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毕业设计外文资料翻译学 院： 电子工程学院 专业班级： 自动化071 学生姓名： 陈新鹏 学 号： 030713103 指导教师： 马娟丽 外文出处： Multi-focus Image Fusion Algorithms Research Based on Curvelet Transform 附 件：1.外文资料翻译译文； 2.外文原文 指导教师评语：签名： 年 月 日基于曲波变换的多聚焦图像融合算法研究摘要：由于光学透镜聚焦深度的限制，往往很难得到一个包含所有相关聚焦目标的图像。多聚焦图像融合算法可以有效地解决这个问题。基于广泛应用的多聚焦图像融合算法的分析，本文提出一种基于多聚焦图像融合算法的曲波变换。根据曲波变换分解的不同频率区，分别讨论低频系数和高频系数的选择规律。本文中低频系数和高频系数被分别与NGMS（就近梯度最大选择性）和LREMS（局部区域能量最大的选择性）融合。结果表明，提出的多聚焦图像融合算法可以获得和图像聚焦融合算法相同的图像，在客观评价和主观评估方面较其他算法有明显的优势。关键字：曲波变换；多聚焦图像；融合算法1.简介 如今，图像融合被广泛应用于军事、遥感、医学和计算机图像等领域。图像融合的主要目的将来自两个或更多相同场景的信息相结合以获得一个包含完整信息的图像。比如，廉价相机的主要问题是我们不能获得不同距离的每个目标以获得一个聚焦所有目标的图像。因此，我们需要一种多聚焦图像融合方法来聚焦和获得更清晰的图像。 经典融合算法包括计算源图像平均像素的灰度值，拉普拉斯金字塔，对比度金字塔，比率金字塔和离散小波变换（DWT）。然而，计算源图像平均像素灰度值的方法导致一些不期望的影响例如对照物减少。小波变换的基本原理是对每个源图像进行分解，然后将所有这些分解单元组合获取合成表示，从中可以通过寻找反变换恢复融合图像。这种方法显然是有效的。但是，小波变化只能通过变换边缘特征反映出来，却不能表达边缘的特点。同时，也因为它采用各向同性所以小波变化无法显示边缘方向。由于小波变换的限制，Donoho 等人提出了曲波变换的概念，它采用边缘作为基本元素，较为成熟并可以适应图像特征。此外，曲波变换具有各向异性和有更好的方向，可以提供更多图像处理的信息。通过曲波变换的原则我们知道：曲波变化除了具有多尺度小波变换和地方特色外，它还具有方向特征和支持会话的基础特征。曲波变化可以适当代表图像边缘和相同逆变换精度的光滑区。继曲波变化低波段和高波段融合算法系数的研究后，提出一种思想：低-带系数采用NGMS方法和不同的方向高带系数采用LREMS方法。2.第二代曲波变化 第二代曲波变换和第一代的曲波变换不同的是，没有导入脊波变换的实施过程，但直接提交曲波基本格式的具体表达，这可以说是深入解释曲波变换。在此根本文献让离散算法快速实现。频率区域中窗口函数的概念：: (1) ,和是一维的窗口函数；,定义字段 -1,1 实数函数，时间内容函数在频域内假定会议接近于，曲线函数定义的两个维数： (2)随着频率，比例,方向角和位置,为粗略的尺寸（低域）位置曲线函数定义为： (3)比较公式2和公式3可知“粗略”规模曲波函数相对于其他曲波函数构想并没有介绍方向参数。所以曲波变换在低频段区域靠近小波变换，但在j规模，曲波变换平等的瓜分坡度区间加入契形区。二维连续函数曲线变换定义为公式： (4)同时曲线变换在离散实例中定义为公式： (5)窗口函数支持会话是二维离散信号发散：FFT,公式5显示了该图像是分解使用快速离散曲波变换的FFT方法：（1） 图像被分解二维的FFT，获取序列,（2） 根据不同比例和方向重复采样或插入要接收的值（3） 让按比例放大窗口函数来接收新序列并让保存二维FFT，因此得到比例j方向l和位置离散曲波变换系数。3. 图像融合算法的研究图像融合算法依赖于：图A曲波变换系数融合图像F曲波变换系数曲波变换图像A 曲波逆变换融合算法 图像B融合图像F曲波变换图B曲波变换系数图1 曲波变换基础上的图像融合算法的过程A：低频率系数融合算法 曲波变换在低频率地区接近小波转换，图像组件包括主要能源图像并决定其轮廓，它可以通过正确选择低频率的视觉系数提高图像效果。现有融合规则主要有最大像素法、最小像素法，计算平均像素灰色的级别值，图像法、LREMS法、本地源区域偏差方法6。 最大像素法、 最小像素法和计算平均像素灰度级别源图像方法的值没有考虑到局部邻接相关性，所以融合结果不能获得更好的结果。局部区域能源法和偏差法恰当的考虑到了局部邻接相关性，但没有考虑到图像边缘和定义。考虑到这种缺陷，本文提出的NGMS，它主要描述图像详细信息和图像聚焦级别。八种局部邻接相关性拉普拉斯算法总和被用于图像定义的评估，它被定义为9：曲线变换是牵引源图像A,B被曲波分解，然后采取不同的融合算法来选择不同的曲波变化系数，结果获得融合图像曲波变换系数，最后反曲波变换获得融合的图像。根据图1显示： (6)B：高频系数融合算法 曲波变换有过度的方向特征，因此可以精确地表示图像的特征边缘的方向，并且该高频系数区域即表达图像的边缘细节信息。 像素绝对值最大法、LREMS法、局部地域差法、方向对比度法等，都被运用于高频系数。由于曲波变换的特点，LREMS法被该文件引用。假设图像高频系数是CH，那么融合算法像： （7）CHA和CHB表示曲波变换高频系数的图像A和图像B，CHF(x,y)表示保存的x,y融合高频系数。ECHA(x,y)表示局部区域能源保存的x,y的图像A的曲波变换高频系数，ECHB(x,y)表示局部区域能源保存的x,y的图像B的曲波变换高频系数。4.实验结果与分析 为了能够生动正确的验证和保证算法的有效性以达到熟练使用多聚焦图像技术，请见图2和图3的实验。 图a和图b是表2的源文件，图c是使用小波变换的方式形成的聚焦图像，图d、e、f都是采用曲波变换方式，但是他们的融合算法不同。为了计算应用于低波段源图片法的平均像素阵列的灰度值及图d中的高波段使用的是LREMS技术.在图e中，也就是本篇论文采用的方法，图片的高波段采用的是LREMS技术而在低波段的区域采用的是NGMS技术。在图片f中的高低波段区域都是采用的是LREMS技术。图3也是一样。图片a和b是原图片，图片c是使用波纹取出转移技术的结果。图片d、e、f都是采用的是曲波转移方式。图片d中采用的是计算平均像素的阵列应用于低波段区域，而图像e采用的是应用于高波段的LREMS技术和应用于低波段NGMS技术，而在图f中都是采用的是应用于高波段的LREMS技术。图像融合的优化问题还是没有得到解决。目标图像视觉效果和图像压缩比率是衡量图像处理的技术指标。在视觉效果中，曲波变换和曲波变换能够在聚焦上获得明显的效果。但是使用曲波技术的模糊图像要比使用波形技术的图像处理效果要好。应用于低频段区的局部区域能源法和高频段区的局部地区能源优于其他曲波变换的方法，在本文所提算法中可以得到详细纹理的焦点与已删除的模糊图像。在此有目标熵，交错熵，平均梯度，标准偏差和学习偏差。熵，交错熵以及平均梯度在该文件中被运用。目标图像融合的结果现实于表1和表2。图2多聚焦图像融合的实验图3多聚焦图像融合的实验表1 图2多聚焦图像融合实验目标比较算法目标熵过剩熵平均梯度A3.5123860.08888918.026218B3.5523860.08302618.107795C3.5608530.08005918.032043D3.5628600.06041118.310158表2 图3多聚焦图像融合实验目标比较算法目标熵过剩熵平均梯度A3.3977590.62260142.552248B3.4078530.57993842.879251C3.4043990.53337342.642053D3.4279280.48303442.782833 A：基于小波变换的图像融合。 B：计算应用于低频段区和高频段区的源图像法和LREMS法（有曲波变换分解）的平均像素灰度级。 C：应用于低频段区和高频段区的LREMS法（有曲波变换分解）。 D：应用于低频段区的NGMS法和高频段区的LREMS法（有曲波变换分解）（该文件运用的方法）。然后就可以从我们方法得到的结果得出结论，这种方法优于小波变换方法以及其他基于曲波变换的同时具有客观评价和视觉的方法。5.结论 在该文中，我们提出了应用于低频段区的NGMS法和高频段区的LREMS法都是以曲波变换算法为基础的。相对于DWT和其他基于曲波变换的功能规则它具有一定的优势。因此，我们提出的方法得到了一种多聚焦图像融合的有效方法。外文原文Multi-focus image fusion algorithms researchbased on Curvelet transformQiang Fu, Fenghua Ren, Legeng Chen, Zhexin XiaoGuilin University of Electronic TAbstract: Due to the limited depth-of-focus of optical lenses, it is often difficult to get an image that contains all relevant objects in focus. Multi-focus image fusion algorithms can solve this problem effectively. Based on the analysis of the most widely used multi-focus image fusion algorithms, a new curvelet transform based multi-focus image fusion algorithm is proposed in this paper. According to the different frequency areas decomposed by Curvelet transform, the selection rules of the low frequency coefficients and the high frequency coefficients are discussed respectively. Low frequency coefficients and the high frequency coefficients are fused with NGMS (Neighborhood Gradient Maximum Selectivity) and LREMS (Local Region Energy Maximum Selectivity) separately in this paper. It is shown that the multi-focus image fusions by the proposed algorithm can obtain the same scene in focus image fusion, and have protruding advantage over other algorithms on subjective evaluation and objective evaluation.Keywords: Curvelet transform; multi-focus image; fusion algorithm. IntroductionNowadays, image fusion was broadly applied in military, remote sensing, medicine, and computer vision etc. The main objective of image fusion is to combine information from tow or more source images of the same scene to obtain an image with completely information. For example, the main general problem of inexpensive cameras is that, we can not take every object on different distances to obtain an image with focus on all objects in the same scene. In this case, a multi-focus image fusionmethod is needed to get in focus or sharply images 1-2. Classical fusion algorithms include computing the average pixel-pixel gray level value of the source images, Laplacian pyramid, Contrast pyramid, Ratio pyramid, and Discrete Wavelet Transform (DWT). However, computing the average pixel-pixel gray level value of the source images method leads to undesirable side effects such as contrast reduction. The basic idea of DWT based methods is to perform decompositions on each source image, and then combine all these decompositions to obtain composite representation, from which the fused image can be recovered by finding inverse transform. This method is shown to be effective. However, wavelets transform can only reflect through edge characteristics, but can not express along edge characteristics. At the same time, the wavelet transform cannot precisely show the edge direction since it adopts isotropy. According to the limitation of the wavelet transform, Donoho et al. was proposed the concept of Curvelet transform, which uses edges as basic elements, possesses maturity, and can adapt well to the image characteristics. Moreover, Curvelet Transform has anisotropy and has better direction, can provide more information to image processing 1-2.Through the principle of Curvelet transform we know that: Curvelet transform has direction characteristic, and its base supporting session satisfies content anisotropy relation, except have multi-scale wavelet transform and local characteristics. Curvelet transform can represent appropriately the edge of image and smoothness area in the same precision of inverse transform. The low-bands coefficient adopts NGMS method and different direction high-bands coefficient adopts LREMS method was proposed after researching on fusion algorithms of the low-bands coefficient and high-bands coefficient in Curvelet transform. The Second Era Curvelet Transform 8, 10-11The second eras Curvelet transform is different to the first eras Curvelet transform that is without importing Ridgelet transform within implementing process, but directly present idiographic express format of base of Curvelet, this can be say in deed meaning Curvelet transform. Hereon fundamentally literature gives it fast discrete implement algorithm. Conception of window function in frequency region: (1)Where , and is one dimension low window function;, is definition field -1,1 real number function, event content Function supposed session in frequency region is close to，Two dimensions Curvelet function defines: (2)With in frequency, scale, direction angle and position . Where ,But coarse scale (low domain), positionCurvelet function define: (3)After comparing formula (2) and formula (3) can know that coarse scale Curvelet function did not introduce direction parameter relative to others scale Curvelet function conception. So Curvelet transform is close to wavelet transform in low bands region, but in j scale, Curvelet transform equality slope interval Carve up entries cuniform area.。Two dimension continuum functions Curvelet transform define as formula (4): (4)And Curvelet transform define as formula (5) in the discrete instance: (5) Where is window function support session,Where is two dimension discrete signal discrete FFT,Formula (5) shows that image was decomposed using fast discrete Curvelet transform with FFT method:(1) Image was decomposed two dimensions FFT, getting the sequence,According to different scale and direction , repeat sampling or insert value toreceive(3) Let multiply window function to receive new sequence, and let pot two dimensions FFT，Accordinglyget scale j, direction l and position discrete Curvelet transform coefficient. Researching of Image Fusion AlgorithmImage fusion algorithm process base on Curevelet transform is: tow source image A, B was decomposed by Curvelet transform, then adopt different fusion algorithm to select different Curvelet transform coefficient, receive result fusion image Curvelet transform coefficient, at last inverse Curvelet transform to get fusion image. According to figure 1 show:Image A Curvelet Transform coefficientImage B Curvelet Transform coefficientFigure 1 process of image fusion algorithm base on Curvelet transformA. low frequency coefficient fusion algorithmCurvelet transform is close to wavelet transform in low frequency region, image component including main energy decide image contour, so it can enhance effect of the image vision by correctly selecting low frequency coefficient. Existing fusion rule mostly have max pixel method, min pixel method, computing the average pixel-pixel gray level value of the source images method, LREMS method, local region deviation method 6. Max pixel method, min pixel method and computing the average pixel-pixel gray level value of the source images method did not take into account local neighbor relativity each other, so fusion result can not get better effect; local region energy method and deviation method onside take into account local neighbor relativity each other, but did not take into account image edge and definition. Accounting to this lack, NGMS method was proposed in this paper, it mainly describes image detail and image in focus grade. Eight local neighbor relativity sum of Laplacian algorithm was adopted to evaluate of Image definition, it defines as 9: (6)B. high frequency coefficient fusion algorithmCurvelet transform have excessive direction characteristics, so can precisely express image edge orientation, and that region of high frequency coefficient namely express image edge detail information. Pixel absolute max method, LREMS method, local region deviation method, direction contrast method etc. was used in high frequency coefficient. LREMS method was adopted in this paper base on characteristics of Curvelet transform. Hypothesis image high frequency coefficient is CH, then fusion algorithm such as: (7)Where CHA and CHB express Curvelet transform high frequency coefficient of image A and image B, CHF(x, y) show high frequency coefficient in pot(x, y) fusion high frequency coefficient, ECHA (x, y) show Curvelet transform high frequency coefficient of image A in pot(x, y) local region energy, ECHB (x, y) show Curvelet transform high frequency coefficient of image B in pot(x, y) local region energy. Experiments result and analyzeIn order to validate right and validity algorithm by using multi-focus image to experimented in this paper. Experiment is shown in figure2 and figure3. Figure(a)and (b) is source image in figure2; figure(c) is result of using wavelet transform to fusion image; figure(d), (e) and (f) all were adopted decomposed by Curvelet transform, but their fusion rule is different; computing the average pixel-pixel gray level value of the source images method used in low-bands area and LREMS method used in high-bands were adopted in figure(d), NGMS method used in low-bands area and LREMS method used in high-bands area are adopted in figure(e)(this paper method), LREMS method used in low-bands area and LREMS method used in high-bands area were adopted in figure(f). The same is to figure3, figure(a)and (b) is source image; figure(c) is result of using wavelet transform to fusion image; figure(d), (e) and (f) all were adopted decomposed by Curvelet transform, but their fusion rule is different; computing the average pixel-pixel gray level value of the source images method used in low-bands area and LREMS method used in high-bands were adopted in figure(d), NGMS method used in low-bands area and LREMS method used in high-bands area are adopted in figure(e) (this paper method), LREMS method used in low-bands area and LREMS method used in high-bands area were adopted in figure(f).Result of fusion image evaluating still cannot solve. Subjective vision effect and image ration analyst were used to evaluate quality of result fusion image. With subjective vision effect, Curvelet transform and wavelet transform can get panorama in focus image, but fusion image using Curvelet transform is better to wavelet transform; method of local region deviation using in low-bands area and high-bands area using local region energy was better to other methods in Curvelet transform, in this paper algorithm can got more detail, texture in focus and removed blur image.There was target of entropy, across entropy, average grads, standard deviation and leaning deviation etc. Target of entropy, across entropy and average grads was used in this paper. The image fusion result of the target is shown in table1 and table 2.Figure2. Experiment of multi-focus image fusionFigure3. Experiment of multi-focus image fusionTable1 multi-focus image fusion experiment of figure2 targets compare算法目标熵过剩熵平均梯度A3.5123860.08888918.026218B3.5523860.08302618.107795C3.5608530.08005918.032043D3.5628600.06041118.310158Table2 multi-focus image fusion experiment of figure3 targets compare算法目标熵过剩熵平均梯度A3.3977590.62260142.552248B3.4078530.57993842.879251C3.4043990.53337342.642053D3.4279280.48303442.782833A: Image fusions based on wavelet transformB: computing the average pixel-pixel gray level value of the source images method used in low-bands area and LREMS method used in high-bands (decomposed by Curvelet transform)C: LREMS method used in low-bands area and LREMS method used in high-bands area (decomposed by Curvelet transform)D: NGMS method used in low-bands area and LREMS method used in high-bands area (decomposed by Curvelet transform) (this paper method)Then we can get the conclusion from abovethe results obtained by our method are superior to wavelet transform method and others methods based on Curvelet transform in both objective and visual evaluations. ConclusionIn this paper we presented NGMS method used in low-bands area and LREMS method used in high-bands area are based on Curvelet transform algorithm. It has an advantage over DWT and others fusion rules based on Curvelet transform. Therefore, our proposed approach leads to an effective method for multi-focus image fusion.R