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1、The Algorithm of Rapid Medical Image Registration by Using Mutual Information Yongjun Ma College of Computer Science and Information Engineering Tianjin University of Science & Technology Tianjin, P.R.China Jieyu Tian College of Computer Science and Information Engineering Tianjin University of Sci
2、ence & Technology Tianjin, P.R.China mercury_ AbstractThis paper presents a rapid algorithm for medical image registration, the purpose is to solve problems, which are the inferiority of low speed and huge calculation in medical images registration based on normal mutual information. We present a tw
3、o-step search strategy to speed-up registration process according to the different regions between the target image and the source image. In a first step the coarse granularity search determines the limits of target range; between-class distance is used in the initial step for discriminating similar
4、ity. In a second step the fine-grained search computes similarity measure by using normalized mutual information to achieve final image registration. Experimental results show that the method, which keeps precision of registration, can solve the problem of low speed, and achieve good effects. Keywor
5、ds-Medical Image; Rapid Registration; Mutual Information I. INTRODUCTION The application of medical imaging system provides different modes of images for medical diagnostic. Multi-modal medical images can offer a variety of medical information, which have their own characteristics for the doctor. Fo
6、r example as in 1, X-ray Computer Tomography (CT) has high resolution for human skeleton; Nuclear Magnetic Resonance Imaging (MRI) can obtain clear soft-tissue picture; Single-photon Emission Tomography (SPECT) and Positron Emission Tomography (PET) are good for checking the human body function. As
7、we all know, the single-mode image can not provide sufficient information that doctors need, so different modes of images often require registration and fusion in order to obtain as much information as we need. In the process of image fusion, registration is a key and pre-condition in 2-3, whose aim
8、 is to make the relevant points of two images to reach consensus on the space. The quality of registration results directly affects the consequent of image fusion, which affects diagnostic accuracy and reliability directly in the meantime. It is why the technology of medical image registration has a
9、lways been the focus of bio-medical engineering. Generally, there are two types of method in image registration that are feature-point-based and pixel-gray-based, which are described in 4. Feature-point-based method is one type registration algorithm, which is used simply and widely, according to th
10、e corresponding feature points between images to carry out geometric registration. But the greatest drawback of such method is that the precision of registration is restricted by segmentation accuracy, selection of position, and number of the feature points. Meanwhile, it is not good for the images
11、of which the boundary is not clear. In addition, pixel-gray-based method can obtain high precision of registration results by the principle of gray similitude, and does not require any preprocessing steps to carry out registration. Mutual information (MI) algorithm, which is pixel-gray-based, is an
12、image registration method. The cost function is selected by the similarity measure in mutual information algorithm, and gets the minimum cost during searching technology. This method can get very accurate registration results, and does not need any other priori knowledge; therefore, mutual informati
13、on has become peoples research focus currently, which has emerged in 5-7. Nonetheless, compared with feature-point-based registration method, MI algorithm has high complexity to time and space, and has slow speed to computation, that is the cost of statistical method. This paper provides a solution
14、to improve computation speed by optimizing search method. The remainder of this paper is organized as follows. The next Section presents the principle of mutual information technique in image registration and discusses the normalized mutual information. In Section the algorithm of rapid registration
15、, used for speeding up registration process is described. Registration result using rapid method and normal method are presented in Section . In the Section conclusions are given. II. MUTUAL INFORMATION TECHNIQUE IN IMAGE REGISTRATION A. Principle of Image Registration Medical image registration inc
16、ludes image positioning and conversion, which makes the corresponding points fully consistent with spatial location and anatomical structure in two images. Medical diagnosis requires the results of the registration to match exactly in the two images with all the anatomic points, or at least all the
17、diagnostic value of points in surgical area as in 3. Digital images can be described by a two-dimensional matrix, if 1( , )Ix yis the source image, and2( , )Ix yis the target image, which means the gray value of the point( , )x y, and the relationship of registration can be represented as: 21( ,)( ,
18、)Ix yf Ix y= (1) And f is a geometry function in two-dimensional space. The main task of registration is to find the best relationship f which makes two images to achieve the best match in spatial transformation. 978-1-4244-4713-8/10/$25.00 2010 IEEEB. Mutual Information as Similarity Measure Mutual
19、 information, as the similarity measure to different modality image registration, does not require a linear relationship existing between the source images. Information theory approach assumes that the gray value of the position in one image can predict the gray value of corresponding location in th
20、e other image when the two images achieve registration completely as in 6. Otherwise, the prediction is invalid when two images do not match with each other completely. Mutual information that is a measure of statistic correlation about two random variables comes from the information theory; it can
21、be described by the “entropy”, which represents the complexity and uncertainty of a system. The entropy of an image reflects the distribution of pixel gray in image processing, it means more gray levels and more scattered gray, make the value of entropy greater, and meanwhile the dynamic range of gr
22、ay is full application and gray curve is flat in the histogram. The marginal entropy of A and B in 7 can be defined as ( )( )log( )AAH Ap ap a= (2) ( )( )log( )BBH Bp bp b= (3) The definition of the joint entropy is ( , )( , )log( , )ABABH A Bpa bpa b= (4) Where ( )Ap aand ( )Bp bare marginal probab
23、ility distribution for two random variables A and B, and ( , )ABpa b is joint probability distribution. The mutual information of two variables A and B is given by (,)()()(,)IA BHAHBHA B=+ (5) When two multi-modal images are matched, A and B can be considered the variables about image gray, a and b
24、are the gray values. The probability distribution will be get by normalized joint gray level histogram of two images, which is defined as h(a,b). The joint probability distribution and marginal probability distribution is ,( , )( , )( , )ABaA bBh a bpa bh a b= (6) ( )( ,)AABbBpapa b= (7) ( )( , )BAB
25、aApbpa b= (8) The mutual information can be defined as ( , )( , )( )( )( , )( , )log( )( )ABABa Ab Bpa bI A BH AH BH A Bpa bp a p b=+=(9) It is the difference between the sum of marginal entropy and joint entropy of two images. Therefore, when the positions of two images are identical, the informati
26、on shared between them must be maximized and the mutual information of the gray values about these two images is the maximum. Basically, the mutual information can be estimated by the general distribution between the joint probability distribution PAB(a,b) and marginal probability distributions pA(a
27、) and pB(b). C. Normalized Mutual Information The mutual information measure is applied to medical image registration successfully, but on the other side, the size of the two images overlap has a great influence to the measure of mutual information because the mutual information is proportional to t
28、he amount of overlapping of two images. With the reduction in overlapping regions, and decreasing the number of pixels, which participate in mutual information statistics, will lead to mutual information value decreasing. Meanwhile, the increase in the number of mismatched pixels may lead to value o
29、f mutual information increasing as in 8. Therefore, maximizing the value of mutual information can not guarantee getting right-on registration results. Normalized mutual information (NMI) is proposed to solve this problem. The objective function can reflect the relationship between mutual informatio
30、n value and registration parameters more accurately by NMI, which can be written as: (,)()()(,)NMI A BH AH BH A B=+ (10) The similarity measure of two images can be measured by using normalized mutual information. The normalized mutual information value is greater, the registration result is better.
31、 III. ALGORITHM OF RAPID REGISTRATION Normal mutual information registration is suitable for quasi-overlapping regions between the target image and source image by using all available images gray values directly because it does not need to extract features. The disadvantage of the process is large n
32、umber of calculations and low speed; it can be solved by two-step search strategy to target range. Firstly the coarse granularity search determines the interesting range in the target image, and then fine-grained search computes similarity measure to achieve final registration. This process avoids c
33、omputing the useless values of mutual information to speed up the process of registration. A. Process of Searching Target Area The search for the target area in the source image is shown in Figure 1, A is the target image and B is the source image. The feature space is made up by all gray values of
34、the image. We can get the size of the searching area in the source image-B such as the No.1 region according to the size of target image-A. We compute the value of NMI of the target region after every search through the rotation of the source image and the translation of searching area by pixels, th
35、e final result of registration is the region that has the maximum value of NMI, such as No.2 region in image-B. Figure1. Regional search for source image AB B. Two-step Searching Strategy The histogram, mutual information entropy, and NMI with the target image have to be computed when searching for
36、the target region if the basic process of registration is chosen. Calculation of this process is the largest and the most time-consuming in the whole registration process. We use two-step searching strategy to minimize the calculation of it. The method as follows: The pixel ratio of target image is
37、given byMN, 1( , )I i jis the gray value of the pixel (i, j), and the mean gray of target image is 11111( ,)MNijIIijMN= (11) Similarly, 2( , )Ii j is the gray value of the pixel point (, )i j in the current searching area, and the mean gray of current searching area is 22111( ,)MNijIIijMN= (12) We u
38、se the calculation of between-class scatter in fisher linear discriminate classification for reference as in 9; the between-class distance, which is the distance between the searching area2Iand the target image1I, is given by 211111211111|( ,)( ,) |21|21( ,)( ,)MNMNijijMNMNijijIi jIi jIIIIIi jIi j=+
39、 (13) There must be similarity between searching area2Iand target image1I during moving the searching area, which means that the smaller between-class distance the better 1Iand 2I can match. We choose the best between-class distance, whose range is 0, 0.2 due to01and experimental data. Within this r
40、ange, two area are understood as the same class, otherwise, it explains that there is considerable variability between searching area and target image, we does not need calculate the NMI for them, and only need continue to search next area. This process is called the coarse granularity search, which
41、 can determine the uninterested regions and delete them from source image by. Algorithm is as follows a) Calculation of the mean of gray of target image 1I. b) Calculation of the mean of gray of current search area 2I. c) Calculation of the between-class distance | 21|21IIII=+ d) if(0.2 &0) % Requir
42、ements value range 1212(,)max(,)NMI IIMI II= % Calculate NMI else break % Exit, pass current area We choose the interested region that is classified as one class with the target image region to fine-grained search after the coarse granularity search, meanwhile the searching area, which fail to match
43、 the target image, are separated from whole source image. The purpose of the fine-grained search is calculating the NMI of interested region, and getting the maximum of NMI, that is the final result of registration. The process of coarse granularity search is like image segmentation, means that inte
44、rested region, whose value of mutual information is calculated only, is know from the source image. There must be similarity between image remained and target image after image segmentation if registration is successful. The similarity between searching region and target image is changing with the t
45、ranslation of searching area by pixels. Areas of interest will be gradually minimized by between-class distance, and then the value of normalized mutual information can be calculated to determine the optimal result of registration. In this way, calculation is reduced significantly, and registration
46、speed is much faster than normal mutual information registration. IV. EXPERIMENT OF REGISTRATION A. Results of the Experimental The CT image of thoracic cavity is source image, and the region of heart is target image in the experiment of registration. In process of registration, normalized mutual in
47、formation (NMI) is used as the method of measure, which measures the similarity of two images. According to the definition of mutual information, the greater the value of NMI is, the better effect of registration is. Experimental results are shown in Figure 2. A is target image, whose pixel ratio is
48、 9070; B is source image, whose pixel ratio is 353353; C1 is the result of registration based on normal mutual information algorithm; C2 is the result of registration based on rapid search algorithm. Apparently, there are very few obvious the precision of registration between these two methods. A. T
49、arget Image B. Source Image C. Result of Normal Registration D. Result of Fast Registration Figure2. Comparison of registration results Figure3. impact on the accuracy of registration B. Performance Analysis The computer used for the main work is ordinary PC. The model of CPU is Core II E7400, main
50、frequency is 2.8GHz, and memory is 2G. The software environment is Matlab 7.1. Running results are as follows: It takes 1899 seconds to obtain the best result of registration, whose value of NMI is 1.4075, by using normal mutual information registration. The values of NMI are different by using two-
51、step search strategy to target range because of taking different values range of between-class distance. The results are shown in Figure 3. When the step that is the number of pixels to shift in x and y directions for translation check is fixed and unchanging value, we can obtain the optimal entropy
52、 of NMI (NMI=1.4075) by using rapid registration algorithm, it is the same as using normal mutual information algorithm, and the value range of between-class distance is within 0, 0.2. The precision of registration declines markedly if theout of the range. Because the accuracy of registration depend
53、s on the entropy of normalized mutual information (NMI), the experiment shows that the value range ofthat is our choice can not reduce the accuracy of registration. Table1 shows the running time of the procedure of registration, it is affected by the value range of between-class distance. When the r
54、ange of is 0, 0.2, the result of rapid registration algorithm, which keeps the precision of registration, has the same accuracy as the result of normal mutual information, and meanwhile, the running time of procedure reduces to the 1/6 of original. V. CONCLUSION AND PROSPECT This paper proposes a ra
55、pid medical image registration algorithm, which based on mutual information, through studying the principle and algorithm of medical image registration. Two-step search strategy is used to speed-up registration process. Firstly, the coarse granularity search minimizes target range in source image by
56、 using between-class distance between search area and target image. Secondly, fine-grained search computes normalized mutual information. Experimental results show that this method can solve the problem of low speed; it keeps precision of registration at the same time, and achieves good effects. Thi
57、s algorithm can finish the process of registration well, but there is no such as “gold standard” in medical image registration. Therefore, efficiency of algorithm should be gradually improved in application of medical clinical diagnosis, so as to meet the application for multi-modal images in biomed
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