IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 47, NO. 6, JUNE 2009
1685
An Adaptive and Fast CFAR Algorithm Based on
Automatic Censoring for Target Detection in
High-Resolution SAR Images
Gui Gao, Li Liu, Lingjun Zhao, Gongtao Shi, and Gangyao Kuang
Abstract—An adaptive and fast constant false alarm rate
(CFAR) algorithm based on automatic censoring (AC) is proposed
for target detection in high-resolution synthetic aperture radar
(SAR) images. First, an adaptive global threshold is selected to obtain an index matrix which labels whether each pixel of the image
is a potential target pixel or not. Second, by using the index matrix,
the clutter environment can be determined adaptively to prescreen
the clutter pixels in the sliding window used for detecting. The G0
distribution, which can model multilook SAR images within an
extensive range of degree of homogeneity, is adopted as the statistical model of clutter in this paper. With the introduction of AC,
the proposed algorithm gains good CFAR detection performance
for homogeneous regions, clutter edge, and multitarget situations.
Meanwhile, the corresponding fast algorithm greatly reduces the
computational load. Finally, target clustering is implemented to
obtain more accurate target regions. According to the theoretical
performance analysis and the experiment results of typical real
SAR images, the proposed algorithm is shown to be of good
performance and strong practicability.
Index Terms—Constant false alarm rate (CFAR), synthetic
aperture radar (SAR), target detection.
I. I NTRODUCTION
ITH the increasing volume of image data which are collected from air- and spaceborne synthetic aperture radar
(SAR) sensors, it is becoming increasingly desirable to develop
the techniques for SAR image interpretation. A task which is
of particular importance for SAR image interpretation is to
recognize vehicle targets or groups of targets in background
clutter [1]–[4]. As automatic detection is the first important step
of an automatic target recognition (ATR) system, fast detection
of targets, such as tanks, armored personnel carriers, trucks, and
howitzers, can afford to meet the expanding requirements of
intelligence, surveillance, and reconnaissance.
W
Manuscript received October 28, 2007; revised June 14, 2008. First published December 12, 2008; current version published May 22, 2009. This work
was supported by the National Natural Science Foundation of China under
Projects 60772045 and 40801179.
G. Gao is with the School of Electronics Science and Engineering,
National University of Defense Technology, Changsha 410073, China (e-mail:
dellar@126.com).
L. Liu, L. Zhao, and G. Shi are with the National University of Defense
Technology, Changsha 410073, China (e-mail: feiyunlyi@hotmail.com;
nudtzlj@163.com; shigongtao@si-na.com).
G. Kuang is with the Remote Sensing Information Processing Laboratory, School of Electronic Science and Engineering, National University
of Defense Technology, Changsha 410073, China (e-mail: kgyyeats@vip.
sina.com).
Digital Object Identifier 10.1109/TGRS.2008.2006504
At the fist step of the whole SAR ATR system, target detection has great influence on the successive processing [5], [6].
So far, there are many algorithms of target detection for SAR
image available in literature. Among these algorithms, constant
false alarm rate (CFAR) detection, because of its characteristics of simple computation, constant false alarm probability,
adaptive threshold, and fast detection of targets from complex
background, has been extensively studied [7], [8] and even
applied in several SAR ATR systems [9], [10].
The commonly used CFAR detection algorithms include
[6], [7], [11], [21] the cell averaging CFAR (CA-CFAR),
greatest of CFAR (GO-CFAR), smallest of CFAR (SO-CFAR),
order statistic CFAR (OS-CFAR), etc. The CA-CFAR (the twoparameter CFAR algorithm proposed by Lincoln Laboratory
is actually a CA-CFAR technique based on the assumption
of Gaussian background [9], [22]) technique works well in
situations where a single target is present in locally homogeneous clutter. In the presence of heterogeneous environment
(including the clutter edge and multitarget situations), however,
the performance of the CA-CFAR detector degrades rapidly [6].
The OS-CFAR algorithm is designed to overcome the problem
of the loss in detection performance suffered by the CA-CFAR,
when interfering targets are in the background cells and clutter
statistics estimation is corrupted. Therefore, it has significant
advantage when detecting targets in multitarget situations.
However, in homogenous scene, the OS-CFAR algorithm performs worse than the CA-CFAR algorithm [6]. Furthermore,
the optimal statistic is usually obtained by experience instead of
by theory. Moreover, the operation of ordering will inevitably
increase the computational load. The GO-CFAR algorithm
provides good detection performance in clutter edge situations. Compared with the CA-CFAR algorithm, its detection
performance degrades in homogeneous clutter scene because
of the loss of the correlated information among pixels. The
SO-CFAR algorithm can achieve better performance in multitarget situations. In clutter edge situations, however, it produces
more false alarms than the CA-CFAR algorithm does because
the corresponding detection threshold is lower.
The CA-CFAR, OS-CFAR, GO-CFAR, SO-CFAR, etc. are
the basic CFAR detection algorithms [6], [11], [12], [21]. Each
of them has its advantages, disadvantages, and situations of
potential application. No single detector performs well in all
kinds of scenes. If we introduce a methodology to select these
basic CFAR detectors mentioned earlier, adaptively according
to the position of the tested pixel, there will be a significant
0196-2892/$25.00 © 2008 IEEE
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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 47, NO. 6, JUNE 2009
improvement in detection performance. Based on the consideration, current research works on CFAR algorithms have focused
on developing adaptive CFAR algorithms [12].
Many researchers have attempted to design adaptive CFAR
algorithms. The variability index CFAR (VI-CFAR) proposed
by Smith and Varshney [12], [13] is a representative one.
The VI-CFAR processor provides CFAR performance in both
homogeneous and nonhomogeneous situations of clutter. Based
on the VI-CFAR, Huang et al. propose the region classification CFAR (RC-CFAR) [14]. According to [15], the RCCFAR subdivides the reference cell into four parts so that
the number of target samples in each part becomes too less;
thus, it is less credible to judge whether the environment is
nonhomogeneous. Drawing the inspiration from the VI-CFAR,
Farrouki and Barkat present the ordered data variability index
automatic censoring (AC) CFAR detector to realize adaptive
target detection in complex background [16]. Assuming the
Weibull clutter background, Bisceglie proposes a solid-stencil
CFAR detector (the so-called the Bisceglie algorithm [7], [17]),
including comprehensive procedures such as sorting, censoring,
etc. The similar idea of censoring is proposed by Rickard
and Dillard [18]. It is reported [7], [17] that the Bisceglie
algorithm is suitable for the clutter of location-scale type (LStype). LS-type clutter can be regarded as the regularization of
the clutter distribution with two parameters. The experiment
results [7], [17] show that the algorithm performs well in both
homogeneous and nonhomogeneous environments. It is reasonable to say that the Bisceglie algorithm is an excellent CFAR
detection algorithm. Further investigations can be carried out on
the clutter models, automatic selection of the censoring depth,
selection of the sliding-window type, etc. Moreover, an innovative CFAR algorithm called cell averaging statistic Hofele
(CASH) CFAR is introduced in [21]. The advantage of the
CASH CFAR algorithm is that it avoids alternate covering and
aggregation of objects. The required processing power of the
CASH CFAR algorithm is also significantly less than that of the
OS- and cell averaging ordered statistic CFAR algorithms [21].
Furthermore, a notable CFAR algorithm [8] (simply mentioned
as the Salazar algorithm in this paper) has been presented by
Salazar, which chooses the β ′ (beta-prime) distribution [19]
as the statistical model of background clutter in a single-look
SAR image. The main principle of the algorithm is described
as follows: The β ′ distribution is proper to model clutter with
widely varying degrees of homogeneity [19] [including homogeneous clutter, heterogeneous clutter edges, and multitarget
situations (multitarget situations are equivalent to extremely
heterogeneous clutter)]. Therefore, the CA-CFAR technique
based on the β ′ distribution has the ability of keeping CFAR
[8]. The algorithm does have CFAR characteristic for detecting
target in homogeneous clutter, clutter edges, and multitarget
situations. Moreover, because the contrast of the target pixels
is larger than that of the surrounding clutter, the algorithm
also offers higher detection probability in homogeneous clutter
and clutter edges [8]. However, as for multitarget situations,
the deficiency of the algorithm is that the CFAR threshold becomes large when the estimated clutter statistics are corrupted
by interfering targets, which leads to a significantly reduced
detection rate.
In this paper, an adaptive and fast CFAR algorithm based
on AC is proposed for target detection in SAR image. The
proposed algorithm is an improvement of the Salazar algorithm.
Simultaneously, the corresponding fast algorithm is designed.
This paper is organized as follows. In Section II, an introduction
to the principles and the detailed flow of the algorithm are
given. In Section III, the algorithm is described in detail.
In Section IV, the corresponding fast algorithm is designed.
Section V theoretically analyzes the performance of the presented algorithm. In Section VI, we provide the experimental
results and the detection performance comparison of the proposed algorithm and other algorithms using typical real SAR
data. The last section concludes this paper.
II. P RINCIPLES AND D ETAILED F LOW OF THE A LGORITHM
A. Principles of Algorithm
The following suggestions can be derived from the algorithms mentioned earlier.
1) An indexing value is utilized in the VI-CFAR [12]–[14]
to automatically judge the type of surrounding clutter
of the test pixel to choose a proper detector, but the
indexing value should be acquired adaptively instead of
by experience.
2) A new way provided by the Bisceglie algorithm [7], [17]
with additional procedures of prescreening and sorting
can help to avoid the influence of interfering targets on
the detection performance in multitarget situations.
3) The β ′ distribution adopted as the clutter model in the
Salazar algorithm [8] can properly describe the homogeneous clutter, clutter edges, and multitarget situations,
which makes it possible to obtain an integrative design
for target detection algorithm in homogeneous clutter
and clutter edges. Only target detection in multitarget
situations should be considered separately.
4) By computing proper index values and deciding whether
a clutter pixel in the sliding window belongs to an interfering target or not, we can censor all the interfering
pixels. For the rest pixels, we perform the CA-CFAR
algorithm.
The presented detection algorithm is designed based on
the points mentioned earlier. As shown in Fig. 1, the whole
detection process is summarized as follows. First, we select
the square hollow-stencil sliding window, which is suitable for
high-resolution SAR target detection [6]. During the process
of the sliding window scanning the whole image, we consider
the clutter area (clutter region) surrounding the test cell in the
sliding window. It is assumed that there are NC pixels in the
area. Then, the clutter pixels that may belong to the interfering
targets (we suppose there are D pixels censored, namely, the
censoring depth is D ) are censored by the index values that
label the clutter pixels in the sliding window to be a potential
pixel of interfering targets or not. Thus, the pixels that may
not belong to the interfering targets are remained (there are
NC − D pixels remained). The CA-CFAR technique is carried
out on the rest NC − D pixels to yield the estimation of the parameters for the clutter model (the G0 distribution). Moreover,
GAO et al.: CFAR ALGORITHM BASED ON AUTOMATIC CENSORING FOR TARGET DETECTION IN SAR IMAGES
Fig. 1.
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Algorithm of target detection in this paper.
we compute the local detection threshold of the CFAR detector
by setting the false alarm probability. Finally, we succeed in
detecting targets by comparing the value of the test cell with the
threshold. Simultaneously, because a small number of scatters
in SAR images typically dominate the target’s returns and,
after detection, these bright peaks may not be connected as a
region, the pixels in the binary image after CFAR operation
have to be clustered. At last, the potential target region is
obtained.
Some points need to be explained.
1) Although many statistical models of SAR images have
been proposed (see [23]–[27]), the theoretical analysis
and the experiment results of many typically real SAR
scenes in literature [19] have confirmed that the G0
distribution is suitable for modeling multilook clutter
with widely varying degrees of homogeneity. The parameter estimation of the G0 distribution is easy, and
the computational complexity is low. Thus, we select
the G0 distribution to model the clutter region in local
sliding window in this paper. The intensity form of the
G0 distribution, denoted byG0I , is given by [19]
fZI (I) ∼ G0I (α, γ, n) =
nn Γ (n − α) I n−1
,
γ α Γ(n)Γ(−α)(γ + nI)n−α
−α, γ, n, I > 0 (1)
where I is the intensity variable, n is the equivalent
number of looks, α is the shape parameter, and γ is the
scale parameter.
2) Generally speaking, targets have stronger backscattering
than natural clutter; thus, the target pixels have higher
gray value (abnormal point). However, the number of
target pixels is much fewer than that of clutter pixels in
a SAR image. Before performing target detection with
the sliding window, a proper global threshold can be
selected to scan the whole image to determine the target
pixels. Pixels whose intensities are larger than the global
threshold are considered as target pixels, and the index
value is assigned with one; otherwise, the index value is
assigned with zero. Therefore, an index matrix is obtained
to automatically select the censoring depth for target
detection.
Fig. 2. Detailed flow of target detection algorithm in this paper.
B. Algorithm Details
To summarize, as shown in Fig. 2, the algorithm consists of
the following steps.
Step 1) The global threshold of the input SAR image is
computed.
Step 2) The index matrix is generated. For every pixel in the
image, if it has an intensity value greater than the
global threshold, its index value is one. Otherwise,
its index value is zero.
Step 3) The size of target area, protected (guard) area, and
background (clutter) area in the sliding window are
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Step 4)
Step 5)
Step 6)
Step 7)
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 47, NO. 6, JUNE 2009
chosen according to the prior knowledge of the
target size. The false alarm probability is initialized.
The NC clutter pixels in the sliding window of
detection process are censored automatically by the
index matrix. The clutter pixels that may be the
pixels of interfering targets (suppose there are D
pixels censored) are removed. Thus, NC − D pixels
are left. Then, we estimate the parameters of the
clutter model (the G0 distribution) using the left
NC − D pixels and compute the local detection
threshold Tl .
By comparing the intensity of the test cell with the
local threshold, we obtain the binary value of the
pixel.
If it is the end of the whole input image, turn to Step
7). Otherwise, move on to the next pixel and repeat
the process from Step 4).
The detected target pixels in the binary image are
clustered.
C. Computation of the Local Threshold Tl of CFAR Detector
As shown in Fig. 1, in order to avoid the influence of
the strongly backscattering parts of targets on the parameter
estimation of the clutter distribution in the local sliding window,
we select the square hollow-stencil sliding window centered at
the test cell [9], [10]. The guard area exists to ensure that the
clutter pixels are collected at some distance away from the test
cell to prohibit target pixels from leaking into the background
and corrupting clutter statistics estimation. Moreover, the pixels
used to compute the clutter statistics are in a hollow square
centered on the test cell. With this aim, the inner side length
of the square should be larger than the expected size of the
target, and the outer side length of the square is selected to make
enough clutter pixels be included to estimate clutter statistics
accurately.
The intensity distribution of the left NC − D clutter pixels
in the sliding window after censoring is considered by (1). The
left NC − D clutter pixels are used to compute the moment
estimation of the parameters, leading to the following:
α̂ = − 1 −
III. A LGORITHM D ESCRIPTION
A. Computation of the Global Threshold Tg
nE(I 2 )
nE(I 2 ) − (n + 1)E 2 (I)
γ̂ = (−α̂ − 1)E(I).
(6)
(7)
Because the tailed part of the histogram of SAR image represents target pixels, Tg can be determined adaptively according
to the histogram. Let I be the corresponding intensity random
variable; under the condition that the confidence of being a
target pixel is 1 − ϕ, Tg can be obtained from
For a given value of the false alarm probability, denoted by
pfa , the corresponding local threshold Tl for the CFAR detector
is obtained from
P {I > Tg } = 1 − ϕ
Tl
(2)
where P is the probability, and ϕ ∈ [0, 1] is the empirical value
that indicates the proportion of clutter pixels to the whole
image, namely, the confidence of a pixel being a target pixel.
ϕ is large in a large SAR image, approaching one. Furthermore, let F be the cumulative distribution function obtained
from the histogram of the image under detection; (2) can be
rewritten as
1 − F (Tg ) = 1 − ϕ.
(3)
Then, Tg can be conveniently obtained from the histogram of
the whole image by (3).
1 − pfa =
Consider a SAR image of size N × M , and let Ii,j be the
intensity of the pixel localized at the ith row and the jth column;
we define the index value as Vi,j
Vi,j =
1,
0,
Ii,j > Tg
other.
(4)
As for the G0I distribution, the aforementioned integral does
not have an analytic expression. Local threshold Tl can be
obtained by dichotomy (for details, see [20]).
For a single-look image, the G0I distribution degrades to the
′
β distribution [19]
fZI (I) =
−αγ −α
,
(γ + I)1−α
V = {Vi,j |1 ≤ i ≤ N ; 1 ≤ j ≤ M } .
−α, γ, I > 0
(5)
(9)
(6) and (7) lead to the estimation of the parameters
E(I 2 )
E(I 2 ) − 2E 2 (I)
γ̂ = (−α̂ − 1)E(I).
(10)
(11)
Similarly, for a given value of the false alarm probability pfa ,
the corresponding local threshold Tl for the CFAR detector is
obtained from (8)
1/α̂
Tl = γ̂ pfa − 1 .
Thus, the index matrix of the image is given by
(8)
0
α̂ = − 1 −
B. Index Matrix
fZI (I) dI.
(12)
Accordingly, for the test cell with intensity I0 in the sliding
window, the target is detected according to the following
GAO et al.: CFAR ALGORITHM BASED ON AUTOMATIC CENSORING FOR TARGET DETECTION IN SAR IMAGES
Fig. 3.
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Clustering flow of target pixels.
Fig. 4. Illustration of size for the sliding window.
decision rule:
H1
>
T
I0
< l
H0
(13)
where H1 is the hypothesis that the test cell is a target pixel,
and H0 is the hypothesis that the test cell is a clutter pixel. The
local threshold Tl is adaptively obtained pixel by pixel.
D. Target Pixel Clustering
In high-resolution SAR images, a target, also mentioned as
extended object, consists of many resolution cells. Because
the reflection of a target surface may appear as fluctuation,
the corresponding target pixels in the binary image obtained
from CFAR detector are generally not capable of forming a
connected region and may be separated into several parts. Thus,
it is necessary to cluster target pixels in the binary image.
We suppose that the real length and width of the target
of interest are L and W , respectively. Both the range and
cross-range resolution of the image are ∆A. In fact, the area
represented by target pixels is usually smaller than that of the
real target; thus, the number of target pixels or the size of the
target region detected by a CFAR detector has a superior value
Smax , namely,
S ≤ Smax = L × W/(∆A × ∆A).
(14)
Moreover, the distance between pixels i and j within the
same target region, denoted by d(i, j), satisfies the following:
d(i, j) ≤ dmax =
L2 + W 2 /∆A.
(15)
Accordingly, we use the following flow shown in Fig. 3
to cluster target pixels in the binary image obtained after
detection.
As we can see from the last step of the flow in Fig. 3, after
the previous process, there still exist smaller regions or larger
regions in the image, which are obviously unsuitable for the
size of a target region. These undesired regions will certainly
cause false alarms. In order to simplify the successive process,
these regions are eliminated. The steps in detail are as follows:
First, scanning the whole image, for every labeled region after
clustering, we count the bright pixels in the region. Then, we
remove the regions whose areas do not match the target’s area
range ST = {S|Smin ≤ S ≤ Smax }, where Smax is obtained
from (14) and Smin is determined empirically.
IV. F AST A LGORITHM
The same as all the other CFAR algorithms for target detection using sliding window, the target detection algorithm shown
in Fig. 1 also has the limitation of great computational complexity for parameter estimation in the local sliding window, when
the size of window is large, which limits the practicability of
the algorithm [6], [22].
Further investigating on the presented algorithm, we can find
out that computing the global threshold and the index matrix is
much less time consuming than the successive CFAR detecting
process. Hence, we should first consider designing the fast
CFAR algorithm.
Most running time of the CFAR algorithm is cost on parameter estimation in each sliding window [6], [22]. In fact, when
scanning the whole image, the sliding window moves right or
down by one pixel, and the corresponding two sliding windows
centered at two adjacent test cells are largely overlapped. Take
the moving-right case for example. As shown in Fig. 4, consider
two test cells I0left and I0right , which are adjacent to each
other in the horizontal direction. When the center of the sliding
window moves from I0left to I0right , the left h pixels in the
sliding window of I0left move out, and the right h pixels in the
sliding window of I0right move in. Moreover, NC − h pixels
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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 47, NO. 6, JUNE 2009
remain unchanged. The statistical values of these unchanged
pixels have been used for the parameter estimation in the sliding
window of I0left ; thus, reusing them in the sliding window of
I0right will necessarily increase the computational burden. In
Fig. 4, the size of r is selected to ensure enough clutter pixels
for clutter statistics estimation. The guard area with width of
(h − 2r)/2 exists so that the clutter pixels are collected some
distance away from the test cell and target pixels are prohibited
from contaminating clutter statistics estimation. Let the real
length and width of the interested target be L and W (suppose
L > W ), respectively; then (h − 2r)/2 > L/∆A, where both
the range and cross-range resolutions of the image are ∆A.
For the convenience of analyzing the computational complexity of the algorithm and designing the fast algorithm, we
make the following simplifications.
1) Consider the extreme case. Suppose that the proposed
CFAR detector is free of the censoring process, which
means that all the clutter pixels in the sliding window
contribute to parameter estimation. Then, there would
be greater computational complexity compared with the
process with censoring that only parts of the clutter
pixels in the sliding window are used for parameter
estimation. This is the worst case of the proposed algorithm proposed.
2) We take the example of the single-look image to analyze
the computational complexity. Because the parameter
estimations for multilook and single-look images only
differ in the number of looks, the analysis of computational complexity and the design of fast algorithm for
single-look images are also suitable for multilook images.
3) The analysis for the case of the sliding window moving
from top to bottom is just the same as the case of the
sliding window moving from left to right.
A. Design of Fast Algorithm
We can see from (10) and (11) that two variables are needed
for the parameter estimation of the statistical distribution,
namely, the mean of clutter intensity E(I) and the mean of the
square of the clutter intensity E(I 2 ). Let µleft and λleft be the
intensity mean and the mean of the square of the intensity of
the clutter pixels in the sliding window of I0left , respectively.
Correspondingly, let µright and λright be the intensity mean and
the mean of the square of the intensity of the clutter pixels in
the sliding window of I0right , respectively. Then, the relations
between these variables are as follows:
NC · µleft −
µright =
Ii +
h
Ii2 +
NC
i=1
NC
h
Ii′
h
Ii′2
i=1
i=1
NC · λleft −
λright =
h
i=1
(16)
(17)
where NC is the number of all the clutter pixels in the sliding
window,
and h is the height or width of the square sliding
window. hi=1 Ii denotes the sum of the intensity of the clutter
pixels
the left column of the sliding window of I0left .
h in
′
pixels
i=1 Ii represents the sum of the intensity of the clutter
in the right column of the sliding window of I0right . hi=1 Ii2 is
the sum of the square of the intensity of the
clutter pixels in the
left column of the sliding window of I0left . hi=1 Ii′2 is the sum
of the square of the intensity of the clutter pixels in the right
column of the sliding window of I0right .
Hence, except the first test cell in the image, for all the
other horizontally adjacent test pixels, µright and λright can be
obtained by µleft and λleft according to (16) and (17). Thus,
during the process of the sliding window scanning the image,
posterior estimation can be obtained by the previous estimation.
This result is significant for reducing computational load.
B. Analysis of the Computational Complexity for the
Fast Algorithm
As for the first test cell in the image, combining Fig. 4
with (10) and (11), NC − 1 multiplications and one addition
are needed for computing µ, and NC + 1 multiplications and
NC − 1 additions for λ. Thus, two multiplications and two
additions are needed for α̂, while one multiplication and one
addition for γ̂. Hence, for the first test cell, a total of NC + 5
multiplications and 2NC + 1 additions are needed. If the time
of performing a multiplication and that of performing an addition are equal, there are a total of 3NC + 6 operations.
For all the other test cells except the first test cell, the
parameter estimation of the clutter pixels in the sliding window
of a test cell can be obtained by the statistics of its left adjacent
pixel. Suppose the size of the image is N × N , according
to (16) and (17), the computational complexity of parameter
estimation
for
the other N 2 − 1 test cells is shown in Table I
h
( i=1 Ii and hi=1 Ii2 have been obtained when computing
µleft and λleft ).
Assuming that the time of performing one multiplication
and that of performing one addition are equal, the parameter
estimation for the N 2 − 1 test cells needs (N 2 − 1)(3h + 12)
operations in all. Thus, when the operation for the first pixel is
added, the whole image needs altogether (N 2 − 1)(3h + 12) +
3NC + 6 operations.
C. Comparison With Other Algorithm on
Computational Complexity
In order to evaluate the performance of the proposed algorithm quantitatively, we take performance comparisons among
the fast algorithm mentioned earlier, the worst case of the
proposed algorithm without fast computational strategy, and
the widely used two-parameter CFAR detector proposed by
Lincoln Laboratory. The worst case of the proposed algorithm
without fast computational strategy and the Salazar algorithm
has equal computational complexity. The computationalcomplexity analysis of the Salazar algorithm and the twoparameter CFAR algorithm are given in Table II and Table III,
respectively. N 2 (3NC + 6) operations are needed for the parameter estimation of the whole image by the Salazar algorithm
and N 2 (3NC + 2) operations by the two-parameter CFAR
algorithm. Based on the aforementioned comparison, there is no
GAO et al.: CFAR ALGORITHM BASED ON AUTOMATIC CENSORING FOR TARGET DETECTION IN SAR IMAGES
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TABLE I
COMPUTATIONAL COMPLEXITY OF ESTIMATING THE PARAMETERS FOR ALL THE OTHER TEST CELLS EXCEPT FOR THE FIRST TEST PIXEL
TABLE II
COMPUTATIONAL COMPLEXITY ANALYSIS OF THE SALAZAR ALGORITHM (THE WORST CASE WITHOUT USING THE FAST ALGORITHM)
TABLE III
COMPUTATIONAL COMPLEXITY ANALYSIS OF THE TWO-PARAMETER CFAR ALGORITHM
significant difference of the computational complexity between
the Salazar and two-parameter CFAR algorithms. Based on the
simplifications mentioned in Section IV, Table I gives the worst
performance of the proposed fast algorithm. Hence, the ratio of
the computational complexity of the Salazar algorithm to that
of the proposed algorithm is at least
τ1 >
(N 2
N 2 (3NC + 6)
− 1)(3h + 12) + 3NC + 6
N 2 (3NC + 6)
NC
≈ 2
≈
≈ 4r.
N (3h + 12)
h
V. A LGORITHM P ERFORMANCE A NALYSIS
(18)
The ratio of the computational complexity of the twoparameter CFAR algorithm to that of the proposed algorithm
is at least
τ2 >
≈
(N 2
N 2 (3NC + 2)
− 1)(3h + 12) + 3NC + 6
N 2 (3NC + 2)
NC
≈
≈ 4r
N 2 (3h + 12)
h
algorithms are, respectively, at least four times that of the
proposed algorithm. Generally speaking, in order to evaluate
the statistical performance of the clutter accurately, the width of
the reference sliding window is usually much larger; therefore,
both τ1 and τ2 increase greatly. Accordingly, the proposed
fast algorithm does significantly improve the computational
efficiency theoretically.
In this section, theoretical analysis is given to show the
performance of the proposed algorithm. For the sake of simplicity, we consider the single-look clutter environment (the
conclusions for the single-look case can be extended to the
multilook case) and the ideal case that the target intensity
fluctuation follows a negative-exponential distribution [5].
According to (8) and (9), the false alarm probability of the
detector is obtained by
(19)
where r is the width of the reference sliding window shown
in Fig. 4.
Equations (18) and (19) indicate that the computational
complexities of the Salazar and two-parameter CFAR algorithms are, respectively, at least 4r times that of the proposed
algorithm no matter how large is the image size. When the
width of the sliding window is the smallest, i.e., r = 1, τ1
and τ2 have the inferior value of four, namely, the computational complexities of the Salazar and two-parameter CFAR
pfa = 1 −
Tl
−αγ −α
dI =
(γ + I)1−α
Tl
+1
γ
α
.
(20)
0
The detection probability is
pd =
1
σT
∞
Tl
exp −
I
σT
dI = exp −
Tl
σT
(21)
where σT is the mean value of the negative-exponential distribution, and it denotes the power level of the target. Using
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(11) and (12), and let signal-to-clutter ratio (SCR) be SCR =
σT /σB (σB is the average value of clutter intensity), then we
rewrite (21) as
pd = exp
⎫
⎧
⎨ (α + 1) p1/α
⎬
fa − 1
⎩
SCR
.
(22)
⎭
Equation (22) shows that the detection probability of the
algorithm is closely related to the clutter environment (related
by the degree of homogeneity α) surrounding the targets and
the SCR under the condition that the false alarm probability is
given. This coincides with our intuitive understanding. Given
pfa = 10−3 , Fig. 5 shows the performance curves of target
detection with different clutter situations and SCR values. In
Fig. 5(a) and (b), it can be seen that, with a fixed α, the target
detection probability increases as SCR increases. Moreover, the
detection performance with a small α is notably better than that
with a large α. The value of α denotes the clutter environment
that the target detection is in face of. As for homogeneous
clutter and clutter edge, the value of α is relatively smaller,
while for multitarget situations, the value of α is relatively
larger. Therefore, without the proposed censoring procedure,
which is able to eliminate the influence of the interfering
targets, the detection performance in multitarget situations is
determined to degrade significantly in contrast with that in
homogeneous clutter and clutter edge situations.
The aforementioned analysis indicates that, for the singlelook case, the proposed algorithm and the Salazar algorithm
exhibit the same detection performance in homogeneous clutter
and clutter edge situations. As for multitarget situations, considering (22), intuitively, given false alarm probability pfa in
advance, due to the introduction of the censoring procedure,
lots of relatively brighter interfering targets in clutter region are
discarded. This directly leads to the change of two parameters.
One is that the degree of homogeneity for the region increases
due to the decrease of the abnormal target pixels in the clutter
region, namely, the value of α decreases. Another is that the
SCR for the test cell increases compared with that for clutter
region. It is easy to observe from (22) that the increase of
SCR or the decrease of α will cause an increase in detection
probability. Moreover, this is the reason why we introduce
censoring procedure to improve the detection performance in
multitarget situations.
The previous analysis demonstrates that the SCR and the
clutter homogeneity degree surrounding targets also increase
as the censoring depth increases. However, one disadvantage
is that, as the detection probability increases, the false alarm
probability increases, too. This definitely brings some CFAR
loss. For widely varying real scenes, CFAR loss is influenced
by many factors. Hence, it is unable to theoretically deduce
the relation between CFAR loss and the censoring depth. Still,
from the flow of the proposed algorithm, it can be noted that
the proposed algorithm has a great ability to control the false
alarm rate. First, the proposed algorithm performs robustly
over an error range of the censoring depth. The reason is that
the interfering target pixels are brighter and they contribute
to the tail of the histogram of SAR images. Although the
Fig. 5. Detection performance with different SCRs and clutter situations.
(a) Curves of Pd versus SCR. (b) Curves of Pd versus α.
global threshold (decided by the censoring depth) varies over
a wide range corresponding to the tailed part of the histogram,
abnormal target pixels censored have slight changes, and their
influence on the statistical characteristic of most local clutter
regions is limited. Hence, there is a wide range for the proper
selection of the global threshold. When the global threshold
is within this range, the proposed algorithm exhibits good
detection performance. As a result, this allows the selection
of the global threshold and the censoring depth not to be so
exact. Second, clustering procedure further reduces the false
alarm rate.
VI. E XPERIMENTAL R ESULTS AND A NALYSIS
Fig. 6(a) shows an airborne X-band HH polarization singlelook SAR image of some region in Beijing, with a resolution
of 0.5 × 0.5 m and a size of 200 × 500 pixels. Fig. 6(b)
shows a sketch of Fig. 6(a). The left part of the image shown
in Fig. 6(a) is the concrete runway, and the right part is grass.
Small trees are spreading in the grass. At the border of the
grass and the concrete runway, namely, the clutter edge, there
is bush. To the left of the bush, there are some small concrete
blocks which are arranged with equidistance and connected by
iron fence. Fig. 6(c) shows an optical photograph of the clutter
GAO et al.: CFAR ALGORITHM BASED ON AUTOMATIC CENSORING FOR TARGET DETECTION IN SAR IMAGES
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Fig. 6. Results of target detection for a typical SAR scene. (a) Original SAR image. (b) Illustration of scene content. (c) Optical photo corresponding to clutter
edge. (d) Detection result of the Salazar algorithm with pfa = 10−3 . (e) Detection result of the proposed algorithm with pfa = 10−3 . (f) Detection result of
the Salazar algorithm with pfa = 10−4 . (g) Detection result of the proposed algorithm with pfa = 10−4 . (h) Detection result of the proposed algorithm with
pfa = 10−5 . (i) Clustering result of (d). (j) Clustering result of (e).
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edge area. There are also tanks in the scene, numbered 1–4.
The surrounding of target 1 is grass area, the distance between
targets 2 and 3 is very small (denotes the multitarget situation),
and target 4 is located at the clutter edge. The scene shown in
Fig. 6(a) is a typical type of scene which can be used to evaluate
the performance of detection algorithm completely.
Salazar has made conclusions [8] that the mismatch of the
clutter modeling results in great CFAR loss, which accounts for
that the Salazar algorithm outperforms the conventional twoparameter CFAR detector. Thus, we only compare the proposed
CFAR algorithm with the Salazar algorithm. Fig. 6(d) shows the
detection results by the Salazar algorithm given the theoretical
false alarm probability pfa = 10−3 . Correspondingly, Fig. 6(e)
shows the results by the proposed algorithm given the same
false alarm probability. Fig. 6(f) shows the detection results
by the Salazar algorithm given pfa = 10−4 . Fig. 6(g) and (h)
shows the results by the proposed algorithm given pfa = 10−4
and pfa = 10−5 , respectively.
We take both the resolution and the practical size of target
into consideration. In order to prevent the test target pixels
leaking into the clutter region of the corresponding sliding window, Fig. 6(d)–(h) shows the results of selecting square sliding
window with length of h = 71, the ring window with length of
31, and the annular area with width r = 20. These parameters
are fixed for the entire image. The global threshold Tg for
the proposed algorithm is obtained with a confidence level of
1 − ϕ = 90%. Comparing the results in Fig. 6(d) and (e), given
the same theoretical false alarm probability for both algorithms,
for detecting target 1 in homogenous clutter area and target
4 in clutter edge area, we can see that both the proposed
algorithm and the Salazar algorithm have comparatively good
detection results and the derived target contours are complete
and clear. Whereas for multitarget situation, e.g., for targets 2
and 3, which are close to each other, the proposed algorithm
obviously outperforms the Salazar algorithm. Since the clutter
statistics estimation is influenced by the adjacent target pixels,
only a few pixels of targets 2 and 3 are detected by the Salazar
algorithm with much information lost, while the two close
targets are well detected by the proposed algorithm. In other
words, the proposed algorithm also has better performance for
target detection in multitarget situation.
With comparisons between Fig. 6(d) and (e), we can find out
that, although the proposed algorithm does better in detecting
targets, there are relatively more “small areas” in the image.
These small areas, mainly brought about by the concrete blocks
with relatively strong backscattering, most concentrate in the
clutter edge between the concrete runway and the grass.
Fig. 6(f)–(h) shows that, given the theoretical false alarm
probability pfa = 10−4 , using the Salazar algorithm, the closely
located two targets are both undetected and the information of
the target located in the homogeneous area and the clutter edge
are lost to more or less extent, while the proposed algorithm
can keep much more target information, and the results are
much better. These results strongly illustrate that the proposed CFAR algorithm significantly outperforms the Salazar
algorithm.
In order to make further comparisons between the Salazar
algorithm and the proposed algorithm, suppose that the tar-
Fig. 7.
Comparison of the ROC curves of two algorithms.
get pixels are those pixels with values larger than the global
threshold value Tg . If the number of all these target pixels is
Nt arg et and the size of the image is N × M , then the number
of clutter pixels in the image is Nclutter = N × M − Nt arg et .
The number of target pixels detected is Ndt , and the number
of false alarm pixels is Ndc . Then, the actual detection ratio is
defined as
Pd =
Ndt
.
Nt arg et
(23)
The actual false alarm ratio is
Pf =
Ndc
.
Nclutter
(24)
As shown in Fig. 7, combining (23) with (24), we get the
receiver operating characteristic (ROC) curves of the Salazar
and proposed CFAR algorithms. These curves indicate that
the proposed CFAR algorithm has better performance than the
Salazar algorithm.
Fig. 6(i) and (j) shows the results of targets clustering from
Fig. 6(d)–(e), respectively. The inferior threshold for removing
areas is 30. As shown in Fig. 6(d), the result of the Salazar
algorithm for detecting the closely located two targets is poor,
and much information of targets is lost after CFAR detection.
Target 3 is taken as clutter false alarms and removed during
the process of area removing. However, all the four targets are
detected by the proposed algorithm.
To sum up, taking the case with pfa = 10−3 , for example, we
give the integrative comparisons of the final detection results
by the Salazar algorithm followed by targets clustering and
by the proposed algorithm shown in Fig. 2. The results are
shown in Table IV. All the experiments are accomplished by
nonoptimized Matlab codes with a hardware environment of
PIII 500M CPU and 512M memory. In view of time consuming, Salazar algorithm and the proposed algorithm without
using fast algorithm nearly have equal running time. However,
by using fast algorithm, the consumed time is only 1.6398s,
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TABLE IV
WHOLE PERFORMANCE COMPARISONS BETWEEN THE TWO ALGORITHMS: pfa = 10−3
Fig. 8. Results of target detection from an urban SAR scene. (a) Optical photograph of a test scene without targets. (b) Location index of 13 targets (T1–T13).
(c) SAR image of the scene with targets. (d) Detection result of the proposed algorithm with pfa = 10−3 and 1 − ϕ = 95%. (e) Detection result of the proposed
algorithm with pfa = 10−3 and 1 − ϕ = 99%. (f) Detection result of the Salazar algorithm with pfa = 10−3 .
which is 1/61 of the time by Salazar algorithm and 1/62
of the time by the proposed algorithm without fast strategy.
Theoretically, by using the proposed fast algorithm in the period
of estimating parameters, which is the main time-consuming
process, the computational speed of the proposed fast algorithm
should be 4r = 80 (the width of the annular window is r = 20)
times as fast as that by using the Salazar algorithm. Taking
account of the compiling time of Matlab itself and the time
consumed for comparison with the global threshold, the performance of the fast algorithm is in accord with the theoretical
analysis.
Aside from Fig. 6, we give some more results of real SAR
images to evaluate the proposed algorithm. Fig. 8 shows another
test SAR image containing vehicles in a complex urban clutter
setting, which is collected in 2005. The airborne SAR platform
operated at X-band and collected the data in stripmap mode
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HH polarization, with a resolution of 0.5 m both in range and
in cross-range.
Fig. 8(a) shows an optical (ground truth) photograph of the
scene used in this paper. As we can see, there are a lot of
trees and buildings but no vehicle target. The objects numbered
1 and 2 are two typical buildings in Fig. 8(a). According to
Fig. 8(b), the left-bottom and right-bottom parts of the image
shown in Fig. 8(a) are urban areas. There is a concrete runway
in Fig. 8(a). Fig. 8(c) shows the corresponding SAR image of
this scene placed with 13 military vehicles shown in Fig. 8(b).
The image size is 1375 × 1880 pixels.
We use the same sliding window as the processing of Fig. 6.
Fig. 8(d) shows the detection results by the proposed algorithm
with the theoretical false alarm probability pfa = 10−3 and
the censoring depth 1 − ϕ = 95%. Correspondingly, Fig. 8(e)
shows the results by the proposed algorithm with the same
false alarm probability and the censoring depth 1 − ϕ = 99%.
Fig. 8(f) shows the detection results by the Salazar algorithm
with pfa = 10−3 .
Comparing the results in Fig. 8(d)–(f), given the same theoretical false alarm probability for both algorithms, for detecting
targets T1–T12 in homogenous clutter area and target T13 in
clutter edge area, we can see that both the proposed algorithm
and the Salazar algorithm have comparatively good detection
results and the derived target contours are complete and clear.
Whereas for buildings numbered 1 and 2 and the urban areas
which can be denoted as multitarget situation, the proposed
algorithm outperforms the Salazar algorithm. Since the clutter
statistics estimation is influenced by the adjacent target pixels,
few pixels of buildings numbered 1 and 2 and the urban areas
are detected by the Salazar algorithm with much information
lost, while they are well detected by the proposed algorithm
although the censoring depth varies from 95% to 99%. In other
words, the proposed algorithm also has better performance for
target detection in multitarget situation.
All the experiments are accomplished by the same Matlab
codes and the same hardware environment as the processing of
Fig. 6. In view of time consuming, Salazar algorithm and the
proposed algorithm without using fast algorithm nearly have
equal running time. The proposed algorithm is 42.3168 min,
whereas the Salazar algorithm is 41.6014 min. However, by
using fast algorithm, the consumed time is only 40.0471 s,
which is 1/62.3287 of the time by Salazar algorithm and
1/63.4005 of the time by the proposed algorithm without fast
strategy. Taking account of the compiling time of Matlab itself
and the time consumed for comparison with the global threshold, the performance of the fast algorithm is in accord with the
theoretical analysis.
VII. C ONCLUSION
An adaptive and fast CFAR algorithm based on AC is
proposed in this paper. First, an adaptive global threshold is
used to acquire the index matrix that labels whether it is a
potential target pixel or not for each pixel in the image. Then,
the clutter pixels in the sliding window of detection process
are censored automatically by the index matrix in order to
decide the clutter environment of detection adaptively. The G0
distribution, which can model multilook SAR images within
an extensive range of degree of homogeneity, is introduced to
describe the statistical characteristic of clutter. With the additional process of the AC, the detector has CFAR characteristic
and good performance when detecting target in homogeneous
regions, the clutter edge, and multitarget situations. Simultaneously, the corresponding fast algorithm can greatly reduce
the computational load. Finally, the more accurate extraction of
target regions can be obtained by target clustering process. The
experimental results of the typically real SAR scene validate the
effectiveness of the proposed algorithm.
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Gui Gao received the B.S. degree in information engineering and the M.S. and Ph.D. degrees in remote
sensing information processing from the National
University of Defense Technology, Changsha, China,
in 2002, 2004, and 2007, respectively.
He is currently an Associate Professor with
the School of Electronic Science and Engineering,
National University of Defense Technology. He is
the author of over 50 papers. His research interests
include synthetic aperture radar automatic target
recognition, statistical modeling of SAR image, and
data mining.
Li Liu received the B.S. degree in communication
engineering and the M.S. degree in remote sensing
and geographic information system from the National University of Defense Technology, Changsha,
China, in 2003 and 2005, respectively, where she is
currently working toward the Ph.D. degree.
She is currently a Visiting Student at the University of Waterloo, Waterloo, ON, Canada. Her current
research interests include SAR image texture classification and Markov random field techniques.
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Lingjun Zhao received the B.S. degree in information engineering and the M.S. degree in circuits
and system from the National University of Defense
Technology, Changsha, China, in 2003 and 2004,
respectively, where she is currently working toward
the Ph.D. degree.
Her current research interests include synthetic
aperture radar (SAR) image classification and urban
SAR image interpretation, particularly automatic
object (buildings, road, etc.) extraction from urban
areas.
Gongtao Shi received the B.S. and M.S. degrees in
communication engineering from Air Force Engineering University, Xi’an, China, in 2003 and 2006,
respectively. He is currently working toward the
Ph.D. degree at the National University of Defense
Technology, Changsha, China.
His current research interests include synthetic
aperture radar (SAR) image processing and SAR
ground moving target indication.
Gangyao Kuang received the B.S. and M.S. degrees
from the Central South University of Technology,
Changsha, China, in 1988 and 1991, respectively,
and the Ph.D. degree from the National University
of Defense Technology, Changsha, in 1995.
Since 1996, he has been the Codirector of the
Remote Sensing Information Processing Laboratory,
National University of Defense Technology, where
he has worked on synthetic aperture radar (SAR)
signal and image processing, automatic target detection and recognition, information fusion, and various
remote sensing projects. He is currently a Professor in the School of Electronic
Science and Engineering, National University of Defense Technology. He is the
author/coauthor of over 200 papers and one book. His current interests include
remote sensing, SAR image processing, change detection, SAR ground moving
target indication, and the classification of polarimetric SAR images.