基于多聚焦图像融合的新方法

1、英 文 翻 译系 别 专 业 班 级 学生姓名 学 号 指导教师 A New Method for Multi-Focus Image Fusion Using Countourlet TransformAbstract Image fusion based on Contourlet transform will produce a pseudo-Gibbs effect for the lack of translation invariance. We proposed a method which combined Contourlet transform with image blo

2、cking fusion to solve this problem. Firstly a new fusion rule based on Contourlet transform was proposed to get the initial fused image. Secondly, source images and the initial fused image were partitioned into equal size image blocks. The source image blocks, which were more similar to the correspo

3、nding initial fused image blocks, were chosen as the final fused image blocks. For the border part between the clear part and blurring one, the initial fusion results were kept. Experimental results show that this method can effectively eliminate the image distortion arising from Contourlet transfor

4、m lack of translation invariance. The fusion effect is better than the effect of image blocking and Contourlet transform fusion methods. Keywords: image fusion; Contourlet transform; translation invariance; image blocking; block effecI. Introduction Because of the good details performance capabiliti

5、es with the multi-resolution analysis, its now widely used in image fusion processing. Fusion algorithms commonly used in transform domain include wavelet transform and multi-scale geometric analysis. Because separable wavelet has limited direction, which leads to the defects that the edges and deta

6、ils of the fused image appear blurry. To solve this problem, multi-scale geometric analysis arises. Image fusion algorithms based on Contourlet transform have been proposed in succession, seen in Ref.Contourlet transform has the advantages of highly directional and anisotropy, which leads to the bet

7、ter image fusion effects than wavelet transform. But Contourlet transform and wavelet transform are all lack of translation invariance. Image fusion process will produce pseudo- Gibbs effect which causes image distortion. Image blocking fusion algorithm is translation invariant due to directly selec

8、ting clear image blocks as fusion results without the step of sampling. However, blocking effects will appear on the border part between the clear areas and blur areas. According to the respective advantages of the two algorithms, we propose a new method combining Contourlet transform with image blo

9、cking fusion, which is translation invariant and can suppress image blockingeffect effectively.II. Fusion Algorithm Based On Contourlet TransformA. Contourlet Transform principle Contourlet Transform is a “real” two-dimensional image representation proposed by Minh N.Do and Martin Vetterli in 2002.

10、Contourlet Transform is achieved by two steps: Laplace pyramid decomposition (LP) and directional filter banks (DFB) filtering. Firstly, decompose the original image into one low-pass sub-image and one band-pass sub-image by LP decomposition. The band-pass sub-image is the difference image between t

11、he original image and the low-pass prediction image. Then decompose the band-pass sub-image into several direction sub-bands through the directional filter banks. Repeat above process to the low-pass sub-band will achieve multi-resolution and multi-directional decomposition of the image. Contourlet

12、transform not only has multi-scale and time-frequency local characteristics, but has directional characteristic that can accurately capture the image edges into different scales and different frequency sub-bands. B. Fusion Algorithm Fusion rule is the core of image fusion algorithms,their advantages

13、 and disadvantages will directly affect thefinal image fusion effect. Because the sub-bands of lowfrequencyand high-frequency obtained by Contourletdecomposing represents different physical meaning, Different fusion rules are adopted when fusing. 1) Low-frequency sub-band fusion rule The low-frequen

14、cy sub-band reflects the generalinformation of the image. Because the low-frequency subbandcoefficients of the two source images are very close,so we compute the average value of the two sub-bandcoefficients as the low-frequency sub-band coefficient ofthe fused image. 2) High-frequency sub-bands fus

15、ion rule Recently, the high-frequency sub-bands fusion rulesoften ignore the relationship between the low-frequency sub-band and high-frequency sub-bands which can reflectthe local or directional contrast of images. The humanvisual system is very sensitive to local contrast of theimage, so it will g

16、et better fusion effects if combineContourlet transform with local contrast. This paper presents a new high-frequency coefficients option based ongradient energy contrast. The definition of contrast shows the intensity of the image high-frequency information relative to thebackground. Image contrast

17、 can be defined as: (2-1) In (2-1), F is the image local brightness value. F is the background brightness of the image which can beconsidered as the low-frequency component. And F isequivalent to the high-frequency component of thetransformed image. The larger R is, the larger contrast inthe local a

18、rea of the image as well as the higher definition.Based on the above analysis, define the gradient energy ofthe image local area in Contourlet transform domain as follows: （2-2） (2-2)is the formula of energy gradient of the local area centered at pixel location (x, y) of the j-th layer in the k-th d

19、irection subband. j,k H represents the k-th high-frequency direction sub-band coefficients after j-layer Contourlet decomposition . M, N define the size of the local area (3* 3or 5*5). Energy gradient contrast of the local area in Contourlet transform domain is defined as follows: （2-3） where j E de

20、notes the regional gradient energy of lowfrequency sub-band coefficients at jth scale. The option of high-frequency coefficients is shown as (2-4):Ifthen Where Eles if， （2-4） T is the experimental threshold, T0,0.5， is the high-frequency sub-band coefficient of the fused image.and are the high-frequ

21、ency sub-band coefficients of the source images A and B respectivelyC. Fusion experiments In Fig.1(c) and (d), The maximum of the corresponding high-frequency coefficients is chosen as the fused image high-frequency coefficient. In Fig.1(e), The maximum regional energy fusion rule of high-frequency

22、coefficients is adopted. Selection rule for the low frequency coefficients all adopt averaging fusion method.DB2 wavelet basis of Daubechies is selected by wavelet transform fusion. The decomposition levels 3 are chosen by all the algorithms. Seen from the visual results, Image edges are blurred and

23、 virtual shadow appears in Fig.1(c) and (d). Although the fusion result is improved in Fig.1(e), but still can not reach the fusion effects of the algorithm proposed in this paper, seen in Fig.1(f). (a) vision focus image (b) close-focus image (c) wavelet (d) contourlet I (e) contourlet II (f) NewFi

24、gure 1. Comparision results of different fusion algorithmsIn order to evaluate the image fusion resultsobjectively, the three indicators root mean square error(RMSE), peak signal to noise ratio (PSNR), and entropyare calculated, as shown in Table 1.Fusion MethodEvaluation IndicatorsEntroyPSNRRMSEwav

25、elet4.409333.46807.3108contourlet I4.616534.59187.2619contourlet II4.693233.66547.1979new4.717235.17827.0987TABLE I. Objective Eveluation Of Image Fusion Seen from Table 1, the fusion algorithm presented in this paper is superior to other methods. However, Contourlet transform does not have translat

26、ional invariance as well as wavelet transform, the fused imagewill produce distortion.III. Combination Of Contourlet And Image BlockingA. Fusion scheme The proposed fusion implementation steps are as follows: 1) Fuse the source images A and B based on the newproposed contourlet transform fusion algo

27、rithm to get theinitial fused image F0 . 2) Divide the input images A and B and the initial fused image F0 into equi-sized square blocks whose size are m n. Calculate the similarity measure SM values of the corresponding subblocks of A ,B and F0 respectively. The higher the value of SM indicates the

28、 high similarity of two images. If the similarity between the source image block and the initial fused image block is greater, the greater the probability is that the ultimate fused image blocks comes from the source image block. (3-1) (3-2) 3) Creat a sign matrix Sign(r,c): (3-3) where M, N is the

29、length and width of the source image. r =1,2,.,M / m , c = 1,2,., N / n . r,c are actually the image block position coordinates in the image. 4) Check consistency on the sign matrix, then get the final fused image F by the following calculation:If Sign(r,c) =1 and the sum of each element in thesign

30、matrix entered at (r,c) of 3 3 neighborhood isequal to 9, then: （3-4） Else if: Sign(r,c)=0 and the sum of each element in the sign matrix centered at (r,c) of 3 3 neighborhood is equal to 0, then: （3-5）else： （3-6）B. Fusion experiments To verify the algorithms superiority and reliability, Comparison

31、experiments is made with image blocking fusion and Contourlet transform method. Image blocking size is 8*8. The new Contourlet transform fusion rule proposed in this paper is selected for fusion. Seen from the source images in Fig. 2 (a) and (b), the persons head has a small angle of rotation, i.e.

32、local non-rigid transformation occurs in the source image. Figure 2 shows the results of different algorithms. Visual results show that block effect appears for fusion-blocking. The apparent ripple (ringing) and the false edge of the information occur in Contourlet transform fusion. The edge region

33、of the person head is particularly evident. This is due to Contourlet transform lack of translation invariance .The algorithm proposed in this paper obtains the best visual effects, not only has translation invariance, but block effects have been effectively suppressed. a) focus on the left (b) focu

34、s on the right (c) image blocking (d) Contourlet (d) NewFigure 2. The results of different fusion algorithmsIn order to evaluate the image fusion results objectively, select the mutual information6and edge retention7as the image quality evaluation indicators. Because these two indicators can measure

35、 image quality without reference image, which meets the requirements of this article. The mutual information reflects the amount of information obtained from the original image. Edge retention can measure how many edge details transferred from the source to the fused image. The greater the two value

36、s are, the better fusion performance of the fusion methods gets. Table 2 shows that the proposed algorithm is better than the other two algorithms. TABLE II. Performance EvaluationFusion MethodEvaluation IndicatorsMutual informationEdge retentionblocking6.53490.6472contourlet6.35860.6253new 6.75190.

37、6617IV. Conclution Taking advantage of Contourlet transform and images blocking fusion algorithms, we propose a new image fusion method combining Contourlet transform and fusionblocking. Contourlet transform fusion algorithm with a new designed fusion rule is used for the border part between the cle

38、ar area and blurring one. The source image blocks, which are more similar to the corresponding initial fused image blocks, are chosen as the final fused image blocks. The new proposed algorithm effectively overcomes the translation invariance of Contourlet Transform and obtains a better visual effec

39、t than the traditional fusion methods. 基于多聚焦图像融合的新方法摘 要 基于Contourlet变换的抽象图像融合会产生伪吉布斯效应的缺乏平移不变性。为解决这个问题我们提出了一种结合Contourlet变换与图像块融合的新方法。首先基于Contourlet一个新的融合规则，提出了获取初始融合图像变换。其次，源图像和初始融合图像被划分成相同大小的图像块。源图像的块更类似于相应的初始融合图像块，被选择作为最终的融合图像块。初步的融合结果对于清晰区域和模糊之间的边界部分进行保存。实验结果表明，该方法能有效消除轮廓波产生的图像失真变换缺乏平移不变性。融合效果更优

40、于图像块和Contourlet变换的融合方法。关键词：图像融合；Contourlet变换；平移不变性；图像块；块效应一、引言因为多分辨率分析的好的细节表现能力，现在被广泛应用于图像融合处理。常用的变换域融合算法包括小波变换和多尺度几何分析。由于可分离小波具有有限的方向，从而导致了融合图像的边缘和细节显得模糊的缺陷。为了解决这个问题，提出了多尺度几何分。基于Contourlet的图像融合算法变换已经提出在继承，见参考文献。Contourlet变换的优点是高度方向性和各向异性，从而得到比小波变换更好的融合效果。但Contourlet变换和小波变换都缺乏平移不变性。图像融合过程中会产生伪吉布斯效应，

41、导致图像失真。图像阻断融合算法是平移不变性由于直接选择清晰的图像块作为融合结果没有抽样的步骤。然而，阻断效应将出现在明确的区域和模糊区域之间的边界部分。根据两种算法各自的优点，提出了一种新的方法结合Contourlet变换与图像块融合，能有效地抑制图像阻断作用。二、基于Contourlet变换的融合算法2.1 Contourlet变换原理 Contourlet变换是一个“真正”以2002年提出的Minh N.Do和Martin Vetterli表示的二维图像。Contourlet变换的实现基于两个步骤：拉普拉斯金字塔分解（LP）和方向滤波器组（DFB）过滤。首先，分解原始图像为一个低通子图像和

42、一个带通子图像由唱片分解。带通子图像是原始图像和所述低通预测图像之间的差分图像。然后通过方向滤波器组分解的带通子图像分成几个方向的子带。重复上述过程，以低通子带将实现多分辨率和图像的多方向分解。 Contourlet变换不仅具有多尺度和时频局部特性，而且具有方向性的特点，可以准确地捕捉到图像边缘成不同尺度和不同的频率子带。2.2 融合算法 融合规则是图像融合算法的核心，它们的优点和缺点将直接影响最终图像的融合效果。由于低频和高频进行Contourlet分解得到的子带代表不同的物理含义，所以采用不同的融合规则。1、低频子带融合规则低频子带反映了图像的一般载文信息。因为这两个源图像的低频子和系数非

43、常接近，图像的低频子带反映了一般信息。因为这两个源图像的低频子带系数很接近,所以我们计算两个副环带系数的平均值作为融合图像的低频子带系数。2、高频子带融合规则最近，高频子带的融合规则常常忽略可以反映当地或方向对比度的图像低频子带和高频子带之间的关系。人类的视觉系统对图像的局部对比度非常敏感的，所以它会得到更好的融合效果，结合Contourlet变换的局部对比度。本文提出了一种基于梯度能量对比了新的高频系数的选择。对比度的定义显示图像的高频相对于背景中的信息的强度。图像的对比度可以被定义为： (2-1)式中，F是图像局部亮度值。F是可被认为是低频分量的图像的背景亮度。和F相当于变换图像的高频分量

44、。较大的R是，在图像的局部区域中的较大的对比度，以及更高的清晰度。基于以上分析，定义图像局部区域的Contourlet变换域如下的梯度能量： （2-2）（2）为中心，对第k个子带方向第j层的象素位置（x，y）的局部区域的能量梯度的公式。，表示第j层轮廓波分解后的第k个高频方向的子带系数。M，N中定义的局部区域（33或55）的大小。在轮廓波变换域中上述局部区域的能量梯度相反的定义如下： （2-3）其中表示在第j个尺度低频子带的系数的区域的梯度能量。高频系数的选项被显示为（4）：Ifthen 其中， 或者， （2-4） 式中T为实验门槛，T0,0.5，是融合图像的高频子带系数，与分别是源图像A和B的高频子带系数。2.3 融合实验 在图2-1（c）和（d）所示，对应的高频系数的最大值被选择作为融合图像的高频系数。在图1（e）中，高频系数的最大区域采用能源融合规则。对于低频系数选择规则全部采用平均融合方法，DB2小波则选择小波变换融合。分解3级是由所有的算法选择。从视觉效果来看，图像边缘模糊和虚影出现在图2-1（c）和（d）。虽然融合结果在图1（e）改进，但仍不