Joint Decision and Naive Bayes Learningfor Detection of Space Multi-TargetTao HUANG

1;2�, Zhulian LI1, Yu ZHOU

1, Yaoheng XIONG1, and Haitao ZHANG

1

1Yunnan Astronomical Observatory, Chinese Academy of Sciences, Kunming, Yunnan 650011, China2University of Chinese Academy of Sciences, Zhongguancun, Beijing 100049, China

(Received August 12, 2013; Accepted March 24, 2014)

In the photoelectric tracking system, the detection of space multi-target is crucial for target localization and tracking.The difficulties include the interferences from CCD smear and strong noise, the few characteristics of spot-like targetsand the challenge of multiple targets. In this paper, we propose a hybrid algorithm of joint decision and Naive Bayes(JD-NB) learning, and present the duty ratio feature to discriminate the target and smear blocks. Firstly, we extract theproper features and train the parameters of the Naive Bayes classifier. Secondly, target blocks are preliminarilyestimated with the Naive Bayes. Lastly, the 4-adjacent blocks of the candidate target blocks are jointed to analyze thedistribution pattern and the true target blocks are secondarily extracted by the method of pattern matching.Experimental results indicate that the proposed JD-NB algorithm not only possesses a high recognition rate of betterthan 90% for the target block, but also effectively overcomes the disturbance of the smear block. Moreover, it performswell in the detection of small and faint targets when the SNR of the block is higher than about 0.014.# 2014 The Japan Society of Applied Physics

Keywords: space target, detection, Naive Bayes, joint decision, pattern matching

1. Introduction

Space targets mainly include planets, satellites, spacedebris, space stations and space shuttles, as well as cosmicobjects flying into the earth’s outer space, such as cometsand asteroids. The detection and recognition of space targetsrefer to the discrimination of the types, properties and threatsfor the purpose of accurately grasping the real-time spacesituation. Compared with the radar measurement systems forspace targets, photoelectric detection systems possess thefollowing advantages: high accuracy, intuitiveness, immu-nity to ground clutter, mature technology and low cost.Visible imaging devices such as the electronic fence,1)

photometric system and satellite laser ranging system2)

mainly focus on observing satellites and space debris.3)

According to incomplete statistics, the total number ofsatellites is about 3700 and that of debris is more than11000, which should be monitored and managed scientifi-cally to ensure space safety.

The effective detection of the satellites and debris issignificant for accurate positioning and tracking. Since thesespace targets are usually several hundred kilometers ormore away from ground stations, their shape and texturecharacteristics are almost drowned and they usually presentthemselves as spots occupying only several pixels. Mean-while, the impacts of atmospheric turbulence4,5) and imagingdevice noise lead to further difficulty in detection. Due to thelow signal-to-noise ratio (SNR), the few characteristics andthe disturbance of charge coupled devices (CCD) smear6,7)

and other space targets, false alarms and missing detectionoften occur. Moreover, to obtain more information of spacetargets, the multi-target tracking (MTT) is proposed, whichbrings a greater challenge to space target detection. MTT

must detect all the small targets simultaneously appearing inreal-time satellite images, and it requires guaranteeing therecognition rate of true targets. To address this current hottopic, scholars have proposed various algorithms: thresholdsegmentation, local entropy method, multi-frame accumula-tion, global search, multi-level matching, dynamic program-ming, neural networks training, etc. The simplest approach isglobal threshold segmentation such as the Otsu8) thresholdsegmentation and valley-emphasis algorithm.9) The Otsumethod can provide satisfactory results for thresholding animage with a histogram of clear bimodal distribution.However, it fails to select the optimal thresholds in somecases, especially in which the gray-level histogram isunimodal or close to unimodal. Ng9) later proposed a revisedOtsu method known as valley emphasis, which weighs theobjective function of the Otsu method with the valley pointof the histogram. However, these algorithms are sensitive tonoise and prone to detecting many false targets, thus peopletend to use local threshold segmentation, for example thelocal adaptive threshold.10) Additionally, the local entropymethod11) deems that a small target leads to a change of localentropy that can serve as the detection criterion. In thismethod, the target areas are determined and then the exactlocation of each target is calculated. However, the number oftargets should be known in advance, and the positioningaccuracy is closely related to the size of the partial window.The methods mentioned above, belonging to the detectbefore track (DBT) algorithm, are generally used in thedetection of spot-like targets (SNR is usually high). Whilethe algorithms of energy accumulated,12) global searchingand multi-level matching, which are classified as trackbefore detect (TBD)13) algorithm, tend to be employed inpoint-like target tracking (SNR is usually low). The TBDmethods generally consist of two steps: the suspicioustargets are all extracted from a single frame in the first step,�E-mail address: baolong86213@163.com

OPTICAL REVIEW Vol. 21, No. 4 (2014) 429–439

429

and the true targets are isolated according to the cumulativeinformation of the sequential images in the second step,such as energy, grayscale, track, etc. However, multi-frameaccumulation requires numerous continuous images andmuch time. Moreover, a popular method of dynamicprogramming14,15) can effectively detect the trajectory of apoint target, and it requires fewer computing resources.However, with the expansion of the speed window, thecalculation amount will increase rapidly and the detectionproperty will degrade. Neural network based methods,16,17)

which spring up rapidly in target detection and tracking,have the advantages of time-saving and fine fault tolerance.Nevertheless, the hardware implementation of neural net-work is very complicated and the detection result heavilydepends on the richness of training samples.

In order to solve the issue of space multi-target detection,we propose a new hybrid algorithm of joint decision andNaive Bayes (JD-NB) learning based on the similar idea ofthe neural network method, which shares the respectivesuperiority of the recognition rate with the neural networkand requires much less detection and training time. The JD-NB algorithm also improves the performance of the classicalNB classifier,18,19) and it has not been found in the area ofspace target detection. The proposed JD-NB algorithm,shown in Fig. 1, has favorable capabilities of detection andanti-jamming. In our method, we need no prior knowledgeon the number of targets, and it can detect targets in a singleimage whose SNR is not too low without accumulativemulti-frame images. Firstly, a large number of sampleimages are collected and divided into blocks to establisha labeled sample set. Secondly, the four features, overallexpectation, overall variance, overall third-order centralmoment and duty ratio, are extracted successively. Then themodel parameters of the NB classifier are obtained by off-line learning through the sample set established above. Next,the candidate target blocks are preliminarily estimated by thetrained classifier in the real-time image. Lastly, the truetargets are singled out in the extended judgment of the

proposed joint decision and pattern matching methods,which greatly suppress the disturbance by CCD smear.

The organization of this paper is as follows. Thedescription of feature extraction is given in Sect. 2. Thenthe procedure of JD-NB algorithm is presented in Sect. 3and the experiment results are presented in Sect. 4. Finally,the conclusions and future work are given in Sect. 5.

2. Feature Extraction and Analysis

Block processing, a general method in image recognition,will generate a group of sample image blocks that can beclassified into three types: target block, smear block, andbackground block. Thus the detection problem becomes atypical classification problem, the most critical point ofwhich is feature extraction. The appropriate features withina certain range can magnify the differences among thevarious categories while reduce the differences of similarobjects. Therefore, the feature extraction is consideredfirst.

2.1 Space target analysisTypical sample image blocks obtained by blocking the

satellite images are presented in Fig. 2, which are theresearch subjects in this supervised classification problem.Figures 2(a)–2(d) belong to the target category. The targetspresent are either bright or dim, and the target in Fig. 2(d) isonly one part of a target. While Figs. 2(e) and 2(f ) presentthe background of the starry sky with either strong or weaknoise. The noise points of images are generally introducedby the imaging equipment (noise, bad column, and hotpixels) and the space environment (mainly cosmic rays). Thecosmic ray events frequency on the CCD images exposedat a ground-based observatory are low and their profile isnarrower than the satellite profile, but CCD images fromsatellite payloads contain a larger number of cosmic raytracks.20) However, in our photoelectric detection system forsatellite and space debris, the integral time of the CCD isalways less than ten seconds (from several milliseconds to

Fig. 1. (Color online) Flow diagram of the joint decision and Naive Bayes algorithm (JD-NB). Firstly, a great amount of sample imagesare divided into blocks to establish a labeled sample set. Secondly, the features are extracted to train the Naive Bayes classifier off-line.Thirdly, the real-time collected image is provided to the Naive Bayes classifier and the candidate targets are preliminarily judged. Lastly,the true targets are singled out in the extended judgment by the joint decision and pattern matching methods.

OPTICAL REVIEW Vol. 21, No. 4 (2014)430 T. HUANG et al.

several seconds) and the aperture of our telescope is only120 cm. Therefore, the cosmic rays appearing in the CCDimages of our telescope are usually point noises that occupyno more than one pixel. Additionally, the long tail, faint tail,and short tail, respectively shown in Figs. 2(g)–2(i), aremainly the CCD smears of stars, space debris, and non-targetsatellites. No matter whether the target is a high-orbitsatellite or low-earth-orbit (LEO) satellite, we expect that itwould not be interfered by strong noise and smear, whichmay cause false alarm and missing detection. A high-orbitsatellite, whose image is relatively small and faint, issusceptible to the decoys of other bright spots and strongnoise. Owning to the slow motion of the high-orbit satellitewith respect to the ground station, the track correlationprocessing of multi-frame images is allowed, and the targetis not easily lost once it has been correctly detected. Whilethe imaging of a LEO satellite is relatively large and bright,and its moving speed is generally up to several kilometersper second. Thus, the target must be discriminated targetfrom smear in a short time. Nevertheless, the short smear inFig. 2(i) and the bright target in Fig. 2(a) are too similar tobe easily distinguished.

In interline transfer CCD, the smear6,7) results from thelight leakage into the vertical shift registers as a chargepacket is clocked through a brightly illuminated area. Inframe transfer CCD, smear is produced by incident lightas the already generated image is shifted from the imagesensor area to the storage area. Excessive smear is visually

objectionable and reduces the dynamic range. The smearsignal is proportional to the illumination intensity and thevertical height of the spot. When the CCD is reading data,an external mechanical shutter can avoid the continuousirradiation from the light source. Therefore, it can reduce oreliminate the smear. However, the time interval of the shortexposure is sometimes only dozens of milliseconds inphotometric measurement systems. If the mechanical shutterof the CCD camera opens and closes so frequently, it may beeasily damaged causing much inconvenience to the opera-tion and maintenance of the system. In realistic situations,the mechanical shutter is usually in a normally open stateor completely removed, thus it is difficult to avoid thephenomenon of smearing.

2.2 Feature extraction2.2.1 Overall moment

The locations of space targets are undefined in the imageblocks, and the images of the same space target are alsodifferent at different time. According to this characteristicof the satellite image, it is not profitable to calculate theseven moments of Hu,21) which may greatly increase thecalculation amount. In this paper, the two-dimensionalimage is regarded as one-dimensional vector. Then wedirectly select such moment features that can be easilycalculated: the overall expectation, the overall variance,and the overall skewness. It is assumed that the size of theimage block is L�W, and these moment features aredescribed as

�g ¼

XLi¼1

XWj¼1

f ði; jÞ

L�W; ð1Þ

�2g ¼

XLi¼1

XWj¼1

½ f ði; jÞ � �g�2

L�W; ð2Þ

Sg ¼

XLi¼1

XWj¼1

½ f ði; jÞ � �g�3

L�W � �3g

: ð3Þ

2.2.2 Duty ratioExperiments reveal that only the moment features

mentioned above cannot separate target blocks from smearblocks very well. To distinguish the three categories ofimage blocks shown in Fig. 2, a common method is tosegment the interested object from the image and extract theshape features such as aspect ratio, dispersion, etc. Never-theless, in this paper, we introduce the concept of duty ratiofrom the digital circuits area and employ it as an effectivefeature to distinguish between the target and smear block. Ina periodic event, duty ratio is defined as the ratio of the eventduration to the total period of a signal. When the alt-azimuthtelescope is tracking the space target, it is always an acuteangle between the telescope rack and the horizontal plane.And it is barely for the telescope rack moving perpendicu-larly to the ground plane. Depending upon this character-

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

Fig. 2. Typical image blocks: (a) bright target; (b) small target;(c) dim target; (d) part of target; (e) strong noise; (f ) weak noise;(g) strong smear; (h) weak smear; (i) part of smear. These blocksare classified into three categories: target block, background blockand smear block. (a)–(d) are judged to be target blocks, (e) and (f )belong to the category of background blocks, and (g)–(i) are smearblocks.

OPTICAL REVIEW Vol. 21, No. 4 (2014) 431T. HUANG et al.

istic, we project each column pixels of the image block intoa row vector following some regulation. If the column pixelssatisfy some condition, the corresponding element of the rowvector is set to the high level, otherwise it is cleared to thezero level. For the blocks shown in Fig. 3, we can determinea reasonable threshold th. Provided that the size of the imageblock is L�W, a curve can be obtained for each imageblock using Eq. (4), as shown in Fig. 3.

For j ¼ 1 to W

Pulseð jÞ ¼ 1 if 8f ði; jÞ > th ði ¼ 1 to LÞ0 others

;

�ð4Þ

where Pulse is the row vector mentioned above, and f ði; jÞdenotes the grayscale of a pixel. Since these curves resemblethat of a digital pulse, the vector Pulse of Eq. (4) can be aperiod signal, and the duty ratio of the image block definedin this paper is

D ¼ �

T; ð5Þ

where � presents the number of elements with a high level inthe vector Pulse, and T denotes the length of the vectorPulse. The duty ratio calculated above can be utilized todiscriminate the target and smear blocks. The thresholdselection will affect the value of duty ratio, and we mustdetermine a proper threshold through repeated experiments.Moreover, to suppress the impact of random noise points inthis algorithm, it is assumed that only the grayscales of threeconsecutive pixels in each column are larger than thethreshold th can present the corresponding element of Pulseto be the high level. This is equivalent to a low-pass filterfiltering high-frequency noise. The pulse in digital circuits iscalled a Time Pulse, while the pulse of the image blockproposed in this paper can be temporarily named SpatialPulse.

2.3 Feature analysisTo study the effect of these features, we separately select

36 target blocks, 36 smear blocks, and 36 background blocksfrom the sample image blocks, and then extract the fourfeatures of these blocks. The distribution curves of the fourfeatures for the three categories of blocks are shown inFig. 4. Figure 4(a) shows that the target and smear blocksenjoy higher expectation and variance than the backgroundblocks as a whole. Meanwhile, the expectations of thosebackground blocks with strong noise are also large. Thevariance feature successfully separates the target and smearblocks from the background blocks, but it has a smalloverlapping area between target blocks and smear blocks,which is shown in Fig. 4(b). The overall skewness isdesigned to describe the symmetry of gray distribution forthese blocks. The target and smear blocks possess a greatproportion of background pixels, and the grayscales ofalmost all the points are smaller than the expectation.Therefore, these blocks are usually negatively skewed (rightside). Figure 4(c) shows that the absolute value of skewnessof the target or smear block is smaller than that of thebackground block in general, and the curve of the targetblock is a little lower than that of the smear block as a whole.Additionally, duty ratio represents the proportion of thetarget or smear in the entire image block. It is shown inFig. 4(d) that the duty ratios of the target blocks almostdistribute between those of the smear and backgroundblocks. That is to say, this feature can effectivelydiscriminate between these three classes of blocks. Inconclusion, the combination of these four features ispromising for space target detection, as will be demonstratedin the experiments described below. After the feasibility

Column Projection

Column Projection

0 10 20 30 40 50 60

0

0.2

0.4

0.6

0.8

10.1406

0 10 20 30 40 50 60

0

0.2

0.4

0.6

0.8

10.5000

Fig. 3. (Color online) Feature of duty ratio. The duty ratio isintroduced from the digital circuits. The column pixels of the blockare projected following some regulation, and then the row vectorshown in the right curve graph is generated for each block. Thedigits at the top of these two curve graphs denote the duty ratios ofthese two blocks.

0 10 20 30 400

10

20

30

40

50

Serial Number of Image Block

Exp

ectio

n

(a)

0 10 20 30 400

1000

2000

3000

4000

Serial Number of Image Block

Var

ianc

e

(b)

BackgroundTargetSmear

0 10 20 30 40−40

−30

−20

−10

0

10

Serial Number of Image Block

Ske

wne

ss

(c)

0 10 20 30 400

0.2

0.4

0.6

0.8

Serial Number of Image Block

Dut

yfac

tor

(d)

Fig. 4. (Color online) Feature distributions of target blocks,background blocks and smear blocks. (a) Expectation distribution,(b) variance distribution, (c) skewness distribution, (d) duty ratiodistribution. 36 target blocks, 36 smear blocks and 36 backgroundblocks are selected in this experiment of feature analysis, and thefour features are extracted respectively. The red line denotes thetarget blocks, the black line represents the background blocks, andthe blue line indicates the smear blocks.

OPTICAL REVIEW Vol. 21, No. 4 (2014)432 T. HUANG et al.

analysis, let us focus on the design of the classifier based onthe NB.

3. Joint Decision and Naive Bayes Learning

3.1 Naive Bayes learningFor a supervised learning problem, we wish to approx-

imate an unknown target function f : X ! Y , or equiva-lently, PðY=XÞ. We assume Y to be a multivariate randomvariable, and X to be a vector containing n attributes. Inother words, X ¼ hX1; X2; . . . ; Xni, where Xk is the randomvariable of polynomial distribution denoting the k-thattribute of X. To reduce the complexity, we assume theattributes X1; X2; . . . ; Xn are all conditionally independentof each other for given Y .18) Applying the Bayes rule,PðY ¼ yj=XÞ can be expressed as

PðY ¼ yj j X1 . . .XnÞ ¼PðY ¼ yjÞ

Yk

PðXk j Y ¼ yjÞXj

½PðY ¼ yjÞYk

PðXk j Y ¼ yjÞ�;

ð6Þwhere yj denotes the j-th possible value for Y , Xk denotes thek-th possible vector value for X, and Eq. (6) is the classifier.We can learn PðY=XÞ from the training data to estimatePðX j YÞ and PðYÞ. If the n input attributes Xk each takes onI possible discrete values and Y is a discrete variable takingon J possible values, the learning task is to estimate two setsof parameters:18)

�kij ¼ PðXk ¼ xki j Y ¼ yjÞ�j ¼ PðY ¼ yjÞ :

(ð7Þ

One possible value of each input attribute Xk is xki, and onepossible value of Y is yj. There are nIJ such �kij parameters,and only nðI � 1ÞJ of these are independent, given that theymust satisfy

Pi �kij ¼ 1 for each pair of k and j values. �j is

the parameter that defines the prior probability over Y .We can estimate the parameters using the maximum

likelihood criterion. Given a training set fðxðtÞ; yðtÞÞ; t ¼1; . . . ; T g, the joint likelihood of the data is

Lð�kij; �jÞ ¼ logYTt¼1

pðxðtÞ; yðtÞÞ: ð8Þ

Maximizing this function with respect to �kij and �j givesthe maximum likelihood15) estimates,b�kij ¼ PðXk ¼ xki j Y ¼ yjÞ

¼ ]DfXk ¼ xkiV

Y ¼ yjg]DfY ¼ yjgb�j ¼ PðY ¼ yjÞ ¼ ]DfY ¼ yjg

jDj

;

8>>>>><>>>>>:ð9Þ

where the ]Dfxg operator returns the number of elements inset D that satisfy property x, and jDj denotes the number ofelements in training set D. Note that even though the NB18)

assumption is extremely strong, this algorithm works well onmany problems.

It is necessary to train the NB model sufficiently using thesample library, provided that the size of the sample image isL�W and that of the block is L0 �W0. Meanwhile, the

length and width of the overlapping area are, respectively,Dl and Dw. Thus, each image can be divided into m� nimage blocks,

m ¼ L� L0

L0 �Dlþ 1

n ¼ W �W0

W0 �Dwþ 1

:

8>><>>: ð10Þ

In this work, 125 images acquired using the ANDOR iXon888 EMCCD are adopted as training samples, the sizes ofwhich are all 512� 512. Considering the computationefficiency and the characteristics of targets, the sizes ofblocks are uniformly 64� 64, and the overlapping sizes areall set to be 8 pixels. Thus, each image can be divided into9� 9 blocks and 10125 blocks are generated in total. Sincethe NB learning algorithm belongs to the supervisedclassification, the sample set must be labeled manually.Then we establish the training sample library I ¼ fI0; I1; I2g,where I0 ¼ fI0agAa¼1, I

1 ¼ fI1bgBb¼1, and I2 ¼ fI2c gCc¼1. A, B,and C, respectively, refer to the numbers of backgroundblocks, target blocks, and smear blocks, and Ij represents thesample set of some category.

Before extracting the features of image blocks, the medianfiltering or Gaussian filtering is performed for suppressingthe interference of stochastic noise. Following Eqs. (1)–(5),the feature vector of each sample block is calculated, andthen the distribution of each feature is discussed. If someoriginal input attribute is continuously valued, the featurethat is applied for the NB learning must be discretized. Forinstance, the skewness and duty ratio can be processed asshown in Table 1. In our experiment, X ¼ hX1; X2; X3; X4i,where X1, X2, and X3 have four value regions, and X4

enjoys three value regions. Meanwhile, Y ¼ hy1; y2; y3i.There are 45 b�kij-type parameters and 3 b�j-type parametersin total. We learn the model parameters with Eq. (9) fromthe sample set already established. To avoid the possibilityof estimated b�kij or b�j being zero, we usually optimizeEq. (9) by Laplace smoothing,18) which can be describedas

b�kij ¼]DfXk ¼ xki

VY ¼ yjg þ 1

]DfY ¼ yjg þMb�j ¼]DfY ¼ yjg þ 1

jDj þ J

;

8>><>>: ð11Þ

where M refers to the number of distinct values that Xk cantake, and J denotes the number of values that Y can take.

3.2 Joint decisionAfter achieving the model parameters of the NB classifier,

we need to verify its performance and study the decision

Table 1. Feature discretization for skewness and duty ratio.

Xi

1 2 3 4

Skewness >�1:5 �3:5 to �1:5 �8 to �3:5 <�8

Duty ratio 0 to 0.02 0.02 to 0.20 >0:20

OPTICAL REVIEW Vol. 21, No. 4 (2014) 433T. HUANG et al.

method to recognize the true targets. The testing image isdivided into 81 blocks in an overlapping manner, which arenumbered 1, 2, . . . , 81 from left to right and from top tobottom. Then the specific feature vectors of these blocks areextracted, and the probability PO of each block judged astarget block is calculated with Eq. (12). With the particularjudgment strategy of three-step framework below, we canfinally confirm the blocks possessing true targets.

POðY ¼ 1jX1 . . .XnÞ ¼PðY ¼ 1Þ

Yk

PðXkjY ¼ 1ÞXj

PðY ¼ yjÞYk

PðXkjY ¼ yjÞ:

ð12Þ1. Preliminary decision. Those image blocks with PO

greater than Th1 are labeled 1. They are viewed as candidatetarget blocks, and the initial target set is described as

Ob ¼ ftjPOðtÞ > Th1; 1 � t � 81g; ð13Þwhere POðtÞ represents the probability of the t-th block thatis judged to be a target block, and t is the block index of theimage. To reduce the occurrences of missing detection andfalse alarm simultaneously, the threshold Th1 should not betoo large or too small.

2. Neighbor analysis. The blocks of the Ob set are eachtaken to be the center, and the 4-adjacent blocks are searchedand examined to supply auxiliary information for extendedjudgment. The probability of each neighbor block beingjudged as a smear block is computed with

PSðY ¼ 2jX1 . . .XnÞ ¼PðY ¼ 2Þ

Yk

PðXkjY ¼ 2ÞXj

PðY ¼ yjÞYk

PðXkjY ¼ yjÞ:

ð14ÞThe four neighboring blocks of the selected target block areshown in Fig. 5, which represents four typical distributionpatterns. The block labeled 1, 0, or 2 represents, respec-tively, the target block, the background block, or the smearblock. It is illustrated in Fig. 5(a) that the target resides inthe center area of the image block and the 4-adjacent blockshave no target or smear pixels. When the target is located atthe corner or edge of an image block, there are two or moreneighboring blocks possessing the same target simulta-neously. Figures 5(b) and 5(c) show these two patterns.Furthermore, Fig. 5(d) represents a distribution pattern inwhich a small part of the smear is misjudged as the target.That is to say, the central block, which is likely to be part ofthe smear block, is falsely judged as a target block in thepreliminary decision.

3. Pattern matching. The neighboring blocks are labeledfollowing the rules of Eq. (15), where tnb denotes the 4-adjacent blocks of the t-th block in the Ob set. The scale oftnb is usually 4, and the corresponding indexes of the 4-adjacent blocks are t � 1, t þ 1, t � 9, and t þ 9. If the targetis located at the corner or edge of the full image, the scale oftnb will be 2 or 3, which can be processed by the same rulesof Eq. (15).

SignðtnbÞ ¼1 if POðtnbÞ > Th1

2 if PSðtnbÞ > Th2

0 otherwise

:

8><>: ð15Þ

Here, Th1 sharing the same value as that in Eq. (13) is thethreshold of PO. If some block is not classified into the targetblock, this block will be regarded as a smear or backgroundblock, thus Th2 may be valued smaller than Th1. SignðtnbÞ isthe category label for one of the 4-adjacent blocks of the t-thtarget block, and the combination of all the SignðtnbÞ valuesof some target block will generate one distribution pattern ofFig. 5. If the distribution pattern is that in Fig. 5(a), it needsno processing. If it takes the pattern of Fig. 5(b) or 5(c), theneighboring target blocks are removed from the Ob set toeliminate the repetitive target. If it is that in Fig. 5(d), thet-th block, which is likely to be the smear block, is directlydeleted from the Ob set. After the secondary judgment, theupdated Ob set gives the indexes of the target blocks and thenumber of targets. It is always difficult to directly distinguisha true target from a smear corner. However, adopting themethods of secondary extraction and association analysis tosupply an auxiliary judgment, we complete the joint decisionand finally obtain a determined target set.

In Table 2, we summarize the entire procedure of theproposed JD-NB algorithm.

4. Experiment Results

4.1 Classification experimentIn order to fully demonstrate the robustness of our

proposed algorithm, we increase the difficulty of classifica-tion and specially select 30 typical test images for theclassification and recognition experiments. In these images,there are 21 images (70%) containing long or short smears,4 images (13%) having faint smears, 4 images (13%)possessing small and dim targets, 19 images (63%) havingsmears and targets simultaneously, and 13 images (43%)containing multiple targets. Due to the fact that there is anoverlapping region in image blocking, targets and smearsmay occur simultaneously in several neighboring imageblocks. According to the statistics, in these 2430 blocks fromthe 30 test images, there are 2286 background blocks, 101

1

0

00

0

1

0

10

0

1

0

10

1

1

0

20

0

(a) (b) (c) (d)

Fig. 5. Typical distribution patterns with target block at thecenter. The blocks labeled 1, 0, and 2 represent, respectively, thetarget block, the background block, and the smear block. (a) Thetarget resides at the center area of the image block. (b, c) The targetis located at the corners or edges of an image block. (d) The blockwith q small smear is mistaken for the target block, it will presentas (d). The digit 2 in (d) may be above or below or on the left orright side of the digit 1. Thus pattern (d) has 4 states, (b) and (c)also have 4 states, while (a) is only one state. In total, there are 4distribution patterns and 13 states.

OPTICAL REVIEW Vol. 21, No. 4 (2014)434 T. HUANG et al.

target blocks, and 43 smear blocks. Note that in thisexperiment, we only calculate the accuracy of classification.

Table 3 shows the classification probabilities of the threecategories of blocks with our method. The probability ofbackground blocks that are recognized correctly is very high.Nevertheless, the smear block and target block are a littleeasily classified as the background block. It indicates that theJD-NB may perform not so well in the detection of faintsmears and targets. The recognition rate of smear blocksis 0.7674, which is actually caused by the faint smearsappearing in the specially selected test images. At the sametime, the target and smear blocks are seldom mistaken foreach other, which indicates the result of discriminatingbetween the target and smear is satisfactory.

To further verify the validity of the JD-NB algorithm,several algorithms are selected to compare the recognitionrates, which are shown in Table 4. On one hand, the JD-NBalgorithm based on the NB theory is compared with the NB

with different Th1. The three groups of results for NB showthat decreasing the threshold can increase the probability oftarget blocks being correctly identified. Nevertheless, ithas no benefit for the valid identification of smear andbackground blocks. In addition, when the threshold risesfrom 0.8 to 0.85, the PO of target blocks decreasesconsiderably. In other words, the PO of those target blockspolluted by strong noise may mainly distribute between 0.8and 0.85. Therefore, Th1 related closely to the classificationresult is temperately taken as 0.75 in JD-NB, and Th2 is setto be 0.6. When the threshold decreases to a certain value,the risk of the smear and background blocks being classifiedas target blocks will increase. The JD-NB improves theperformance for the recognition of the smear block and

Table 3. Classification probability with JD-NB algorithm.

JD-NB Background Target Smear

Background 0.9987 0.0013 0Target 0.0792 0.9010 0.0198Smear 0.2093 0.0233 0.7674

Table 2. Procedure of the JD-NB algorithm.

Joint decision and Naive Bayes learning (JD-NB)

1. Input:Training set: I0 ¼ fI0agAa¼1, I

1 ¼ fI1bgBb¼1, I2 ¼ fI2c gCc¼1.

Test image: IT .2. Extract the feature vector X ¼ fX1; X2; X3; X4g from the training set with Eqs. (1)–(5),where X1 ¼ �g, X2 ¼ �2

g, X3 ¼ Sg, and X4 ¼ D.

3. Estimate the parameters b�kij and b�j of the NB classifier:

b�kij ¼]DfXk ¼ xki

VY ¼ yjg þ 1

]DfY ¼ yjg þM; b�j ¼

]DfY ¼ yjg þ 1

jDj þ J.

4. Estimate PO for each image block of IT :

POðY ¼ 1jX1 . . .XnÞ ¼PðY ¼ 1Þ

Yk

PðXkjY ¼ 1ÞXj

PðY ¼ yjÞYk

PðXkjY ¼ yjÞ.

5. Construct the target-block set:Ob ¼ ftjPOðtÞ > Th1; 1 � t � 81g.

6. Predicate PS for the 4-adjacent blocks of each target block in the Ob set:

PSðY ¼ 2jX1 . . .XnÞ ¼PðY ¼ 2Þ

Yk

PðXkjY ¼ 2ÞXj

PðY ¼ yjÞYk

PðXkjY ¼ yjÞ.

7. Label the 4-adjacent blocks above to built the distribution patterns in Fig. 5:

SignðtnbÞ1 if POðtnbÞ > Th1

2 if PSðtnbÞ > Th2

0 otherwise

8<: .

8. If the pattern resembles Fig. 5(b), 5(c), or 5(d), delete the corresponding target block tfrom the Ob set.

9. Output: Updated Ob set.

Table 4. Recognition rate of various methods.

Method Back-Back Target-Target Smear-Smear

RBF(0.004) 0.9562 0.8317 0.5333BP(0.001,8,12) 0.9827 0.8238 0.8557BP(0.001,9,16) 0.9808 0.8138 0.8325BP(0.001,12,20) 0.9829 0.8198 0.8372NB(0.85) 0.9987 0.7723 0.6511NB(0.80) 0.9987 0.8713 0.6511NB(0.75) 0.9987 0.9010 0.6511JD-NB(0.75) 0.9987 0.9010 0.7674

OPTICAL REVIEW Vol. 21, No. 4 (2014) 435T. HUANG et al.

maintains a satisfactory recognition rate of the target andbackground blocks. On the other hand, the JD-NB algorithmis compared with the neural network based method, which isalso a common learning algorithm. The two familiar neuralnets, Radial Basis Function (RBF) and Back Propagation(BP), are chosen in this experiment. The learning perfor-mances of these two neural nets, also known as the MeanSquared Error (MSE), are both set to approach theconvergence limit. According to the actual results ofexperiments, we find that the MSE of RBF converges toabout 0.004 and that of BP converges to about 0.001, thusthey are taken to be 0.004 and 0.001 respectively.Obviously, the RBF neural net is not expert in this problem,especially for the recognition of smear blocks. While the BPneural net with two hidden layers performs better, especiallythe recognition rate of smear block. The two values in theparentheses for BP in the table represent the numbers ofneurons in the two hidden layers. Note that all three of theseBP neural nets are tested five times to get the averageperformance. The only weakness of the BP neural net is thatthe recognition rate of target blocks is lower than the JD-NB,which reflects the shortage in the detection of small and fainttargets.

In realistic applications, we expect that the probabilities ofcorrect identification should be as high as possible, while thepossibilities of the smear and background blocks mistaken asthe target block should be as low as possible. Above all, theJD-NB and BP neural net have their own superiorities, andthe pattern matching methods of JD-NB effectively com-pensate the insufficiency of the classical NB in this issue.

4.2 Target detection experimentThe aim of this experiment is to test whether the improved

algorithm can recognize the true targets from the acquiredimage. Selecting 6 typical images, we employ the NBclassifier and joint decision method including the redundantprocessing to remove the repetitive target blocks. Theredundant processing is programmed to automaticallyextract the latter one of the reduplicative target blocks.Meanwhile, the number of true targets can also be providedat the end.

The boxes in Fig. 6 represent those initial targeted blocksdirectly using the NB and threshold determination. Thedigits beside the boxes denote the serial numbers of theblocks in one image. The block with a small portion ofsmear is easily judged to be the target block in the firstdecision, which is shown as the 58th block in Fig. 6(a), the60th block in Fig. 6(b) and the 50th block of Fig. 6(c). Whenrelying only on their own features, the problem cannot besolved well. However, by combining the joint decision andNB, the true target block can be correctly discriminated fromthe confusing smear block, which is shown in Figs. 7(a),7(b), and 7(c). Note that the point with a red ‘�’ is the targetblock finally identified. Sometimes the same target exists intwo or more blocks; in this case, we select the latter one.Additionally, Figs. 6(b), 6(c), 6(e), and 6(f) illustrate theability of multi-target detection. As long as the pixeldistances of multiple targets are larger than half the window

size, this algorithm is applicable. That is to say, two or moretargets should not appear in one window simultaneously intheory. Moreover, Fig. 6(f) demonstrates that our methodis also suited to the detection of small and faint targets.Comparing Fig. 6 with Fig. 7 carefully, we find that PO ofsome target blocks are close to 1 and some hover around 0.8.This indicates that the selection of the threshold is directlyrelated to the classification results. A high threshold resultsin missing detection and a low one causes false alarm.Therefore, the threshold should be checked carefully throughrepeated experiments.

The goal of electro-optical tracking systems is to realizethe positioning and tracking of space targets. In the DBTmethod, gate tracking is required after the appropriateclassification and recognition. In this paper, the usualprocedure is as follows. 1. Segment the target block. 2.Calculate the centroid of the target. 3. Locate the target inthe whole image according to the serial number of the targetblock. 4. Add a window to the target, and calculate the missdistance. 5. Correct the control quantity for the tracking

(a) (b)

(c) (d)

(e) (f)

40 41

58

32

41

53

60

41 42

50

81

41 42

32

4153

81

41 42

50 51

81

Fig. 6. (Color online) Target blocks preliminarily judged forthe 6 testing images. (a) Image 1, (b) Image 2, (c) Image 3, (d)Image 4, (e) Image 5, (f ) Image 6. In this paper, each image isdivided into 81 blocks and each block is judged with the NBclassifier. The target blocks, which are indicated by the greenboxes, are preliminarily extracted in the first decision of the JD-NB.

OPTICAL REVIEW Vol. 21, No. 4 (2014)436 T. HUANG et al.

platform. In single-target tracking (STT), we must furtherdiscriminate the current tracking target from the detectedmultiple targets. While in MTT, we usually adopt themethod of data correlation to determinate all the trajectories.Figure 8 shows the schematic of gate tracking for the 6 testimages with the above detection results, and we find that thetargets are all correctly identified.

4.3 Running time in MatlabGiven the recognition rates and detection examples, in this

subsection, we compare the running time of the BP neuralnet, NB, and JD-NB. All experiments are performed usingMatlab 7.11 (R2010b) on a PC with a dual-core 2.20GHzCPU, a 2GB RAM and Windows 7 operating system. Thesethree algorithms, which are all run 5 times to take theaverages, employ the same features, training samples, andtesting image as shown in Fig. 8(a). Table 5 shows thetraining time and the detection time. The detection timeincludes the time taken for feature extraction, classification,and post-processing. Note that the post-processing operationof JD-NB denotes the joint decision, while the post-processing steps of BP and NB are mainly redundantprocessing. It shows that the training time of BP neural net is

too time-consuming, while the calculation amount of NBlearning is much smaller. Meanwhile, the detection speed ofJD-NB is almost 5 times that of the BP neural net. Comparedwith NB, JD-NB requires longer running time but has betterdetection performance. Additionally, in the JD-NB algo-rithm, feature extraction expends 45.779ms, NB classifica-tion consumes 27.042ms and joint decision costs 36.953ms.

4.4 SNR analysisIf the target is small or dim, that is, the SNR of the image

is too low, our algorithm has a small quantity ofmisjudgment in target detection, as shown in Table 3. Thus,it is necessary to discuss the applicable range of the

0 20 40 60 80 1000

0.2

0.4

0.6

0.8

1

Serial number of 81 blocks

Targ

et −

blo

ck −

pro

babi

lity

PO

0 20 40 60 80 1000

0.2

0.4

0.6

0.8

1

Serial number of 81 blocks

Targ

et −

blo

ck −

pro

babi

lity

PO

0 20 40 60 80 1000

0.2

0.4

0.6

0.8

1

Serial number of 81 blocks

Targ

et −

blo

ck −

pro

babi

lity

PO

0 20 40 60 80 1000

0.2

0.4

0.6

0.8

1

Serial number of 81 blocks

Targ

et −

blo

ck −

pro

babi

lity

PO

0 20 40 60 80 1000

0.2

0.4

0.6

0.8

1

Serial number of 81 blocks

Targ

et −

blo

ck −

pro

babi

lity

PO

0 20 40 60 80 1000

0.2

0.4

0.6

0.8

1

Serial number of 81 blocks

Targ

et −

blo

ck −

pro

babi

lity

PO

(b)(a)

(d)(c)

(f)(e)

Fig. 7. (Color online) Results of true target-block recognition forthe 6 test images in Fig. 6 using the JD-NB algorithm. (a) Image 1,(b) Image 2, (c) Image 3, (d) Image 4, (e) Image 5, (f) Image 6.The probability of each block being judged as a target block isillustrated, and the point with a red ‘�’ denotes the target blockfinally identified. With the joint decision and pattern matching,some false targets and repetitive targets are deleted from theOb set.

(a) (b)

(c) (d)

(e) (f)

Fig. 8. (Color online) Target location for the 6 test imagesin Fig. 6 with the results of Fig. 7. (a) Image 1, (b) Image 2,(c) Image 3, (d) Image 4, (e) Image 5, (f ) Image 6. With the JD-NB algorithm, the true target blocks are singled out and thelocations are further calculated. The yellow boxes are the trackinggates of the targets.

Table 5. Running time in Matlab.

Method BP(8,12) NB JD-NB

Training (s) 213.599 0.897 0.897Detection (s) 0.570 0.072 0.110

OPTICAL REVIEW Vol. 21, No. 4 (2014) 437T. HUANG et al.

proposed JD-NB algorithm. Here we adopt the followingdefinition of image SNR:22)

SNR ¼ s� b

�; ð16Þ

where s means the signal intensity, b refers to thebackground intensity, and � is the standard deviation ofbackground intensity. 6 blocks with small and faint targetsare specially selected. Then we successively calculate theSNR and the probability PO. Figure 9 illustrates these 6target blocks, and Table 6 lists the results.

Targets such as those in Figs. 9(a)–9(d) can be correctlydetected, while Fig. 9(e) has a low probability of PO. Inother words, when the SNR of the target block is lower thanabout 0.014, the performance of this algorithm may declinesignificantly. But this rule is not so straightforward, andmultiple tests for the detection of diverse small targets showthat the faint target like that in Fig. 9(f) whose SNR is aslow as 0.0053 can sometimes be detected. The target inFig. 9(f ) seems small, but the undulation of the backgroundis small and the mean of the background is lower than thoseof other blocks. Meanwhile, owning to the undeterminedcalculation precision of the SNR, the detection error exists inour experiment. Moreover, the relationship between thedetection performance and the referenced definition of SNRis not very explicit. Thus, the SNR in Ref. 22 may be takenas one of the measures for reference only. There may besome unstable factors in our algorithm, but it performs wellin the detection of small and faint targets on most occasions.However, for the detection of dim point-like targets, astronger decision mechanism is required to reduce thehidden risks of missing detection and false-alarm. In thissituation, multi-frame detection may be more reliable thansingle-frame detection.

5. Conclusions and Future Work

For the purpose of space multi-target detection, we haveproposed the joint decision and pattern matching methods toimprove the result of the NB classifier, which enhance the

recognition precision and anti-interference capability. Com-pared with the neural network based algorithm, the JD-NBalgorithm is also a novel and efficient method for spacemulti-target detection. After establishing the sample libraryof satellite images, we design and train the NB classifier. Forthe feature selection, we employ the overall moments andpropose a high-efficiency feature of duty ratio referring tothe concept of digital circuits, which can distinguish betweenthe target and CCD smear well. Experiments demonstratethat the second extraction and pattern matching not onlyeffectively reduce the false alarm of short smears, but alsoensure a high recognition rate of better than 90% for thetarget. In addition, the performance of detecting small andfaint targets is favorable. Our method also can be applied tothe situation of multiple targets. However, if the multipletargets are too crowded, it is necessary to adopt the strategyof adaptive windows. In the JD-NB algorithm, we do notemploy a very complicated algorithm, but instead we try touse the classic NB and fewer features to save the runningtime. The main work of our method is offline processing andwe can train the model parameters of the classifier inadvance, which can be invoked directly in future applica-tions. The parameters may be updated periodically tomaintain a satisfactory status by inputting new trainingsamples. In the process of online identification, thecalculations are mostly additions and condition triggers,which can be readily implemented with the state machine offield programmable gate array (FPGA). Thus, there is a highpossibility of real-time detection.

However, this method may perform not so excellently inthe detection of dim point-like targets and is not so stable inextensive testing. Since the labeling of samples is manualand subjective, the training may be inadequate for thedetection of dim targets. Meanwhile, the selected featureshave some relationship with each other, but the NBalgorithm treats all the features as independent variables.The weighted NB may perform better. Additionally, sincethe NB is a supervised learning algorithm, the labeling ofsamples is time-consuming. In future work, we will includedifferent features and explore better training algorithms toimprove the ability and stability of small multi-targetdetection within a single image.

Acknowledgments

This work was supported in part by the National Natural ScienceFoundation (NSFC) of China under Grant No. 10978025. Theauthors gratefully acknowledge the constructive comments fromthe reviewers, which significantly improved the representation andquality of this paper. Thanks for the guidance of my advisorProfessor Xiong and the support of my colleagues.

References

1) D. J. Russomanno, S. Chari, E. L. Jacobs, and C. Halford:IEEE Sens. J. 10 (2010) 1106.

2) Y. Zhao: Proc. SPIE 5624 (2005) 686.3) M. Laas-Bourez, D. Coward, A. Klotz, and M. Boer: Adv.

Space Res. 47 (2011) 402.4) Y.-Y. Liu, Q.-B. Lu, and W.-X. Zhang: Acta Phys. Sin. 61

(2012) 124201.

Table 6. SNR analysis for the detection of small target.

Block

a b c d e f

SNR 0.0331 0.0190 0.0153 0.0146 0.0105 0.0053Po 0.9989 0.9989 0.9950 0.9989 0.1718 0.9993

(a) (b) (c) (d) (e) (f)

Fig. 9. The blocks with small targets in different sizes.(a) Block 1, (b) Block 2, (c) Block 3, (d) Block 4, (e) Block 5,(f ) Block 6. These image blocks are selected to study theapplication range of the small target detection with the JD-NBalgorithm.

OPTICAL REVIEW Vol. 21, No. 4 (2014)438 T. HUANG et al.

5) N. Baba, H. Tomita, and N. Miura: Opt. Rev. 1 (1994) 308.6) D. Wang, T. Zhang, and H. Kuang: Opt. Express 19 (2011)

4868.7) Y. S. Han, E. Choi, and M. G. Kang: IEEE Trans. Consum.

Electron. 55 (2009) 2287.8) N. Otsu: IEEE Trans. Syst. Man Cybern. 9 (1979) 62.9) H. F. Ng: Pattern Recognit. Lett. 27 (2006) 1644.10) S. G. Sun, D. M. Kwak, W. B. Jang, and D. J. Kim: IEEE Proc.

ISPA 9 (2005) 402.11) P. J. Kemper, Jr.: Proc. SPIE 3389 (1998) 84.12) W. He and L. Zhang: Innovative Algorithms Tech. Autom.,

Ind. Electron. Telecommun. 9 (2007) 493.13) Y. Boers, F. Ehlers, W. Koch, T. Luginbuhl, L. D. Stone, and

R. L. Streit: EURASIP J. Adv. Signal Process. 2008 (2008)413932.

14) W. Yi, L. Kong, and J. Yang: IEEE Proc. CISP 10 (2009)3769.

15) R. Succary, A. Cohen, P. Yaractzi, and S. R. Rotman: Proc.SPIE 4473 (2001) 96.

16) H. Wu, X. Li, Z. Li, and Y. Chen: Adv. Neural Networks 3972(2006) 442.

17) M. V. Shirvaikar and M. M. Trivedi: IEEE Trans. NeuralNetworks 6 (1995) 252.

18) T. M. Mitchel: Machine Learning (McGraw-Hill, New York,1997).

19) P. Domingos and M. Pazzani: Mach. Learn. 29 (1997) 103.20) F. Hroch: Exp. Astron. 9 (1999) 251.21) M. K. Hu: IEEE Trans. Inf. Theory 8 (1962) 179.22) Q. Yang: IEEE Proc. CMSP 5 (2011) 239.

OPTICAL REVIEW Vol. 21, No. 4 (2014) 439T. HUANG et al.