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英 文 翻 译系 别专 业班 级学生姓名学 号指导教师EMD Based Infrared Image Target Detection MethodHe Deng & Jianguo Liu & Hong LiAbstractUnder the complicated background of infrared image, the small target detection is a vital challenging task in modern military. In order to solve this problem, a novel method based on the empirical mode decomposition (EMD) is proposed in the paper, to detect small targets under complicated sea-sky background. The detection process contains two steps: the first step is to suppress the sea-sky background of the infrared image based on EMD; the second step is to segment the target from the background suppressed image through a threshold. The application of infrared images has shown that the performance of the algorithm can detect infrared small target under sea-sky background exactly. Compared with wavelet transformation, the testing results based on EMD method achieve tantamount results wavelet transformation, and even better in some respects. The simulations show that EMD method presented in this paper appears instructive for both theoretical and practical points of view. Keywords: Small target detection , Infrared image , Background suppression ,Threshold ,EMD.1 IntroductionUnder the complicated background of infrared image, the small target detection, identification and tracking applications in modern military are vital challenging tasks. It has been researching for many years on infrared imaging systems and automatic target detection 1.The complexity of this problem arises when the target is small, faint and partially obscured by surrounding objects, embedded in clutters. In these complex situations, the features of both the target and the background are generally nonseparable in the original image space. It is difficult for those detection algorithms to work in the original image space. So, the image has to be transformed into a so-called feature space, in which those features can be separated.Since targets and clutters have different spatial frequency characteristics, a spatial filter could be designed to suppress and detect targets. Bhanu and Jones summarized a lot of algorithms for automatic target detection in static infrared images that were developed up to the early 1990s 2.These algorithms predominately utilize traditional image-processing approaches for optical pictures processing. Recently, the wavelet transformation has emerged as an excellent methodology for small targets detection because it gives a lot of advantages among all other image-processing techniques. Simply speaking, in small and dim target detection application, the wavelet transformation can serve as a matching filter, a multi-resolution image analyzer, a multi-dimensional image analyzer, a singularity detector, and an orthogonal extractor 34.A method based on wavelet transformation, which is to detect small and dim target by background suppression, contains four steps 5: firstly, extracts approximate coefficients of original image, which include some features of original image; secondly, reconstructs the approximate coefficients into a new image which is called background image. The background image shows the approximate feature mainly contains background information; thirdly, uses the background image subtracted from the original image, and then obtains an image which is called the background suppressed image, mainly includes target and noise point information; finally, chooses an adaptive threshold to segment the background suppressed image, so the target can be detected.But in the processing of detection based on wavelet transformation, at least two important aspects must be taken into consideration: 1) the tactics of choosing wavelet basic function; 2) the number of decomposition levels. In order to overcome these difficulties and improve the testing results, a novel method to detect small targets under complex sea-sky background is proposed in the paper. It is based on the empirical mode decomposition (EMD). Compared with wavelet transformation, EMD algorithm shows a superior performance on selectivity and the precision of data analysis. It is a powerful tool for adaptive multi-scale analysis of short time nonlinear and nonstationary signals. EMD method is first proposed by Norden E. Huang 6 in 1998. The method can extract a series of intrinsic mode functions (IMF) by decomposition the local energy associated with the intrinsic time scales of the signal itself. So it is self-adaptive and can depict the timefrequency characteristics of the signal exactly.The outline of the paper is as follows: Section 2 describes the general procedures of small targets detection. Section 3, a novel small infrared target detecting algorithm based on EMD algorithm is presented. Section 4 presents some experimental results and compares the testing results based on EMD method with wavelet transformation in some ways. And Section 5 draws some conclusions.2 Common procedures of small target detectionTarget detection algorithms have been steadily improving, whereas many of them failed to work robustly during applications involving changing backgrounds that are frequently encountered. In general, a small target embedded in cloudy background presents as a gray spot in image, which also contains bright illuminated terrain or sunlit clouds. That is to say, when an infrared sensor is far away from the targets, the targets immerged in heavy noise and clutter background present as spot-like feature which have the signature of discontinuity comparing with its neighbor region, no obvious structural information in infrared image. The gray value of a target is higher than its immediate background in infrared image and is not partially correlative with its local neighborhood. Due to pixel nonuniformity of response of infrared image, the atmospheric transmitting and scattering, the complex background containing large-area of cloud and ocean waves and so on, the background in infrared scene shows spatial correlation between each pixel and its surroundings and being undulant significantly, which in frequency domain lies in low frequency band, belonging to low frequency interfered for target detection 78. Furthermore, it is important to note that noise come from the infrared sensor and the background. Because of the effects of inherent sensor noise, the natural factors such as weather, wind, sun light and so on, there exist some high gray regions in the infrared image as complicated cloud edge, irregular sun light spot, etc., both of which and targets can be considered as homogeneous region and fall in high frequency band of frequency spectrum, belonging to high frequency interfered for target detection. So a spatial frequency filter is designed to suppress the background of an infrared image, and then detect of target through a threshold is very efficient.EMD algorithm decomposes a signal into a series of different frequency components, which is similar to wavelet transformation. The reason why the algorithm has an advantage over wavelet transformation is that the decomposition based on EMD algorithm is selfadaptive. Therewithal, in detected application of small target, the result based on EMD algorithm is equal to wavelet transformation, and even more proponent in some aspects in theory. Some detected results of small target based on EMD algorithm and wavelet transformation are given in Section 4. Some comparisons of the two methods are also given in the same chapter.2.1 Image signal modelingAn infrared image contains small targets can be described as follows: (2-1)where ftarget(x, y), n(x, y), fback(x, y) denote the target signal, the noise signal and clutter background respectively. In this image signal modeling, n(x, y) is generally assumed that it is Gaussian white noise with zero mean. For a single image mentioned above, we dont know the power of the signal and the noise, so the signal to noise ratio (SNR) of the image may be estimated approximately, which is now still at issue. A simple SNR is defined as the ratio of the variance of target and the background image.Definition 1: If an image signal modeling as before depicts, the SNR may be defined as： (2-2)where s and denote the variance of the target and the background image respectively.2.2 Background suppression techniqueSince small targets and clutter backgrounds have different spatial frequency characteristics, a spatial frequency filter could be designed to suppress clutter backgrounds, which provides a possibility to detect small targets. So some adaptive and linear/nonlinear methods based on two-order stationary random signal analysis 910, such as the least-mean-square (LMS) filtering method has been steadily improving and can effectively suppress the clutter background. However, they failed to work robustly during applications involving changing backgrounds that are frequently encountered. In recent years, wavelet transformation has emerged as a methodology of image decomposition into a sequence of images at different scales using a set of compactly supported basis functions called wavelets. Compared with wavelet transformation, EMD method is a new method in analysis of signal, and it is specially fit to nonlinear signal. We will briefly introduce EMD algorithm in Section 3 and apply it to the detection of infrared small target.In order to compare the effects of the background suppression based on the different methods, we must see the advantages and the disadvantages from signal noise improvement ratio (SNIR) and peak signal-to-noise ratio (PSNR). The definition of SNIR and PSNR are described as follows respectively.Definition 2: SNIR of an image may be defined as: (2-3) where SNRin and SNRout denote SNR of an original image and its background suppressedimage respectively.Definition 3: PSNR of an image may be defined as： (2-4)where I(i,j) is an original image with the size of MN, and I(I,j) denotes its background suppressed image with the same size.2.3 Threshold segmentAfter suppressed background of an original image, the capital work is to choose a threshold to segment the small target from the image. The choice of a threshold is important in image processing because too low a value will swamp the difference map with spurious changes, while too high a value will suppress significant changes. One way to choose a threshold is by visual inspection of the image histogram. If the histogram has two distinct modes, it is easy to choose a threshold T to segment small target. Another method of choosing T is by trial and error, picking different thresholds until one is found that produces a good result as judged by the observer. This is particularly effective in an interactive environment. In the paper, we adopt a method which chooses a threshold automatically. Riddler and Calvard11 describe the method as following iterative procedures:1) Select an initial estimate for T.(A suggested initial estimate is the midpoint between the minimum and maximum intensity values in the image.)2) Segment the image using T. This will produce two groups of pixels:G1,consisting of all pixels with intensity valuesT,andG2,consisting of pixels with valuesT.3) Compute the average intensity values 1 and 2 for the pixels in regions G1and G2.4) Compute a new threshold value: 5) Repeat steps 2 through 4 until the difference in T in successive iterations is smallerthan predefined parameter T0.3 EMD methodBasis decomposition techniques such as Fourier decomposition or wavelet decomposition have been used to analyze real world signals. The main shortcoming of these approaches is that the basis functions are fixed, and do not necessarily match the varying natures of signals. Recently, EMD method has been proposed as a new tool for data analysis. It is a signal processing technique particularly suitable for nonlinear and nonstationary series6. This technique performs a time self-adaptive decomposition of a complex signal into elementary, almost orthogonal components that dont overlap in frequency.3.1 EMD basicsEMD can break down a signal to a series of zero means “Intrinsic Mode Functions” (IMFs) which satisfy two conditions: (1) in the whole data set, the number of extreme and the number of zero crossings must either be equal or differ at most by one; (2) at any point, the mean value of the envelope defined by the local maxima and the local minima approach zero. These two characteristics are also the criteria for sifting processes and stopping. Each sifting process contains two steps: (1) construct upper and lower envelopes by connecting all maxima or all minima with cubic splines; (2) subtract the mean of the upper and lower envelopes from the original signal to get a component. While the sifting process should usually be applied several times because the component created by only one sifting process can hardly satisfy all the requirements of an IMF. Once an IMF has been created, the same procedure is then applied on the residual of the signal to obtain the next IMF. The later an IMF is, the lower its frequency is. The decomposition will stop when no more IMFs can be created or the residual is less than a predetermined small value. Given a signal x(t), the effective algorithm of EMD can be summarized as follows 6.1) Identify all extremes of x(t);2) Interpolate between minima (resp. maxima), ending up with some “envelope” emin(t) (resp. emax(t);3) Compute the average m(t)= (emin(t)+ emax(t) /2;4) Extract the detail d(t)=x(t)-m(t);5) Iterate on the residual d(t).By construction, the number of extremes is decreased when going from one residual to the next (thus guaranteeing the complete decomposition is achieved in a finite number of steps), and the corresponding spectral supports are expected to decrease accordingly. While modes and residuals can intuitively be given a “spectral” interpretation, it is worth stressing the fact that, in the general case, their high- versus low-frequency discrimination applies only locally and corresponds by no way to a predetermined subband filtering (as, e.g., in a wavelet transform). Selection of modes much more corresponds to an automatic and adaptive (signal-dependent) time-variant filtering.3.2 Bidimensional EMDEMD serves as a powerful tool for adaptive multiscale analysis of nonstationary signals. As far as the one-dimensional (1-D) case is concerned, studies were carried out to show the similarities of EMD with selective filter bank decompositions12. Its efficiency for signal denoising was also shown in13. These interesting aspects of the EMD motivate the extension of this method to bidimensional signals.The basis of EMD (in 1-D) is the construction of some intrinsic mode functions (IMFs) that are constructed through a so-called “sifting” process (SP). A 1-D SP is an iterative procedure depending on the following four important problems:1) how to define the extremal points of signal; 2) the choice of interpolation method to interpolate those extremal points from the first step; 3) how to define a stopping criterion that ends the procedure; 4) the method of dealing with boundary data of the image. The process of bidimensional EMD is similar to one-dimensional EMD, but for bidimensional EMD, those four problems still exist and will be more crucial.Since the first problem was mentioned earlier, assuming that fm,n is an MN image, we use the definition of extreme as follows14. Definition 4: fm,n is a maximum(resp. minimum) if it is larger(resp. lower) than the value of f at the eight nearest neighbors of m,n.As far as the interpolation is concerned, several techniques have been proposed, for instance, radial basis functions such as thin-plate splines. These methods require the resolution of timeconsuming optimization problems, which make them hard to exploit, especially in a noisy context. Since Delaunay triangulation has good fitting characteristics for scattered or arbitrary data points, then in this paper we first dissect the maximum (resp. minimum) of the image matrix into a series of triangles based on Delaunay triangulation, then interpolate each triangle by the piecewise cubic spline to form upper and lower envelope of the image.We adopt a bidimensional EMD,whose SP is based on Delaunay triangulation, cubic interpolation on triangles and also a fixed number of iterations to build IMFs. The above method is similar to the method in literature 14. The major advantage of the proposedmethod over existing ones is that it takes into account the geometry while preserves a low computational cost. In the paper, the number of iterations is 3.The boundary handling in bidimensional EMD is more difficult than that in onedimensional EMD, but the general approach applies only to a certain type of one or more of the borders. In addition, there is no theoretical proof to testify which kind of approach is better. In the paper, we deal with boundary issue based on the mirror reflection of image data.3.3 The components of image based on EMDThough the method based on EMD is similar to wavelet transformation, it can decompose the image into some IMFs and the residue, in other words, it can decompose the image into different frequencies. The first IMF denotes the highest frequency, the second, the second highest frequency, and so on. In order to extract the target from the infrared image under sea-sky background shown in Fig. 1 (a) according to our method, we adopt the following experimental procedure: firstly, suppress the background of the infrared image based on EMD algorithm; secondly, segment the target using a threshold. Fig. 1 (b)(f) shows five IMFs which is iterated 3 times, and Fig. 1 (g) depicts the decomposition residue. Among them, Fig. 1 (g) is the residue which contains the information of background naturally, so it can be used as the estimation of the background, called background image. Figure 1 (h) denotes the result of the original image(Fig. 1 (a) subtracted the background image(Fig.1 (g). Figure 1 (h) is called background suppressed image. We can see that the target is more prominent than the original image and the background of the background suppressed image is more uniform. There is larger detection probability in the background suppressed image and the target maybe be more easily detected. Through a threshold which is described in detail in Section 2.3. to segment the target in background suppressed image, we get the result shown in Fig. 1 (l), so the target can be detected exactly. 4 Experimental results and analysis4.1 Simulation results based on EMDTo test the pros and cons of EMD algorithm in detecting small target detection under complex background of infrared image, the paper has done a large number of computer simulations. These images are sequences over 100 frames under complex sea-sky background. In the paper, we only choose 4 frames images. The original images and the testing results are shown in Fig. 2 (a1)(e4). Figure 2 (a1)(a4) are original images. In order to observe the results of background suppressed, those background suppressed images are shown in Fig. 2 (b1)(b4). We use a threshold which is described in details above to segment the targets from Fig. 2 (b1)(b4), and get the results shown in Fig. 2 (d1)(d4).In order to testify the validity of the result based on EMD algorithm, we compute the SNR of the experimental images. Firstly, we adopt EMD algorithm to detect small target, and then the position and the size of the target can be found; secondly, subtract the target from the original image and the background suppressed image respectively, then obtain the estimation of background; thirdly, compute the SNR of the o
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