 10?3
(a)
(b)
Figure 5: K-Distributed Clutter with = 1:5; OSCFAR; PFA = 10?3
