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otate the test image about its center by the difference in angles. The images are now aligned. IV. THE HYBRID MUTUAL INFORMATION ALGORITHM An important characteristic of an image is the high degree of correlation among the neighboring pixels. In other words, these neighboring pixels possess similar feature values, and the probability that they belong to the same cluster is great. This spatial relationship is important in clustering. Recently, a new clustering algorithm called K- harmonic means(KHM) has been introduced by Zhang et al.[10,11] in 2000, which is arose from an optimization criterion based on the harmonic mean. This algorithm shows promised in finding good clustering solutions quickly, and outperforms k-means and Gaussian expectation-maximization in many tests. The KHM algorithm also has a novel feature that gives more influence to data points that are not well-modeled by the clustering solution. In this paper, the KHM algorithm is used to extract the feature point sets of the medical images based the edge point vector group { E1, E2, L , E n }, and we select the number of clustering centre K=150 that means the feature point sets has 150 points. The more detail bout KHM algorithm, reference to[10,11]. Mutual Information is an error metric (or similarity metric) used in image registration based on ideas from information theory [1]. The strategy is this: minimize the information content of the difference image. The mutual information between two unlabeled point-sets is a function of the chosen spatial mapping (for example, rigid, similarity, affine). The energy function of the feature points matching will be presented based on mutual information following. Denote the feature point-sets of pre-registration medical images by X = { Xi , i = 1,2,..., N1} and Y = { Yi , i = 1,2,..., N2} respectively. The point sets 2 3 are assumed to be in R or R . Then, a suitable choice for the distance measure between X and Y is: N q DT ( ) = ∑ || X−TY|| . (8) i= 1 In (8), following the KHM clustering algorithm, we choose q = 3.5 , T is the rigid spatial mapping linking the two point-sets in this paper. With the spatial mapping T, the mutual information between the point-sets is a function of the joint probability P: MI() P M( X,) Y P log P N1 N2 ij , ij N1 N2 i= 1 j= 1 P k 1 kj P = l= 1 il = =∑∑ ∑ ∑ , (9) where the joint probability Pij = P{ I = i, i∈ (1, 2,..., N1), J = j, j∈(1, 2,..., N2)} the above joint probability characterizes the likelihood of obtaining a pair of features (, i j ), i form X and j form Y. Intuitively, the likelihood should be large if i and j are homologies and small if they are not. The solution for the joint probability is : Pij ( T) = exp( −α Dij ( T) − λ) . (10) In (10), α and λ are two Lagrange parameters, the constraints on the expected value of the point matching distance measure and the probability sum respectively. The more detailed discussion aboutα and λ , reference to see [14]. E ( P, T, λα , ) = α( P D ( T) − d) + MI ij ij ij ∑ λ( P − 1) + P log P −κMI( P) ij ∑ ∑ ij ij ij ij In (11) The noise level is, . (11) exp( −α DT ( )) d = ∑ D( T) ij ∑ exp( −α DT ( )) ij . κ > 0 is a new parameter which acts as a weight on the mutual information vis-a-vis the entropy and the distance measure. If κ = 1 , the separate entropy term and the joint entropy in the mutual information perfectly match one another. In this paper, we choose κ ∈ [0.3,1] in the optimization processing. Our approaches to minimizing the energy function in (12): * ∂ = arg min EMI ( P, T, λ, α) . (12) The best registration would be achieved if the objective function (metric function) reaches the global minimum. However, the function generally contains a set of local minimums. To solve multiple local minimum problems, a Powell algorithm is developed to solve the registration problem in this paper. V. THE SIMULATION AND EXPERIMENT We implement registration of brain image to confirm performance of proposed algorithm in last section. The algorithms are implemented by using Matlab 7.1 on a Pentium IV, 2.8 GHz, 1GB RAM computer, and image file is from database (www.bic.mni.mcgill.ca/brainweb). In the following experiment, the parameters in translate procedure is initialized as search space in x direction is x∈[-20, 20] and y direction is y∈[-20, 20], the search space in rotation is θ∈[-15°,15°]. A Experiment I. In Fig. 1, the image (a) and image (b) are illustrated. The size of each image is 512×512 pixels under DICOM format and the whole images have good quality and don’t require a pre-treatment. In our experiment, image Fig.1(b) as source image and image Fig. 1(a) serve as target image. The two images are alignments by using MI and the presented hybrid MI (PHMI) method in this paper separately. And our experiment results are shown in Tab.1 and Tab. 2. The Tab. 1 shows the comparison of experiment result for image registration transform parameters (∆x, ∆y, ∆θ), and the Tab. 2 shows the 176
esults of the spatial transform parameters and mutual information value by using the similar method. (a) Target image (b) Source image Figure 1. Brain images for registration TABLE 1. COMPARISON OF REGISTRATION PARAMETERS ∆x (pixel) ∆y (pixel) ∆θ (°) Standard Value of Transformed 12 10 -10 Average MI 12.86 9.42 -10.38 Searching Value PHMI 12.16 10.02 -10.17 TABLE 2. THE SPATIAL TRANSFORM PARAMETERS AND MUTUAL INFORMATION Algorithm MI PHMI Solving times 100 100 Average Value 167.64 130.09 Standard deviation 7.567 3.12 Mutual information 2.157 2.541 Average times (s) 386.2 315.6 B Experiment II. In this experiment, the two brain images (Shown in Fig. 2.) of the same patient are registered to test the performance of the presented new method in separately 100 times. The size of each image is 256×256 pixels, and the MR images is set as source image. The registration results are shown in table 3. After this simulation, we can see that the PHMI algorithm in accuracy and speed with the more obvious advantages than the other two algorithms. (a) MR image (b) SPECT image Figure 2. the two registration images TABLE.3 THE COMPARISON REGISTRATION RESULTS Algorithm MR-SPECT Time(s) Success rate MI 2168 72% PHMI 1275 98% VI. CONCLUSIONS In the paper, we have presented an innovative PHMI method for the automatic registration of medical image, and it has achieved a good performance. This registration is actually a problem of searching optimum parameters in multi-dimension space. The existence of local maxima in object function brings much trouble in optimizing process. In this paper, we use Powell to extend the searching ability, the method can guarantees registration convergence to the global optimum. Though combining spatial information and mutual information as criterion for multimodality medical image registration still remains problems unsolved, the experiments results prove that the proposed method has robustness and effectiveness. ACKNOWLEDGMENT The work was supported by the Natural Science Foundation of Shandong Province (ZR2009CM085) and A Project of Shandong Province Higher Educational Science and Technology Program (NO.J09LF23). REFERENCES [1] Josien P W Pluim,Maintz J B Antoine ,Max AViergever. Image registration by maximization of combined mutual information and gradient information. IEEE Transactions on Medical Imaging , Vol. 19, No. 8, 2002, pp. 809-814. [2] W. M. Wells III, P. Viola, H. Atsumi, S. Nakajima, and R. Kikinis, “Multi-modal volume registration by maximization of mutual information,” Med. Image Anal., vol. 1, no. 1, pp. 35–51, 1996. [3] F. Maes, A. Collignon, D. Vandermeulen, G. Marchal, and P. Suetens, “Multimodality image registration by maximization of mutual information,” IEEE Trans. Med. Imag., vol. 16, no. 2, pp. 187–198, 1997. [4] C. Studholme, D. L. G. Hill, and D. J. Hawkes, “Automated three-dimensional registration of magnetic resonance and positron emission tomography brain images by multiresolution optimization of voxel similarity measures,” Med. Phys., vol. 24, no. 1, pp. 25–35, 1997. [5] G. P. Penney, J. Weese, J. A. Little, P. Desmedt, D. L. G. Hill, and D. J. Hawkes, “A comparison of similarity measures for use in 2D-3D medical image registration,” IEEE Trans. Med. Imag., vol. 17, no. 4, pp.586–595, 1999. [6] YAO YuCui ,YANG LiCai , LI jinLiang. Medical image registration by combined morphology gradient and mutual information[J].Journal of Biomedical Engineering Research, Vol. 25, No. 2, 2006, pp. 75-78. [7] TANG Min. Image registration based on improved mutual information with hybrid optimizer[J ] . Chinese Journal of Biomedical Engineering , Vol. 17, No. 1, 2008, pp. 18-25. [8] WEI Benzheng, ZHAO Zhimin, SONG Yizhong. Anovel algorithmfor multimodality medical image registration based on IPSOalgorithm and hybrid information[J], Journal of Optoelectronics·Laser, Vol. 20, No. 9, 2009, pp. 1271-1274. [9] C. R. Maurer, R. J. Maciunas, and J. M. Fitzpatrick ‘Registration of head CT images to physical space using a weighted combination of points and surfaces’, IEEE Transactions on Medical Imaging, 17(5): pp 753–761, 1998. [10] B.zhang.Generalized K-harmonic means-boosting in unsupervised learning. Technicl Report Hpl-2000-137, Hewlett-Packard Labs,2000. [11] G.Hamerly, C. Elkan, "Alternatives to the k-means algorithm that find better clusterings", Proc. of the ACM Conference on Information and Knowledge Management, CIKM-2002, 2002, 600-607. 177
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Proceedings The Second Internationa
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Table of Contents Message from the
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Zuming Xiao, Zhan Guo, Bin Tan, and
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Message from the Symposium Chairs T
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Second International Symposium on N
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model that can deal with time serie
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training for the Wushu competition
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information, called weak uncertain
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Student side Student side Student s
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If we define element of student as
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QoS, each frame data is divided int
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for Imaging Two and Three Phase Flo
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A. Profiling&following control algo
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Research and Realization about Conv
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PDF document structure is a tree st
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support 10 Mb / s. But ENC28J60 onl
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condition the first byte output of
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According to maximum membership deg
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ubber according to the mass ratio o
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Ⅲ. AN IMPROVED DNA ALGORITHM FOR
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Ⅴ.CONCLUSION REMARKS DNA computer
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its first child q 1 on the left, th
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chains can greatly improve efficien
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II. RELATED WORK A. Mobile Service
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special services. SOAP is used to b
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detection methods of DDoS attacks m
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Step4 calculate the new subordinate
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Figure 1. An analysis of the partit
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The preceding three formulas can be
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And the decay speed of buffer seque
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distance of view point. Given that
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Ⅳ. EVALUATION OF BLENDED LEARNING
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symmetric with respect to the origi
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each sample belongs to each categor
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A. Data Preparing To generate our t
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oth α and β . determination of Qu
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Strong earthquake 0.1< M L
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indirect causes, and the logical re
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egression. Granger causality test i
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B. Evaluation We have evaluated thi
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used as a source and neighboring ce
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Figure 3. Drainage networks generat
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Combinational logic unit failures i
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Tabal.1 Combinational fault logic t
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under the endorsement of both the m
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TABLE I. DESCRIPTION OF PROPOSITION
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others through the selective emotio
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such as weather information, techno
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the opening window, a related page
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1) Process context storage areas. I
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V. CONCLUSION In this thesis, sCPU-
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main types of horizontal search env
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Enterprise Portal security provides
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[2] Kumaravel, N., and Kavitha, V.,
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output, so BP network has been wide
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input to the artificial neural netw
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(2) In a process (tokens from outsi
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The reduction process consists of t
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all eight normal vectors are identi
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is B object , and the number of emp
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xi, j y' = εα ( (1 + tanh( )) −
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Error 8000 7000 6000 5000 4000 3000
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Architecture (AMBA) a new bus archi
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In order to ensure the smooth proce
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In this paper, we adopt two Sobel o
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four layers.The far right of the gr
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TABLE II. OPERATIONAL EMPLOYEE TABL
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A. Object-relational Type To audit
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to execution time. Also, DBA would
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Liping Chen .......................
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