- Email: [email protected]
Complex background suppression based on fusion of morphological Open filter and nucleus similar pixels bilateral filter
Infrared Physics & Technology 55 (2012) 454–461
Contents lists available at SciVerse ScienceDirect
Infrared Physics & Technology journal homepage: www.elsevier.com/locate/infrared
Complex background suppression based on fusion of morphological Open filter and nucleus similar pixels bilateral filter Fei Zhao ⇑, Huanzhang Lu 1, Zhiyong Zhang 1, Shanzhu Xiao 1 National Key Laboratory of Automatic Target Recognition (ATR), National University of Defense Technology, Changsha, Hunan, PR China
h i g h l i g h t s " We present a background suppression scheme which fuse filters of different types. " We develop Nucleus Similarity Degree (NSD) which is a good descriptor in the fusion. " Suppression and enhancement can be achieved at the same time by the fusion. " Detection performance can be improved by the fusion. " Good structure which inherited from spatial filter is maintained.
a r t i c l e
i n f o
Article history: Received 28 March 2012 Available online 3 August 2012 Keywords: Background suppression Cluttered background Point target detection Fused prediction
a b s t r a c t To reduce the influences of the heavy clutter on infrared small target detection, a new background suppression algorithm is presented in this paper which depends on fusion of two different filters. The Nucleus Similarity Degree (NSD) of each pixel is analyzed first, then morphological Open filter which favors point target enhancement and the Nucleus Similar Pixels Bilateral Filter (NSPBF) which favors background prediction are fused. The complex background suppression and target enhancement can be accomplished more effectively by the fusion. Experimental results indicates that the method is efficient for background suppression under the condition of heavy clutter. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction Because of high sensitivity, good concealment and no limit for service time, infrared imaging technique is widely used in Automatic Target Recognition (ATR) weapon system. When targets are far from an infrared detector, they will be imaged as dim points, and the complex background clutters have a detrimental effect on the detection performance of point targets. In order to simplify this process, various background suppression algorithms have been proposed to weaken the influences of complex background clutters, and then the detection algorithms are used to detect the dim targets. Existing background suppression algorithm can be divided into two classes: (1) Multi-frame based algorithms [1,2]. Background pixels are often stationary in time domain, but the pixels which targets have passed are non-stationary. Thus, the background clut⇑ Corresponding author. Tel.: +86 13574112064 (m); fax: +86 07314576358. 1
E-mail address: [email protected] (F. Zhao). Tel.: +86 84575721.
1350-4495/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.infrared.2012.07.010
ters can be suppressed by subtracting the temporal filtered result. These algorithms are efficient for suppress the complex background, but targets with low velocity may be regarded as the background and suppressed. Furthermore, the vibration between consecutive frames makes the multi-frame based algorithms no longer applicable if no jitter compensation algorithms are included [2]. (2) Single frame based algorithms. These algorithms can also be divided into two classes: (a) Transformation domain based algorithms [3–5]. The original image is transformed to a different domain (such as frequency domain [3], wavelet domain [4] and IMFs [5]) at first, and then the background clutters in low-frequency band are filtered out. (b) Spatial filter based algorithms [6–11]. Similar to temporal filter based algorithms, these algorithms are based on the assumption that the background pixels are spatially correlated and target pixels are just the opposite, and the prediction of background can be obtained by a spatial filter. Transformation domain based algorithms can get considerable suppression results, but in ATR weapon systems, high frame-rate (larger than 60 Hz) means the computational efficiency must be considered. Transformation and inverse
455
F. Zhao et al. / Infrared Physics & Technology 55 (2012) 454–461
transformation are often time-consuming. By comparison, spatial-filter-based algorithms are more valuable in practical application. Some spatial-filter-based approaches have been developed to reduce the clutter background of the original image, such as TopHat [6], TDLMS [7,8] and kernel methods [9]. Although all these works are effective in some aspects, the prediction accuracy is degraded when the clutter is heavy. Bae et al. [10] proposed a new bilateral filter using the adaptive standard deviation based on the target similarity index (TSI) for background prediction, but the selection of background region in TSI calculation is difficult. Dong et al. [11] proposed a homogeneous background prediction algorithm (HBPA). The algorithm detects edges and recognizes different region (such as clouds, sky and edges of the clouds) first, and then the prior knowledge of the background will be utilized and different prediction schemes are used to predict the background. Although the algorithm obtains a better result, the processing is so complex that it is not suitable for parallel processing in ATR weapon systems. Accurate prediction of the background and practicability become the topics of spatial-filter-based complex background suppression. In this study, a complex background suppression algorithm which based on fusion of morphological Open filter and nucleus similar pixels bilateral filter is presented. The new approach calculates the Nucleus Similarity Degree (NSD) of each pixel, so the pixels can be classified first, and then morphological Open filter which favors point target enhancement and the Nucleus Similar Pixels Bilateral Filter (NSPBF) which favors background prediction are fused. Therefore we can predict the background more accurately as well as enhance the point target. Due to the pipelined and parallel structure, the method is suitable for parallel implementation in the ATR weapon systems. Experimental results indicate that the method works more effectively for suppression of background clutter. It can predict image details effectively and can reduces the adverse influence of edges in original images. The resulting detection performance is improved. This paper is organized as follows. Section 2 presents the background prediction model and the theory of the spatial-filter-based algorithms in detail. In Sections 3, after the definition of the Nucleus Similarity Degree, the combination of the two filters is given. Section 4 gives the experiment results of the algorithm, and Section 5 concludes the discussion.
2. Background prediction model and spatial-filter-based suppression algorithms An IR image which contains point targets and complex background clutters can be modeled as:
Gði; j; tÞ ¼ Bði; j; tÞ þ Noiseði; j; tÞ
ð1Þ
where G(i, j, t) is the gray value of pixel (i, j) at time t, (B(i, j, t) is the background energy plus the energy of point target, and
Bði; j; tÞ ¼
Bkði; j; tÞ þ T; target exist Bkði; j; tÞ;
target does not exist
ð2Þ
where T is the energy of target, Bk(i, j, t) is the energy of background; Noise(i, j, t) represents the Gauss noise which is defined as N(0, r2) (‘0’ represents mean value and r2 represents the variance). The spatial filter used for prediction can be divided into linear filters and nonlinear filters. When the linear spatial filter is applied to predict the background, each pixel is filtered by accumulating weighted pixels in the local area M N. For convenience, G(i, j, t) and B(i, j, t) are described as Gt(k) and Bt(k), in which 1 6 k 6 M N, and the weight of each pixel in the local area is wt(k) e {wt(1), wt(2), . . . , wt(M N)}. As modeled in (1), each b t ðkÞ weighted pixel obeys N(wt(k)B(k), (wt(k)r)2). Thus the result G of linear filter obeys
0 b t ðkÞÞNB Pð G @
PMN
k¼1 ½wt ðkÞBðkÞ ; PMN k¼1 wt ðkÞ
PMN
1
w2t ðkÞ 2C P 2 r A MN k¼1 wt ðkÞ k¼1
ð3Þ
in which we will get a maximum predict variance r2 when only one weight of wt(k) is equal to ‘1’ as well as the others are equal to ‘0’. When the variance of the prediction achieve the minimum r2/ (M N), we can find that wt(1) = wt(2) = = wt(M N) = 1/ (M N). In this case, all weights are invariant, which is the mean filter (U kernel filter) [9], and the predicted background is the mean value in the local area. This suppression scheme is local mean removal (LMR). LMR is an effective linear de-noising filter, but the prediction performance is poor when the background is complex. Similarly, the prediction ability in the complex background of other invariant weights linear filters (like E kernel filter [9]) are also limited. For the sake of getting accurate background prediction, another linear filter TDLMS [7,8] which adaptively updates the weights is applied.
Fig. 1. Architecture comparison of proposed algorithm and normal spatial background prediction algorithm.
456
F. Zhao et al. / Infrared Physics & Technology 55 (2012) 454–461
Although the variance of the prediction will be larger than the mean filter, the mean of prediction will get close to the real value. Linear filters which update weights adaptively will get a good prediction result. However, the linear combination of all pixels will contain the target energy more or less. Therefore when the predicted background is subtracted from the original image, it will also suppress the target. This is because the goal of linear filter based suppression is to predict the complex background accurately, and preserve the energy of target. In contrast to the linear filter, the nonlinear filter: morphological Open filter can enhance the energy of point targets effectively [6]. If the enhancement and prediction ability can be integrated in a single spatial-filter-based algorithm, we can predict the background accurately as well as enhance the targets effectively. Base on this idea, a novel IR complex background suppression algorithm is presented in this study. Firstly, Nucleus Similarity Degree (NSD) which is a measurement of similarity within local area is calculated, this will indicate the class (background or point targets) which the pixel belongs to, and then the output from two different filters are fused as the final prediction result. The architecture of the proposed algorithm and normal spatial filter based background suppression algorithms are shown in Fig. 1.
As shown in Fig. 2, the pixel which is to be predicted locates in the ith row and the jth column, the local area is defined as a M N window around pixel (i, j), pixel (i, j) is called Nucleus [12]. Nucleus Similarity Degree (NSD) indicates the similarity degree between Nucleus and the local area. Based on the features of complex background clutters in IR images, the NSD is evaluated by considering the following two aspects: (1) Gray value similarity. If the pixel (i, j) belongs to target, there will be few pixels with similar gray value in the local area. On the contrary, more pixels with similar gray value will appear around the background pixel. (2) Spatial distribution correlation. On the basis of gray similarity, background pixels are strong correlated in spatial distribution. Point targets are often presented as isolated points. Depending on aforementioned analysis, the pixels which possess similar gray and correlated spatial distribution with the Nucleus are called Nucleus Similar Pixels (NSPs) in this paper, and the NSD is defined as
Sði; jÞ ¼
XX disfði; jÞ; ðm; nÞg ccðm; nÞ m
3. Proposed method 3.1. Definition of NSD Except intensity information, it is hard to exploit other useful characteristics, such as features of shape and geometric structure, for point targets. Correlation difference between the background and point targets in local area is the foundation of spatial-filterbased algorithms. In this paper, we develop a new measurement of local area correlation for each pixel: the Nucleus Similarity Degree (NSD). Depending on the NSD, the pixels can be classed into background and points targets in general, and the appropriate filter can be used for different purpose. The NSD is defined as follows.
ð4Þ
n
in which, m e [i M/2,i + M/2], n e [j N/2, j + N/2], m and n are integers; dis{(i, j), (m, n)} represents the distance between pixel (m, n) and center pixel (i, j), it is used to measure the spatial distribution of pixel (m, n) .In this study, absolute distance is used as dis{(i, j), (m, n)} = |m i| + |n j|.cc(m, n) represents the connectivity between pixel (m, n) and the Nucleus, its value is ‘0’:disconnected or ‘1’:connected. Gray value similarity is the foundation of connectivity, the gray value similarity between (m, n) and the Nucleus is denoted as
Hðm; nÞ ¼
1; jGði; jÞ Gðm; nÞj < T g 0; jGði; jÞ Gðm; nÞj P T g
ð5Þ
where H(m, n) represents the gary value similarity(‘‘1’’:similar or ‘‘0’’:dissimilar); G(i, j) and G(m, n) represent gray value of pixel (i, j)
Fig. 2. Local area illustration.
F. Zhao et al. / Infrared Physics & Technology 55 (2012) 454–461
and (m, n), Tg represents the threshold, which dominates the rule of gray similarity in the local area, and the selection of Tg is directly related to the NSD calculation result. H(m, n) is the foundation of cc(m, n) in Eq. (4), this is because that connectivity only occurs between pixels with similar gray value. Judging connectivity between pixel (i, j) and (m, n) is complicated, connected component labeling algorithm is needed to label all the connected components in the local area. For simplifying the computation, we perform the connectivity decision as follows: assume that the local area is scanned as the dotted lines indicated. If (m, n) and Nucleus (i, j) are connected, there will exist at least one path which consists of similar gray pixels between them. Therefore, while a pixel is being scanned, the connectivity with adjacent pixels which are closer to (i, j) are used to decide the connectivity. As shown in Fig. 2, the gray squares denote the pixels with similar gray value. When (m1, n1) is being scanned, (m1 + 1, n1 1), (m1 1, n1 1) and (m1, n1 1) are used to for decision of connectivity, and the connectivity between (m1, n1) and (m1, n1 1) is obvious. Connectivity between (m1, n1 1) and (i, j) has been gotten when (m1, n1 1) was scanned (e.g. cc(m1, n1 1) = 1), so we get cc(m1, n1) = 1; When the corner pixels (like (m3, n3)(m4, n4)(m5, n5) and (m6, n6)) are being scanned, the diagonal pixels (like cc(m3 + 1, n3 + 1), cc(m4 1, n4 + 1), cc(m5 1, n5 1) and cc(m6 + 1, n6 1)) are used for connectivity decision. The definition of NSD accords with the visual sense of human. According to Eq. (4), a smaller NSD value will be obtained for point
457
targets in comparison with the background, so we can use appropriate filter to predict the background and enhance the point targets. In the calculation of NSD, Tg in Eq. (5) is an important parameter, a larger Tg will decrease the probability of identifying the point targets as well as increase the probability of identifying the background pixels, and a smaller Tg will perform by contraries. So, finding a right Tg adaptively is important for the algorithm. In this paper, we consider G0 ði; jÞ ¼ jGði; jÞ Gðm; nÞj is a new image in the local area, and selection of Tg can be interpreted as finding a good threshold for the classification of G0 (i, j). So, classification algorithms can be used to determine Tg. In this study, Otsu [13] algorithm which maximizes the between-class variance is chosen to determine the Tg adaptively. Choosing M = N = 9, an NSD image for complex background IR image is shown in Fig. 3. The column (b) is the local original image (41 41 pixels) around the target and the corresponding NSD image. The column (a) is the original image and the corresponding NSD image, and the target is indicated with the black square. As shown in Fig. 3, the dim point target gets a small NSD value, the background, as well as the edges, get a larger NSD relatively. Some noises may also get a small NSD, and they may become false alarms after the thresholding, but most of them can be excluded by trajectory detection due to discontinuity in image sequences. Depending on NSD, background pixels and target pixels can be identified, so results of different filters can be fused depending on NSD.
Fig. 3. NSD of complex background IR image.
458
F. Zhao et al. / Infrared Physics & Technology 55 (2012) 454–461
Fig. 4. (a) NSPBF prediction result. (b) NSPBF suppression result. (c) Morphological Open filter prediction result. (d) Morphological Open filter suppression result. (e) Prediction result of proposed algorithm. (f) Suppression result of proposed algorithm.
3.2. Fusion of prediction In this paper, two different filters are chosen, one is Nucleus Similar Pixels Bilateral Filter (NSPBF), which is suitable for background prediction, and the other is nonlinear morphological Open filter, which is suitable for point targets enhancement. The bilateral filter [14] is defined as
bp ¼ G
X Wðp; qÞGq q2K
d ðp;qÞ Wðp; qÞ ¼ PW r ðp;qÞW W ðp;qÞW ðp;qÞ q2K
r
ð6Þ
d
in which W r ¼ expððGp Gq Þ2 =ð2d2r ÞÞ, W d ¼ expð½ðyp yq Þ2 þðxp xq Þ2 =ð2d2d ÞÞ; Gp and Gq denote the gray value of pixel p and q, K is the local area of pixel p, (xp, yp) and (xq, yq) denote the coordinates of pixel p and qdr and dd are decay parameters. In contrast with the classical Gauss low pass filter, the neighboring pixels are weighted according to the distance as well as the gray value, and the edges can be predicted accurately. In this study, the nucleus similar pixels in local area have been located in the NSD calculation step, so the bilateral filter can only work on NSPs(that means q e NSPs in Eq. (6)), this will obtain a more accurate prediction for the background pixels comparing with
the filter which is worked with all the pixels. Assuming the filter result is F1(i, j), where (i, j) denotes the coordinate of p in Eq. (6). When dr and dd have small values, nearer pixels with more approximate gray values are used to predict the background. Depending on the function of Tg, we can know that the bound of (Gp Gq) in NSP is [0, Tg], so the dr can be set according to Tg to keep an small value adaptively, and dr = Tg/2, dd = 1 are chosen for the decay parameters in this paper. The morphological Open filter is defined as F2(i, j) = max(x,y){2(i, j) = max(x,y){min(x,y)[G(i x, j y) + se(x, y)]}, where se(x, y) is the predefined structure element. Depending on the NSD of each pixel, the final output F(i, j) are fused as
Fði; jÞ ¼ w1 F 1 ði; jÞ þ w2 F 2 ði; jÞ
ð7Þ
where w1 and w2 are weights, and w1 + w2 = 1. When the NSD value S(i, j) of pixel (i, j) is large, it indicates that pixel (i, j) is likely to be background clutters, and w1 should be greater than w2; On the contrary, pixel (i, j) is likely to be point targets, and w2 should be greater than w1. When the NSD distributes in an ambiguous range, w1 and w2 should results in a tradeoff between accurate prediction and target enhancement. In this paper, w1, w2 and F(i, j) are defined as:
F. Zhao et al. / Infrared Physics & Technology 55 (2012) 454–461
459
Fig. 5. Structure of proposed method.
2 w2 ¼ exp Sr2ði;jÞ ; NSD
w1 ¼ 1 w2 ; 2 Fði; jÞ ¼ exp Sr2ði;jÞ ðF 2 ði; jÞ F 1 ði; jÞÞ þ F 1 ði; jÞ;
ð8Þ
parallel. Due to the pipeline and parallel structure, the proposed algorithm is suitable for parallel implementation in the ATR systems.
NSD
As described in Eq. (4), S(i, j) is the NSD value of pixel (i, j).In Eq. (8), the weight w1 is a Gauss function of S(i, j) ,in which rNSD is the standard deviation, which controls the decay speed the function, if rNSD is very small, only the pixels with small NSD will be enhanced as point targets, and the others will be suppressed as the background. Because the energy of the point target may be distributed to several neighboring pixels, rNSD is chosen as 10 by considering the robustness of algorithm. It means that if the NSD of a pixel is 10, the probability that the pixel belongs to the point target is about 0.37, and the probability that the pixel belongs to the background is about 0.63. Finally, the background suppression can be accomplished as R(i, j) = G(i, j) F(i, j), R(i, j) is the residual image. The prediction and suppression results of Fig. 3a are shown in Fig. 4. As shown in Fig. 4a indicates the prediction result of NSPBF, (b) indicates the suppression result of NSPBF, (c) indicates the prediction result of morphological Open filter, (d) indicates the suppression result of morphological Open filter (e) indicates fused prediction result and (f) indicates corresponding suppression result of (e). From Fig. 4, we can see that both the background and the point target are predicted very well by NSPBF, so the target is vanished in (b). Morphological Open filter enhance the targets as well as the sharp edges in the image. The fusion of the two filters can both predict the background accurately as well as enhance the targets, and the variance and false alarms are much lower than (d). The proposed algorithm is summarized and the architecture is shown in Fig. 5. In which, the streamed image data are fed into the buffer to obtain the local area image data in the first step, then the threshold Tg is obtained in the second step. In the third step, the gray similarity of the pixels in local area is calculated. In the fourth step, the NSD is calculated as well as the NSPBF and morphological Open filter are performed. At last, the results of NSPBF and morphological Open filter are fused according to (8). Some delay modules are needed to keep the data synchronized in the whole processing. In Fig. 5, we can find the whole pipeline structure of the method, and in each step, operations can be implemented in
4. Experimental results To verify our algorithm, we took many infrared image sequences with different background for trials, and three representative sequences with different complex IR background are selected for the discussion. They are shown in Fig. 6 and each of them represents different heavily cluttered background (such as clouds in (a), sea, sky and ground clutters in (b), and ground clutters in (c)), the point targets are indicated by squares. In Fig. 6a is from the Air Force Rome Laboratory, (b) and (c) were captured by different long-ware IR detectors, these images have different blank area, so we cut them to the same size 235 300 in the experiment. A good background clutter suppression algorithm should eliminate clutter component and enhance the target signal. From this point of view, the gain of standard deviation (Gain(r) = 20 log(rout/rin),rout is the standard deviation of residual image, rin is the standard deviation of original image)should be minimized and the gain of Signal-to-Clutter-Ratio (SCR) (Gain(SCR) = 20 log(SCRout/SCRin)) should be maximized, which SCR is defined as SCR = (T m)/r, T is the gray value of target, m is the mean value, r is the standard deviation. In view of the original image is heavily cluttered, SCRin is calculated in 9 9 local area around target in original image, the SCRout is calculated in the whole residual image. Gain(r) and Gain(SCR) are analyzed in the each frame of three sequences and the average are shown in Table 1. All of our results obtained by the proposed approach are compared with those of the TDLMS filter and the TopHat filter. The results of different targets which are indicated by black square and white square in Fig. 6a are separated by ‘/’ respectively. From Table 1, we can see that in sequence (a) performance of TDLMS and TopHat degraded. By comparison, the proposed method got better performance in all the cases. It dues to that the new approach can adaptively choose approximate filter depending on NSD, this will satisfy different demands for both background pixels and target pixels.
460
F. Zhao et al. / Infrared Physics & Technology 55 (2012) 454–461 Table 1 Experiment results of six image sequences. Image sequences
SCRin
rin
Algorithms
Gain(SCR)
Gain(r)
(a)
2.5/4.2
39.45
TDLMS TopHat Proposed
2.32/2.65 2.41/0.65 13.44/10.55
19.15 18.75 25.75
(b)
1.9
70.30
TDLMS TopHat Proposed
13.03 7.20 14.68
29.65 20.8 29.94
(c)
1.21
44.24
TDLMS TopHat Proposed
12.39 12.9 19.5
26.84 22.9 30.01
Fig. 7. Comparison of detection performance.
algorithm, TDLMS and TopHat are shown in Fig. 7. It is obvious that the new method had a much larger detection probability in most cases. All the experiment results show that the proposed algorithm can suppress the cluttered background more effectively.
5. Conclusion A new complex background suppression algorithm is proposed in this paper. Compared with single filter based algorithms, the proposed method analyzes the nucleus similarity degree first, then the strong points of morphological Open filter and Nucleus Similar Pixels Bilateral Filter (NSPBF) are combined. The trick produces a more accurate prediction result that aids clutter subtraction through considering choosing appropriate filters and fusion of prediction results. The pipeline and parallel structure benefits the implementation in real-time ATR weapon systems. Experimental results indicated that the method works well for suppression of background clutter and enhancement of the targets, and the detection performance at low SCR is also improved.
References Fig. 6. Original image in the sequences.
The detection performance of the proposed algorithm was also verified in the experiment. Because the number of targets is finite in these sequences, to obtain more common data, we inserted 50 one pixel synthetic targets for processing, the synthetic targets are randomly distributed in the image, and the values of SCRin are randomly chosen from the range (2.0, 3.0). Because the position and energy of synthetic targets are random, we take image (c) for example in this experiment, and the number of simulation times is 20. The receiver operating characteristics (ROC) of the proposed
[1] B. Wang, D. Liu, J. Zhang, Temporal filtering for target detection algorithm based on static background elimination, Journal on Communications 30 (2009) 67–72. [2] A. Tartakovsky, R. Blazek, Effective adaptive spatial–temporal technique for clutter rejection in IRST, SPIE Proceedings: Signal and data processing of small targets 4048 (2000) 85–95. [3] L. Yang, J. Yang, K. Yang, Adaptive detection for infrared small target under sea–sky complex background, Electronics Letters 40 (2004) 1083–1085. [4] W. Wang, B. Han, H. Zhang, A new algorithm of small target detection for infrared image in background of sea and sky, Acta Photonica Sinica 38 (2009) 725–728. [5] H. Deng, J.G. Liu, Z. Chen, Infrared small target detection based on modified local entropy and EMD, Chinese Optics Letters 8 (2010) 24–28. [6] F. Zhang, C. Li, L. Shi, Detecting and tracking dim moving point target in IR image sequence, Infrared Physics & Technology 46 (2005) 323–328.
F. Zhao et al. / Infrared Physics & Technology 55 (2012) 454–461 [7] T. Soni, J. Zeidler, Performance evaluation of 2-D adaptive prediction filters for detection of small objects in image data, IEEE Transaction on Image Processing 2 (1993) 327–340. [8] H. Zhu, Y. Zhao, Detection of weak and small moving infrared targets by adaptive prediction of background, Journal of Infrared Millimeter Waves 18 (1999) 305–310. [9] H. Askar, X. Li, Z. Li, Background clutter suppression and dim moving point targets detection using nonparametric method, in: Proceedings of IEEE 2002 International Conference on Communications, Circuits and Systems and West Sino Expositions, vol. 2, 2002, pp.982–986. [10] T.W. Bae, S.H. Lee, K.I. Sohng, Small target detection using the bilateral filter based on target similarity index, IEICE Electronics Express 7 (2010) 589–595.
461
[11] Wei-ke Dong, Jian-qi Zhang, Ding-ding Yang, De-lian Liu, Homogeneous background prediction algorithm for detection of point target, Infrared Physics & Technology 54 (2011) 70–74. [12] S.M. Smith, J.M. Brady, SUSAN—a new approach to low level image processing, International Journal of Computer Vision 1 (1997) 45–78. [13] N. Otsu, A threshold selection method from gray-level histograms, IEEE Transactions on Systems Man and Cybernetics 1 (1979) 62–66. [14] C. Tomasi, R. Manduchi, Bilateral filtering for gray and color images, in: Proceedings of 6th IEEE International Conference on Computer Vision, 1998, pp. 839–846.
Contents lists available at SciVerse ScienceDirect
Infrared Physics & Technology journal homepage: www.elsevier.com/locate/infrared
Complex background suppression based on fusion of morphological Open filter and nucleus similar pixels bilateral filter Fei Zhao ⇑, Huanzhang Lu 1, Zhiyong Zhang 1, Shanzhu Xiao 1 National Key Laboratory of Automatic Target Recognition (ATR), National University of Defense Technology, Changsha, Hunan, PR China
h i g h l i g h t s " We present a background suppression scheme which fuse filters of different types. " We develop Nucleus Similarity Degree (NSD) which is a good descriptor in the fusion. " Suppression and enhancement can be achieved at the same time by the fusion. " Detection performance can be improved by the fusion. " Good structure which inherited from spatial filter is maintained.
a r t i c l e
i n f o
Article history: Received 28 March 2012 Available online 3 August 2012 Keywords: Background suppression Cluttered background Point target detection Fused prediction
a b s t r a c t To reduce the influences of the heavy clutter on infrared small target detection, a new background suppression algorithm is presented in this paper which depends on fusion of two different filters. The Nucleus Similarity Degree (NSD) of each pixel is analyzed first, then morphological Open filter which favors point target enhancement and the Nucleus Similar Pixels Bilateral Filter (NSPBF) which favors background prediction are fused. The complex background suppression and target enhancement can be accomplished more effectively by the fusion. Experimental results indicates that the method is efficient for background suppression under the condition of heavy clutter. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction Because of high sensitivity, good concealment and no limit for service time, infrared imaging technique is widely used in Automatic Target Recognition (ATR) weapon system. When targets are far from an infrared detector, they will be imaged as dim points, and the complex background clutters have a detrimental effect on the detection performance of point targets. In order to simplify this process, various background suppression algorithms have been proposed to weaken the influences of complex background clutters, and then the detection algorithms are used to detect the dim targets. Existing background suppression algorithm can be divided into two classes: (1) Multi-frame based algorithms [1,2]. Background pixels are often stationary in time domain, but the pixels which targets have passed are non-stationary. Thus, the background clut⇑ Corresponding author. Tel.: +86 13574112064 (m); fax: +86 07314576358. 1
E-mail address: [email protected] (F. Zhao). Tel.: +86 84575721.
1350-4495/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.infrared.2012.07.010
ters can be suppressed by subtracting the temporal filtered result. These algorithms are efficient for suppress the complex background, but targets with low velocity may be regarded as the background and suppressed. Furthermore, the vibration between consecutive frames makes the multi-frame based algorithms no longer applicable if no jitter compensation algorithms are included [2]. (2) Single frame based algorithms. These algorithms can also be divided into two classes: (a) Transformation domain based algorithms [3–5]. The original image is transformed to a different domain (such as frequency domain [3], wavelet domain [4] and IMFs [5]) at first, and then the background clutters in low-frequency band are filtered out. (b) Spatial filter based algorithms [6–11]. Similar to temporal filter based algorithms, these algorithms are based on the assumption that the background pixels are spatially correlated and target pixels are just the opposite, and the prediction of background can be obtained by a spatial filter. Transformation domain based algorithms can get considerable suppression results, but in ATR weapon systems, high frame-rate (larger than 60 Hz) means the computational efficiency must be considered. Transformation and inverse
455
F. Zhao et al. / Infrared Physics & Technology 55 (2012) 454–461
transformation are often time-consuming. By comparison, spatial-filter-based algorithms are more valuable in practical application. Some spatial-filter-based approaches have been developed to reduce the clutter background of the original image, such as TopHat [6], TDLMS [7,8] and kernel methods [9]. Although all these works are effective in some aspects, the prediction accuracy is degraded when the clutter is heavy. Bae et al. [10] proposed a new bilateral filter using the adaptive standard deviation based on the target similarity index (TSI) for background prediction, but the selection of background region in TSI calculation is difficult. Dong et al. [11] proposed a homogeneous background prediction algorithm (HBPA). The algorithm detects edges and recognizes different region (such as clouds, sky and edges of the clouds) first, and then the prior knowledge of the background will be utilized and different prediction schemes are used to predict the background. Although the algorithm obtains a better result, the processing is so complex that it is not suitable for parallel processing in ATR weapon systems. Accurate prediction of the background and practicability become the topics of spatial-filter-based complex background suppression. In this study, a complex background suppression algorithm which based on fusion of morphological Open filter and nucleus similar pixels bilateral filter is presented. The new approach calculates the Nucleus Similarity Degree (NSD) of each pixel, so the pixels can be classified first, and then morphological Open filter which favors point target enhancement and the Nucleus Similar Pixels Bilateral Filter (NSPBF) which favors background prediction are fused. Therefore we can predict the background more accurately as well as enhance the point target. Due to the pipelined and parallel structure, the method is suitable for parallel implementation in the ATR weapon systems. Experimental results indicate that the method works more effectively for suppression of background clutter. It can predict image details effectively and can reduces the adverse influence of edges in original images. The resulting detection performance is improved. This paper is organized as follows. Section 2 presents the background prediction model and the theory of the spatial-filter-based algorithms in detail. In Sections 3, after the definition of the Nucleus Similarity Degree, the combination of the two filters is given. Section 4 gives the experiment results of the algorithm, and Section 5 concludes the discussion.
2. Background prediction model and spatial-filter-based suppression algorithms An IR image which contains point targets and complex background clutters can be modeled as:
Gði; j; tÞ ¼ Bði; j; tÞ þ Noiseði; j; tÞ
ð1Þ
where G(i, j, t) is the gray value of pixel (i, j) at time t, (B(i, j, t) is the background energy plus the energy of point target, and
Bði; j; tÞ ¼
Bkði; j; tÞ þ T; target exist Bkði; j; tÞ;
target does not exist
ð2Þ
where T is the energy of target, Bk(i, j, t) is the energy of background; Noise(i, j, t) represents the Gauss noise which is defined as N(0, r2) (‘0’ represents mean value and r2 represents the variance). The spatial filter used for prediction can be divided into linear filters and nonlinear filters. When the linear spatial filter is applied to predict the background, each pixel is filtered by accumulating weighted pixels in the local area M N. For convenience, G(i, j, t) and B(i, j, t) are described as Gt(k) and Bt(k), in which 1 6 k 6 M N, and the weight of each pixel in the local area is wt(k) e {wt(1), wt(2), . . . , wt(M N)}. As modeled in (1), each b t ðkÞ weighted pixel obeys N(wt(k)B(k), (wt(k)r)2). Thus the result G of linear filter obeys
0 b t ðkÞÞNB Pð G @
PMN
k¼1 ½wt ðkÞBðkÞ ; PMN k¼1 wt ðkÞ
PMN
1
w2t ðkÞ 2C P 2 r A MN k¼1 wt ðkÞ k¼1
ð3Þ
in which we will get a maximum predict variance r2 when only one weight of wt(k) is equal to ‘1’ as well as the others are equal to ‘0’. When the variance of the prediction achieve the minimum r2/ (M N), we can find that wt(1) = wt(2) = = wt(M N) = 1/ (M N). In this case, all weights are invariant, which is the mean filter (U kernel filter) [9], and the predicted background is the mean value in the local area. This suppression scheme is local mean removal (LMR). LMR is an effective linear de-noising filter, but the prediction performance is poor when the background is complex. Similarly, the prediction ability in the complex background of other invariant weights linear filters (like E kernel filter [9]) are also limited. For the sake of getting accurate background prediction, another linear filter TDLMS [7,8] which adaptively updates the weights is applied.
Fig. 1. Architecture comparison of proposed algorithm and normal spatial background prediction algorithm.
456
F. Zhao et al. / Infrared Physics & Technology 55 (2012) 454–461
Although the variance of the prediction will be larger than the mean filter, the mean of prediction will get close to the real value. Linear filters which update weights adaptively will get a good prediction result. However, the linear combination of all pixels will contain the target energy more or less. Therefore when the predicted background is subtracted from the original image, it will also suppress the target. This is because the goal of linear filter based suppression is to predict the complex background accurately, and preserve the energy of target. In contrast to the linear filter, the nonlinear filter: morphological Open filter can enhance the energy of point targets effectively [6]. If the enhancement and prediction ability can be integrated in a single spatial-filter-based algorithm, we can predict the background accurately as well as enhance the targets effectively. Base on this idea, a novel IR complex background suppression algorithm is presented in this study. Firstly, Nucleus Similarity Degree (NSD) which is a measurement of similarity within local area is calculated, this will indicate the class (background or point targets) which the pixel belongs to, and then the output from two different filters are fused as the final prediction result. The architecture of the proposed algorithm and normal spatial filter based background suppression algorithms are shown in Fig. 1.
As shown in Fig. 2, the pixel which is to be predicted locates in the ith row and the jth column, the local area is defined as a M N window around pixel (i, j), pixel (i, j) is called Nucleus [12]. Nucleus Similarity Degree (NSD) indicates the similarity degree between Nucleus and the local area. Based on the features of complex background clutters in IR images, the NSD is evaluated by considering the following two aspects: (1) Gray value similarity. If the pixel (i, j) belongs to target, there will be few pixels with similar gray value in the local area. On the contrary, more pixels with similar gray value will appear around the background pixel. (2) Spatial distribution correlation. On the basis of gray similarity, background pixels are strong correlated in spatial distribution. Point targets are often presented as isolated points. Depending on aforementioned analysis, the pixels which possess similar gray and correlated spatial distribution with the Nucleus are called Nucleus Similar Pixels (NSPs) in this paper, and the NSD is defined as
Sði; jÞ ¼
XX disfði; jÞ; ðm; nÞg ccðm; nÞ m
3. Proposed method 3.1. Definition of NSD Except intensity information, it is hard to exploit other useful characteristics, such as features of shape and geometric structure, for point targets. Correlation difference between the background and point targets in local area is the foundation of spatial-filterbased algorithms. In this paper, we develop a new measurement of local area correlation for each pixel: the Nucleus Similarity Degree (NSD). Depending on the NSD, the pixels can be classed into background and points targets in general, and the appropriate filter can be used for different purpose. The NSD is defined as follows.
ð4Þ
n
in which, m e [i M/2,i + M/2], n e [j N/2, j + N/2], m and n are integers; dis{(i, j), (m, n)} represents the distance between pixel (m, n) and center pixel (i, j), it is used to measure the spatial distribution of pixel (m, n) .In this study, absolute distance is used as dis{(i, j), (m, n)} = |m i| + |n j|.cc(m, n) represents the connectivity between pixel (m, n) and the Nucleus, its value is ‘0’:disconnected or ‘1’:connected. Gray value similarity is the foundation of connectivity, the gray value similarity between (m, n) and the Nucleus is denoted as
Hðm; nÞ ¼
1; jGði; jÞ Gðm; nÞj < T g 0; jGði; jÞ Gðm; nÞj P T g
ð5Þ
where H(m, n) represents the gary value similarity(‘‘1’’:similar or ‘‘0’’:dissimilar); G(i, j) and G(m, n) represent gray value of pixel (i, j)
Fig. 2. Local area illustration.
F. Zhao et al. / Infrared Physics & Technology 55 (2012) 454–461
and (m, n), Tg represents the threshold, which dominates the rule of gray similarity in the local area, and the selection of Tg is directly related to the NSD calculation result. H(m, n) is the foundation of cc(m, n) in Eq. (4), this is because that connectivity only occurs between pixels with similar gray value. Judging connectivity between pixel (i, j) and (m, n) is complicated, connected component labeling algorithm is needed to label all the connected components in the local area. For simplifying the computation, we perform the connectivity decision as follows: assume that the local area is scanned as the dotted lines indicated. If (m, n) and Nucleus (i, j) are connected, there will exist at least one path which consists of similar gray pixels between them. Therefore, while a pixel is being scanned, the connectivity with adjacent pixels which are closer to (i, j) are used to decide the connectivity. As shown in Fig. 2, the gray squares denote the pixels with similar gray value. When (m1, n1) is being scanned, (m1 + 1, n1 1), (m1 1, n1 1) and (m1, n1 1) are used to for decision of connectivity, and the connectivity between (m1, n1) and (m1, n1 1) is obvious. Connectivity between (m1, n1 1) and (i, j) has been gotten when (m1, n1 1) was scanned (e.g. cc(m1, n1 1) = 1), so we get cc(m1, n1) = 1; When the corner pixels (like (m3, n3)(m4, n4)(m5, n5) and (m6, n6)) are being scanned, the diagonal pixels (like cc(m3 + 1, n3 + 1), cc(m4 1, n4 + 1), cc(m5 1, n5 1) and cc(m6 + 1, n6 1)) are used for connectivity decision. The definition of NSD accords with the visual sense of human. According to Eq. (4), a smaller NSD value will be obtained for point
457
targets in comparison with the background, so we can use appropriate filter to predict the background and enhance the point targets. In the calculation of NSD, Tg in Eq. (5) is an important parameter, a larger Tg will decrease the probability of identifying the point targets as well as increase the probability of identifying the background pixels, and a smaller Tg will perform by contraries. So, finding a right Tg adaptively is important for the algorithm. In this paper, we consider G0 ði; jÞ ¼ jGði; jÞ Gðm; nÞj is a new image in the local area, and selection of Tg can be interpreted as finding a good threshold for the classification of G0 (i, j). So, classification algorithms can be used to determine Tg. In this study, Otsu [13] algorithm which maximizes the between-class variance is chosen to determine the Tg adaptively. Choosing M = N = 9, an NSD image for complex background IR image is shown in Fig. 3. The column (b) is the local original image (41 41 pixels) around the target and the corresponding NSD image. The column (a) is the original image and the corresponding NSD image, and the target is indicated with the black square. As shown in Fig. 3, the dim point target gets a small NSD value, the background, as well as the edges, get a larger NSD relatively. Some noises may also get a small NSD, and they may become false alarms after the thresholding, but most of them can be excluded by trajectory detection due to discontinuity in image sequences. Depending on NSD, background pixels and target pixels can be identified, so results of different filters can be fused depending on NSD.
Fig. 3. NSD of complex background IR image.
458
F. Zhao et al. / Infrared Physics & Technology 55 (2012) 454–461
Fig. 4. (a) NSPBF prediction result. (b) NSPBF suppression result. (c) Morphological Open filter prediction result. (d) Morphological Open filter suppression result. (e) Prediction result of proposed algorithm. (f) Suppression result of proposed algorithm.
3.2. Fusion of prediction In this paper, two different filters are chosen, one is Nucleus Similar Pixels Bilateral Filter (NSPBF), which is suitable for background prediction, and the other is nonlinear morphological Open filter, which is suitable for point targets enhancement. The bilateral filter [14] is defined as
bp ¼ G
X Wðp; qÞGq q2K
d ðp;qÞ Wðp; qÞ ¼ PW r ðp;qÞW W ðp;qÞW ðp;qÞ q2K
r
ð6Þ
d
in which W r ¼ expððGp Gq Þ2 =ð2d2r ÞÞ, W d ¼ expð½ðyp yq Þ2 þðxp xq Þ2 =ð2d2d ÞÞ; Gp and Gq denote the gray value of pixel p and q, K is the local area of pixel p, (xp, yp) and (xq, yq) denote the coordinates of pixel p and qdr and dd are decay parameters. In contrast with the classical Gauss low pass filter, the neighboring pixels are weighted according to the distance as well as the gray value, and the edges can be predicted accurately. In this study, the nucleus similar pixels in local area have been located in the NSD calculation step, so the bilateral filter can only work on NSPs(that means q e NSPs in Eq. (6)), this will obtain a more accurate prediction for the background pixels comparing with
the filter which is worked with all the pixels. Assuming the filter result is F1(i, j), where (i, j) denotes the coordinate of p in Eq. (6). When dr and dd have small values, nearer pixels with more approximate gray values are used to predict the background. Depending on the function of Tg, we can know that the bound of (Gp Gq) in NSP is [0, Tg], so the dr can be set according to Tg to keep an small value adaptively, and dr = Tg/2, dd = 1 are chosen for the decay parameters in this paper. The morphological Open filter is defined as F2(i, j) = max(x,y){2(i, j) = max(x,y){min(x,y)[G(i x, j y) + se(x, y)]}, where se(x, y) is the predefined structure element. Depending on the NSD of each pixel, the final output F(i, j) are fused as
Fði; jÞ ¼ w1 F 1 ði; jÞ þ w2 F 2 ði; jÞ
ð7Þ
where w1 and w2 are weights, and w1 + w2 = 1. When the NSD value S(i, j) of pixel (i, j) is large, it indicates that pixel (i, j) is likely to be background clutters, and w1 should be greater than w2; On the contrary, pixel (i, j) is likely to be point targets, and w2 should be greater than w1. When the NSD distributes in an ambiguous range, w1 and w2 should results in a tradeoff between accurate prediction and target enhancement. In this paper, w1, w2 and F(i, j) are defined as:
F. Zhao et al. / Infrared Physics & Technology 55 (2012) 454–461
459
Fig. 5. Structure of proposed method.
2 w2 ¼ exp Sr2ði;jÞ ; NSD
w1 ¼ 1 w2 ; 2 Fði; jÞ ¼ exp Sr2ði;jÞ ðF 2 ði; jÞ F 1 ði; jÞÞ þ F 1 ði; jÞ;
ð8Þ
parallel. Due to the pipeline and parallel structure, the proposed algorithm is suitable for parallel implementation in the ATR systems.
NSD
As described in Eq. (4), S(i, j) is the NSD value of pixel (i, j).In Eq. (8), the weight w1 is a Gauss function of S(i, j) ,in which rNSD is the standard deviation, which controls the decay speed the function, if rNSD is very small, only the pixels with small NSD will be enhanced as point targets, and the others will be suppressed as the background. Because the energy of the point target may be distributed to several neighboring pixels, rNSD is chosen as 10 by considering the robustness of algorithm. It means that if the NSD of a pixel is 10, the probability that the pixel belongs to the point target is about 0.37, and the probability that the pixel belongs to the background is about 0.63. Finally, the background suppression can be accomplished as R(i, j) = G(i, j) F(i, j), R(i, j) is the residual image. The prediction and suppression results of Fig. 3a are shown in Fig. 4. As shown in Fig. 4a indicates the prediction result of NSPBF, (b) indicates the suppression result of NSPBF, (c) indicates the prediction result of morphological Open filter, (d) indicates the suppression result of morphological Open filter (e) indicates fused prediction result and (f) indicates corresponding suppression result of (e). From Fig. 4, we can see that both the background and the point target are predicted very well by NSPBF, so the target is vanished in (b). Morphological Open filter enhance the targets as well as the sharp edges in the image. The fusion of the two filters can both predict the background accurately as well as enhance the targets, and the variance and false alarms are much lower than (d). The proposed algorithm is summarized and the architecture is shown in Fig. 5. In which, the streamed image data are fed into the buffer to obtain the local area image data in the first step, then the threshold Tg is obtained in the second step. In the third step, the gray similarity of the pixels in local area is calculated. In the fourth step, the NSD is calculated as well as the NSPBF and morphological Open filter are performed. At last, the results of NSPBF and morphological Open filter are fused according to (8). Some delay modules are needed to keep the data synchronized in the whole processing. In Fig. 5, we can find the whole pipeline structure of the method, and in each step, operations can be implemented in
4. Experimental results To verify our algorithm, we took many infrared image sequences with different background for trials, and three representative sequences with different complex IR background are selected for the discussion. They are shown in Fig. 6 and each of them represents different heavily cluttered background (such as clouds in (a), sea, sky and ground clutters in (b), and ground clutters in (c)), the point targets are indicated by squares. In Fig. 6a is from the Air Force Rome Laboratory, (b) and (c) were captured by different long-ware IR detectors, these images have different blank area, so we cut them to the same size 235 300 in the experiment. A good background clutter suppression algorithm should eliminate clutter component and enhance the target signal. From this point of view, the gain of standard deviation (Gain(r) = 20 log(rout/rin),rout is the standard deviation of residual image, rin is the standard deviation of original image)should be minimized and the gain of Signal-to-Clutter-Ratio (SCR) (Gain(SCR) = 20 log(SCRout/SCRin)) should be maximized, which SCR is defined as SCR = (T m)/r, T is the gray value of target, m is the mean value, r is the standard deviation. In view of the original image is heavily cluttered, SCRin is calculated in 9 9 local area around target in original image, the SCRout is calculated in the whole residual image. Gain(r) and Gain(SCR) are analyzed in the each frame of three sequences and the average are shown in Table 1. All of our results obtained by the proposed approach are compared with those of the TDLMS filter and the TopHat filter. The results of different targets which are indicated by black square and white square in Fig. 6a are separated by ‘/’ respectively. From Table 1, we can see that in sequence (a) performance of TDLMS and TopHat degraded. By comparison, the proposed method got better performance in all the cases. It dues to that the new approach can adaptively choose approximate filter depending on NSD, this will satisfy different demands for both background pixels and target pixels.
460
F. Zhao et al. / Infrared Physics & Technology 55 (2012) 454–461 Table 1 Experiment results of six image sequences. Image sequences
SCRin
rin
Algorithms
Gain(SCR)
Gain(r)
(a)
2.5/4.2
39.45
TDLMS TopHat Proposed
2.32/2.65 2.41/0.65 13.44/10.55
19.15 18.75 25.75
(b)
1.9
70.30
TDLMS TopHat Proposed
13.03 7.20 14.68
29.65 20.8 29.94
(c)
1.21
44.24
TDLMS TopHat Proposed
12.39 12.9 19.5
26.84 22.9 30.01
Fig. 7. Comparison of detection performance.
algorithm, TDLMS and TopHat are shown in Fig. 7. It is obvious that the new method had a much larger detection probability in most cases. All the experiment results show that the proposed algorithm can suppress the cluttered background more effectively.
5. Conclusion A new complex background suppression algorithm is proposed in this paper. Compared with single filter based algorithms, the proposed method analyzes the nucleus similarity degree first, then the strong points of morphological Open filter and Nucleus Similar Pixels Bilateral Filter (NSPBF) are combined. The trick produces a more accurate prediction result that aids clutter subtraction through considering choosing appropriate filters and fusion of prediction results. The pipeline and parallel structure benefits the implementation in real-time ATR weapon systems. Experimental results indicated that the method works well for suppression of background clutter and enhancement of the targets, and the detection performance at low SCR is also improved.
References Fig. 6. Original image in the sequences.
The detection performance of the proposed algorithm was also verified in the experiment. Because the number of targets is finite in these sequences, to obtain more common data, we inserted 50 one pixel synthetic targets for processing, the synthetic targets are randomly distributed in the image, and the values of SCRin are randomly chosen from the range (2.0, 3.0). Because the position and energy of synthetic targets are random, we take image (c) for example in this experiment, and the number of simulation times is 20. The receiver operating characteristics (ROC) of the proposed
[1] B. Wang, D. Liu, J. Zhang, Temporal filtering for target detection algorithm based on static background elimination, Journal on Communications 30 (2009) 67–72. [2] A. Tartakovsky, R. Blazek, Effective adaptive spatial–temporal technique for clutter rejection in IRST, SPIE Proceedings: Signal and data processing of small targets 4048 (2000) 85–95. [3] L. Yang, J. Yang, K. Yang, Adaptive detection for infrared small target under sea–sky complex background, Electronics Letters 40 (2004) 1083–1085. [4] W. Wang, B. Han, H. Zhang, A new algorithm of small target detection for infrared image in background of sea and sky, Acta Photonica Sinica 38 (2009) 725–728. [5] H. Deng, J.G. Liu, Z. Chen, Infrared small target detection based on modified local entropy and EMD, Chinese Optics Letters 8 (2010) 24–28. [6] F. Zhang, C. Li, L. Shi, Detecting and tracking dim moving point target in IR image sequence, Infrared Physics & Technology 46 (2005) 323–328.
F. Zhao et al. / Infrared Physics & Technology 55 (2012) 454–461 [7] T. Soni, J. Zeidler, Performance evaluation of 2-D adaptive prediction filters for detection of small objects in image data, IEEE Transaction on Image Processing 2 (1993) 327–340. [8] H. Zhu, Y. Zhao, Detection of weak and small moving infrared targets by adaptive prediction of background, Journal of Infrared Millimeter Waves 18 (1999) 305–310. [9] H. Askar, X. Li, Z. Li, Background clutter suppression and dim moving point targets detection using nonparametric method, in: Proceedings of IEEE 2002 International Conference on Communications, Circuits and Systems and West Sino Expositions, vol. 2, 2002, pp.982–986. [10] T.W. Bae, S.H. Lee, K.I. Sohng, Small target detection using the bilateral filter based on target similarity index, IEICE Electronics Express 7 (2010) 589–595.
461
[11] Wei-ke Dong, Jian-qi Zhang, Ding-ding Yang, De-lian Liu, Homogeneous background prediction algorithm for detection of point target, Infrared Physics & Technology 54 (2011) 70–74. [12] S.M. Smith, J.M. Brady, SUSAN—a new approach to low level image processing, International Journal of Computer Vision 1 (1997) 45–78. [13] N. Otsu, A threshold selection method from gray-level histograms, IEEE Transactions on Systems Man and Cybernetics 1 (1979) 62–66. [14] C. Tomasi, R. Manduchi, Bilateral filtering for gray and color images, in: Proceedings of 6th IEEE International Conference on Computer Vision, 1998, pp. 839–846.