Clustering Algorithm Improvement in SAR Target Detection

The synthetic aperture radar (SAR) auto target recognition (ATR) system developed at Lincoln Laboratory is a standard system for target detection/recognition. It has three main stages: a prescreener, a discriminator and a classifier. The clustering algorithm between the prescreener stage and the discriminator stage is used to cluster the multiple detections of a single target to form a region of interest (ROI). This paper introduces the steps of the common clustering algorithm and analyzes its disadvantages. We improve the common clustering algorithm from two aspects of the read sequence of image data and the calculation means of clustering quasi-center coordinates. The clustering results based on two actual images testify efficiency of clustering algorithm improvement.


I. INTRODUCTION
Synthetic aperture radar (SAR) can accomplish imaging allweather as a kind of high-resolution radar.It is usually used to fulfill military reconnaissance and enemy tactical target detection [1].Lincoln Laboratory has developed a complete and standard, end-to-end, ATR system that utilizes 2-D SAR imagery [2], [3].The Lincoln SAR ATR system is conveniently decomposed into a sequence of three processors: a prescreener, a discriminator and a classifier.The threestage framework has become a classical pattern of SAR ATR algorithm used by many research institutes [4], [5].The prescreener uses a two-parameter constant false-alarm rate (CFAR) algorithm.This algorithm is a pixel-pixel adaptive image processing scheme that takes advantage of the fact that in SAR imagery, targets typically appear brighter than non-targets.Since a single target can produce multiple CFAR detections [6], the detections in target-size regions need be clustered together to form a ROI, with the centroid of the cluster aligned with the center of the ROI.Each ROI is passed on to the discriminator for further processing.
So the clustering algorithm between the prescreener stage and the discriminator stage is a key portion of SAR ATR algorithm [7].A good clustering algorithm can get clustering The associate editor coordinating the review of this article and approving it for publication was Wei Liu.centers that are adjacent to the actual target centers.This letter introduces the common clustering algorithm and analyzes its two disadvantages [8] [9].We present a series of schemes of the improved clustering algorithms against disadvantages.The clustering results of the common clustering algorithm and the improved clustering algorithms testify efficiency of improvement.
This letter is organized as follows.Section II describes the common clustering algorithm and analyzes its two disadvantages.Section III improves the common clustering algorithm from two aspects of the read sequence of image data and the calculation means of clustering quasi-center coordinates and presents a series of improved schemes.Section IV analyzes and compares the experiment results of different clustering algorithms.Section V is the conclusion of this letter.

II. DESCRIPTION AND PERFORMANCE ANALYSIS OF THE COMMON CLUSTERING ALGORITHM
Firstly this section introduces simply the three-stage framework of the Lincoln SAR ATR system, and then we will describe in great detail the common clustering algorithm and analyze its two disadvantages.
The Lincoln SAR ATR system has three stages: prescreener, discriminator and classifier.Figure 1 shows a notional block diagram of three-stage SAR ATR system.The prescreener searches through imagery representing many square kilometers of terrain, and outputs a collection of socalled regions of interest (ROIs).Each ROI is a subimage extracted from the original SAR image and centered at a possible target location.The discriminator applies further processing to distinguish between two kinds of ROIs: those containing man-made objects and those containing natural clutter.All ROIs that are judged to containing natural clutter are discarded.Finally, the classifier assigns each remaining ROI to a predefined target category, or to a none-of-the-above category if the ROI appears to contain man-made clutter.
Stage 1. Detection/Prescreening: In this stage of processing, a two-parameter CFAR is used as a prescreener to select candidate targets in the image on the basis of local brightness.The CFAR detector is defined by the rule where X t is the amplitude of test pixel, ûc is the estimated mean of the clutter amplitude, σc is the estimated standard deviation of the clutter amplitude, and K CFAR is a constant that controls the false alarm rate.CFAR detection is used to judge the property of test pixel according to (1).If the detection statistic calculated in (1) exceeds K CFAR , the test pixel is declared to be a target pixel; if not, it is declared to be a clutter pixel.In many instances, the CFAR algorithm will yield multiple detections on a single target.These detections need to be clustered together into a center.Then the clustering centers are sent to next stage to form ROIs each of which is a region of a definite size around each clustering center.
Stage 2. Discriminator: Firstly this stage determines the position and the orientation of a detected object in each ROI.The determining approach is to place a target-sized rectangular template on the image that is slid in range and crossrange and rotated until the energy within it is maximized.Step two of the discriminator stage calculates the discrimination features that are described in detail elsewhere [2].The last step of the discriminator stage combines the features of the selected subset into a single discrimination statistic.This discrimination statistic is calculated as a quadratic distance metric where n is the number of features, M and ˆ are estimates of the mean vector and covariance matrix of the features, and X is the vector of the discrimination features.Finally we can judge whether the ROI contains a man-made object or natural clutter according to the quadratic distance d t (X ).Stage 3. Classifier.Because the discussion contents of this letter mainly relate to the first stage and the second stage of the Lincoln SAR ATR system, no detailed description of the third stage is provided and no further mention of it is made.

B. Description and performance analysis of the common clustering algorithm
The clustering algorithm is used to cluster nonzero pixels within a definite range into a clustering center on images processed by a CFAR detector.Assume a 0-1 binary image of M × N pixels is A = a ij that is obtained from an original SAR image processed by a CFAR detector, where and the distance threshold used to judge a pixel to belong to a target or not is d.Then common clustering algorithm steps are described below.
(1) Read every element a ij from A in the ascending sequence of subscripts i, j.If a ij = 0, continue to read the next element; If a ij = 1, turn to the next step. ( are the coordinates of the lth clustering quasi-center, and k l is the clustered element number of the lth clustering quasi-center).(3) Calculate the regenerate values of the lth clustering quasi-center by (3) So we can get the regenerate values of the lth clustering quasicenter after a ij is clustered, and turn to (1).( 4)After reading all elements of A, we remove the partial clustering centers as false clustering centers whose clustered element numbers are small excessively.
The clustering algorithm is used to provide the clustering centers to determine ROIs for the discriminator stage.Because the size of ROI decides the operation burden of latter signal processing, we should reduce the area of ROI as possible as we can.So the clustering centers should be located around the actual target centers because it will ensure that each ROI determined by each clustering center can contain the whole target with the shortest possible radius.
There is a key problem and an important disadvantage for the clustering algorithm.The key problem is to select a distance threshold to determine the pixels belonging to the same target.An appropriate threshold is necessary to obtain a good clustering result.On the contrary, if the selected distance threshold is on the high side, more clutter pixels are clustered into the target regions and the clustering centers gained finally deviate from the actual target centers badly.Besides, if the distance between two adjacent targets is short, they are easily clustered mixedly into a center between the two targets.On the other hand, if the selected distance threshold is on the low side, a target might be divisively clustered into two or more centers.The important disadvantage is the clutter disturbance.Although a CFAR detector in the prescreener stage can remove most clutter by a low false alarm rate, a few of clutter pixels preserved after CFAR detection might make the clustering centers deviate badly.Furthermore the false alarm rate can't be low excessively because it will result in a large loss of target pixels in CFAR detection.
We can discover two problems of the common clustering algorithm through above analysis.
(1) Read data sequence of image A. The common clustering algorithm reads every element a ij from image A in the ascending sequence of subscripts i, j.Under this read sequence, in order to assure the pixels belonging to the same target could be clustered together, the distance threshold should be high that is usually chosen to be the maximal size of a target.The high distance threshold might result in bad deviations of the clustering centers and mixed clustering of the adjacent targets.So the read sequence of image data should be improved in the common clustering algorithm.
(2) Coordinate calculation means of clustering quasicenter.The clustering quasi-center coordinates are calculated by averaging the coordinates of all pixels belonging to the same target on a 0-1 binary image.So the effect of each pixel belonging to the same target for the coordinates of the corresponding clustering quasi-center is same in the common clustering algorithm.In fact, because the amplitudes and the neighborhood information of different pixels belonging to the same target are different, their effects should be also different.So different pixels of the same target should be weighted differently when we calculate the clustering quasicenter coordinates.

III. IMPROVEMENT OF THE COMMON CLUSTERING ALGORITHM
Considering two problems of the common clustering algorithm, this section will improve it from two aspects: the first is to improve the read sequence of image data and the second is to improve the coordinate calculation means of clustering quasi-center.We define two variables before introducing the improvement of the common clustering algorithm in detail.The semitransparent window in figure 2(b) and figure 2(c) can slide on images whose size is commonly less than a target size.We denote the length and the width of the window respectively by w 1 and w 2 , and define two variables, p ij and q ij , to be respectively the concomitant weight coefficients of

Assume an original SAR image is
b mn (7) Based on (b) and ( 7), the improvements is as follows.

A. READ SEQUENCE IMPROVEMENT OF IMAGE DATA
There are three ideas for the read sequence improvement of image data.
(1) Image data are read in the descending sequence of b ij on image B. In most case the pixel amplitudes of target region are larger than the clutter region, and the target center region are larger than the target edge region.Under the assumption, if image data are read in the descending sequence of pixel amplitudes, it will bring the following advantages: Because each clustering quasi-center is initially located near the corresponding actual target center and the data are read continuously from the target center to the target edge, each clustering quasi-center regenerated in succession moves around the corresponding actual target center, and then the distance threshold can be set low.These will reduce the clutter pixels clustered into the target clustering centers to prevent a bad deviation of each clustering center and avoid clustering mixture of the adjacent targets.
(2) Image data are read in the descending sequence of p ij .From the calculation formula of p ij , we can see that p ij expresses the density of nonzero elements around a ij .In most case, the concomitant weight coefficient p ij of the target region is larger than the clutter region, and the target center region is larger than the target edge region.So if the image data are read in the descending sequence of p ij , it will prevent a bad deviation of each clustering center and avoid clustering mixture of the adjacent targets on the basis of the same analysis as (1).
(3) Image data are read in the descending sequence of q ij .The definition of q ij shows that this improvement integrates ( 1) and ( 2).So we can get the same conclusion as ( 1) and ( 2).

B. CALCULATION MEANS IMPROVEMENT OF CLUSTERING QUASI-CENTER COORDINATES
Like the read sequence improvement of image data, the coordinate calculation means of clustering quasi-center has three improved ideas.These improved ideas aim at reducing the disturbance of clutter pixels for clustering centers.
(1) Convert b ij into an effect factor to participate in the coordinate calculation of clustering quasi-center.The coordinates of clustering quasi-center will be calculated alternatively in the following way: The new calculation means of clustering quasi-center assure that the effect of the clustered pixel for clustering quasi-center coordinates becomes more remarkable if its amplitude is larger.Under the following reasonable presuppositions: the pixel amplitude of target region is larger than the clutter region and the target center region is larger than the target edge region, the effects of clutter pixels for the clustering quasi-centers become smaller, and each clustering quasi-center is more close to the corresponding actual target center.
(2) Convert p ij into an effect factor to participate in the coordinate calculation of clustering quasi-center.The coordinates of clustering quasi-center will be calculated alternatively in the following way: Like the analysis in (1), under the following reasonable presupposition: the concomitant weight coefficient p ij of target region is larger than the clutter region and the target center region is larger than the target edge region, the effects of clutter pixels for the clustering quasi-centers become smaller, and each clustering quasi-center is more close to the corresponding actual target center.
(3) Convert q ij into an effect factor to participate in the coordinate calculation of clustering quasi-center.The coordinates of clustering quasi-center will be calculated alternatively in the following way: This alternative calculation means of clustering quasicenter coordinates integrate (1) and ( 2) for the definition of q ij .So we can get the same conclusion as ( 1) and (2).
Because there are three improved read sequences of image data and three improved calculation means of clustering quasi-center, the final improved clustering algorithm has fifteen schemes.The schemes are selected according to the agreement degree of the actual clustering circumstances and above reasonable presuppositions.In order to facilitate the latter description of clustering results, we define the representations of the common clustering algorithm and fifteen improved schemes.Assume the read sequence of image data in the common clustering algorithm is denoted by E 0 , three improved sequences are denoted by E 1 , E 2 and E 3 respectively, the calculation means of clustering quasi-center coordinates in the common clustering algorithm is denoted by F 0 and three improved calculation means are denoted by F 1 , F 2 and F 3 respectively.Therefore the common clustering algorithm and fifteen improved clustering schemes can be denoted by E g F h uniformly, where g, h = 0, 1, 2, 3.For example, the common clustering algorithm is denoted by E 0 F 0 .

IV. COMPARISON AND ANALYSIS OF CLUSTERING RESULTS
In order to demonstrate the performance of improved clustering algorithm, this section will use the common clustering algorithm and the improved clustering algorithms to cluster on two actual SAR images, which after CFAR detection are shown as figure 3(a) and figure 4(a).Figure 3(a) displays a wood located with three jeeps, and the positions of jeep centers are regarded as the intersection points of a horizontal line and three perpendicular lines according to the energy distribution of jeeps.Figure 4

V. CONCLUSION
The Lincoln SAR ATR system is a standard system for target detection/recognition.Three-stage framework of this system has become a classical pattern of SAR ATR algorithm applied by many research institutes.The clustering algorithm between the prescreener stage and the discriminator stage is important for the performance of SAR ATR algorithm.This letter analyzes two problems of the common clustering algorithm and improves it from two aspects of the read sequence of image data and the calculation means of clustering quasicenter coordinates.There are fifteen schemes of improved clustering algorithm in all.The clustering experiment results of different clustering algorithms indicate that the improved clustering algorithms are better to prevent clutter disturbance and clustering mixture than the common clustering algorithm.

FIGURE 1 .
FIGURE 1. Block diagram of three-stage SAR ATR system.
and if there is a subset of DO = {o|o ∈ D and o ≤ d}, turn to the calculation of next step for the lth clustering quasi-center corresponding with the minimal value of O.
and a 0-1 binary image is A = a ij obtained from S after CFAR detection, and the mask image of S by A is B = b ij , where b ij = s ij • a ij .S, A and B are shown respectively in figure 2(a), figure 2(b) and figure 2(c).

FIGURE 2 .
FIGURE 2. Three images before and after CFAR detection.
(a) displays a road located with seven trucks, where the rectangular panes represent trucks.The clustering experiments based on figure 3(a) and figure 4(a) intend to demonstrate the excellent performances of improved clustering algorithms respectively against clutter disturbance and clustering mixture.Because the improved

FIGURE 3 .
FIGURE 3. Clustering results of different clustering algorithms against clutter disturbance.