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ISBN 978-952-5726-09-1 (Print) Proceedings of the Second International Symposium on Networking and Network Security (ISNNS ’10) Jinggangshan, P. R. China, 2-4, April. 2010, pp. 174-177 Spatial Information Based Medical Image Registration Using Mutual Information Benzheng Wei 1,2* , Zaitao Liu 1 , and Xin Peng 1 1 College of Science and Engineering, Shandong University of Traditional Chinese Medicine, Jinan, 250355,China Email: wbz99@sina.com 2 College of Automation Engineering,Nanjing University of Aeronautics and Astronautics, Nanjing , 210016,China Email: 6and5@sdutcm.edu.cn, pengxin0531@163.com Abstract—Image registration is a problem that arises in many image processing applications whenever information from two or more scenes has to be aligned. A new approach to the problem of multimodality medical image registration is proposed, using a basic concept from spatial information, mutual information, and relative entropy, as a new matching criterion. Firstly, the feature characteristics like location, edge strength and orientation are taken into account to compute a joint probability distribution of corresponding edge points in two images. Then the mutual information based on this function is minimized to find the best alignment parameters. Finally, the translation parameters are calculated by using Powell algorithm. The experiment results showed that the method have achieved a good performance. Index Terms—medical image, image registration, Spatial information, Feature characteristics, Mutual information I. INTRODUCTION Image registration is a valuable technique for medical diagnosis and treatment. In image registration the use of an adequate measure of alignment is a crucial issue. Current techniques are classified in two broad categories: area based and feature based. All methods include some similarity measure. Mutual information (MI) is currently a popular registration method to sca1e the similarities between two image sets and for convenience of calculation and analysis [1] . It was first proposed as a registration measure in medical image registration in 1995 . independently by Viola and Wells [2]and by Collignon [3]. Now MI has been accepted by many researchers as one of the most accurate and robust retrospective registration methods. However, mutual information is not a panacea method. Despite the general promising results, mutual information-based matching can result in misregistration when the images are of low resolution or the images contain little information or there is only a small region of overlap [5]. The mutual information registration function can be ill-defined, containing local maxima. A possible solution to reduce the failure of MI registration can be by using the spatial information and optimization algorithm . At present, many researchers have proposed some hybrid mutual information algorithms to enhance the performance of image registration, such as Pluim et al [1] combined *Corresponding author: Benzheng WEI. © 2010 ACADEMY PUBLISHER AP-PROC-CS-10CN006 174 mutual information with gradient method, Yao Yucui et al [6,7,8] employed mutual information with morphological gradient approach to improve the registration accuracy and robustness. In this paper, a new approach to the problem of multimodality medical image registration is proposed, using a basic concept from spatial information, mutual information, and relative entropy, as a new matching criterion. In addition, this paper focus on the registration approach of multimodality image and a modified particle swarm optimization algorithm is proposed to restrain local maxima of mutual information function and improve the registration accuracy. This paper is structured as follows: In Section 2, we present the mathematical model of spatial information detection approach. Section 3 describes the coarse registration based on the principal axes algorithm. The feature point set extraction approach and energy function of mutual information based the spatial information is presented in Section 4. Then in Section 5, the feasibility of our approach is illustrated where we show registration results for medical 2D examples. Finally, this paper is closed in section 6 with a brief conclusion. II. CONTOUR FEATURE DETECTION Contour feature is a significant part of information extracted from an image which provides more detailed understanding of the image. Common features include corresponding points, edges, contours or surfaces. In order to get a more accurate contour of the medical images, it's necessary to eliminate the interference of image noise and get the actual size of the tilt image as much as possible. According to those edge detection operators, such as Sobel, Log, Candy and other conventional edge detection operator, usually get a low positioning accuracy and a poor performance of antinoise for medical image. Mathematical morphology is a new image processing method based on geometry algebraic and topology, which is proposed by French scholar G. Matherom and J. Seera [8]. It set the objectoriented for research, and the objects can be contacted through the structural elements. Expansion and corrosion is the basic operations of the morphology, and the opening and closing operators can be further expanded by the expansion and corrosion operators. The morphology gradient is a nonlinear difference operator determinate by the difference value of maximum
and minimum structural elements in definition domain, used to achieve the edge detection of the image or signals. Let f ( x, y ) be original image and g( x, y ) be structural element, then the formula of morphology gradient operator is: Grad ( f ) = ( f ⊕ g) − ( f Θ g) (1) Where ⊕ denotes the expansion operator, Θ denotes the corrosion operator. From (1), we can see that the operator make the input image gray-scale step to become even more dramatic. According to the principle of generalized morphological filter, as far as possible to improve the integrity and richness of edge feature detail and obtain the smoothness edge curves, the improved morphology gradient operator is designed based on the expansion, erosion, opening and closing four operators for image anti-noise characteristics. The improved morphology gradient operator is described as IGrad ( f ) = ( f o g) ⊕ g − ( f • g) Θg (2) We call IGrad ( f ) as the improved morphology gradient operator. In order to extract the direction information of the edge pixels and easy to construct vector group at the same time, we select two cross and cross-shaped 3× 3 structural elements, and make them symmetrical and complement each other. Because the random noise may be smaller than the width of the structural elements of the width, which are mixed with the processed images, therefore, it’s very difficult to obtain the best filtering effect by using the separate structural element, so they can be used as the linear combination form due to complementary characteristic of the two structural elements. The optimum weighted coefficients can be determined by the least mean square adaptive method, and the improved morphology gradient filter operator can be written as: FGrad ( f ) = c IGrad1( f ) + c IGrad 2( f ) (3) 1 2 Where c1 , c 2 are the weighted coefficients, the IGrad 1 and IGrad 2 are the improved morphology gradients with the two structural elements. The main purpose that the improved morphological gradient operator is introduced and applied to quickly identify the probable location of the edge and edge points, while the image is rapidly de-noised in the image processing. After the medical image is processed by the proposed new operator, it can be achieved an available gradient image with the direction information. Then the data set of the edge point vector group{ E1, E2, L , E n } can be stored as the data list, where Ei =< ei, θi > , e i is the edge point i in the two-dimensional plane coordinates, and θ i is the edge gradient direction. In addition, the improved morphological gradient filter can overcome the shortcoming of tend to produce the image edge blur which is often caused by the linear filtering method in image smoothing, and it’s easy-to-parallel computing to better meet the real-time image processing requirements. In the experiment, the selected structural elements are[0 10;1 1 1;0 1 0] and [1 0 1;0 -1 0;1 0 1]. III. PRINCIPAL AXES ALGORITHM BASED COARSE REGISTRATION A Principal Axes Algorithm Suppose that image F is of M × N pixels with its upper left pixel being (1,1) , and f ( xy , ) is the gray value at point ( x, y ) . Since some moments of an image region are invariant to geometric transformation such as translation, rotation, and scale change, they are widely applied to object classification and identification. If f ( xy , ) is a 2-D discrete function, then the moment of order ( p + q) is defined as M pq , M N p q = ∑∑ x y f( x, y) (4) x= 1 1 Then the central moment is expressed as M N ' p q M pq , = ∑∑ ( x− x) ( y − y) f( x, y) (5) x= 1 1 Where x = M1,0 / M0,0 , y = M0,1 / M0,0 the ( x, y ) is called centroid coordinates of the object. The moment of the object having rotated by θ , or computed with reference to axes X ' ' and Y , is invariant to rotation transformation. The rotation angle θ is as follows: ' ' ' tan 2θ = 2 M1,1 / ( M2,0 − M0,2 ) (6) Application of the above formula to calculate the difference of two images about the centroid coordinates and principal axis angle separately, and then initial registration parameters ( Δx, Δy, Δ θ )can be obtained and used as the initial registration parameters for coarse registration. B Model estimation As in [9], we assume that the type of transformation is rigid and not deformable; the model that describes the geometric transformation has the following expression: Pd = RPs + T (7) ' ' ' Where, Ps ( x, y, z ) is a source point; Pd ( x , y , z ) is transformed corresponding point;R=[R 11 R 12 R 13 ;R 21 R 22 R 23 ;R 31 R 32 R 33 ] is a rotation matrix; T = [ T , , ] T x Ty Tz is a translation vector. Assumed that the α, βγ , are the angles of the transformed image rotated by x,y,z axes separately, then R can be rewritten as: R = . RRR γ β α C Coarse registration method The principal axes algorithm can be described as follows: Firstly, calculate the centroid, and eigenvectors of the source and target images via an eigenvalue decomposition of the covariance matrices. Secondly, align the centers of mass via a translation. Finally, for each image determine the angle Δ θ , the maximal eigenvector forms with the horizontal axis, and 175
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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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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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in routing table. When search resou
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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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