Medical Image Registration Algorithm with ... - Semantic Scholar
Medical Image Registration Algorithm with Generalized Mutual Information and PSO-Powell Hybrid Algorithm Jingzhou Zhang, Pengfei Huo, Jionghua Teng, Xue Wang, and Suhuan Wang College of Automation, Northwestern Polytechnical University, Xi’an 710129, China
Abstract. The medical image registration algorithm uses the mutual information measure function that has many local extremes. Therefore, we propose our medical image registration algorithm that combines generalized mutual information with PSO-Powell hybrid algorithm and uses the objective measure function based on Renyi entropy. The Renyi entropy can remove the local extremes. We use the particle swarm optimization (PSO) algorithm to locate the measure function near the local extremes. Then we take the local extremes as initial point and use the Powell optimization algorithm to search for the global optimal solution. Section 2.2 of the paper presents the six-step procedure of our registration algorithm. We simulate medical image data with the registration algorithm; the simulation results, given in Table. 2 and 3, show preliminarily that the registration algorithm can eliminate the local extremes of objective measure function and accelerate the convergence rate, thus obtaining accurate and better registration results. Keywords: Medical image registration, Generalized mutual information, Measure function, Optimization algorithm.
1 Introduction Image registration is the process of overlaying two or more images of the same scene taken at different times, from different viewpoints, and/or by different sensors. It geometrically aligns two images—the reference and sensed images [1]. Ever since the concept of mutual information was introduced into the region of image registration has the validity of this new approach been widely accepted. Recently the registration based on mutual information has been widely used in occasions of image registration[2-4]. The registration algorithm based on maximization of mutual information(MMI) only uses statistical performance of gray values whereas neglects the image anatomical characteristics, so it is more robust and accuracy than traditional based on feature [5]. However, a few shortcomings still exist in the MMI registration algorithm, the objective measure function based on mutual information will lead to produce some local optimum in searching process, it would lead that the optimization process end in local optimum rather than global optimum [6]. Through the analysis of Renyi entropy [7], we found that mutual information based on Renyi entropy can not only remove unwanted local optimum but also has the depth of the basin of attraction. A new generalized mutual information measure function based on Renyi entropy has been given in this paper on the basis of the two characteristics of Y. Tan, Y. Shi, and K.C. Tan (Eds.): ICSI 2010, Part I, LNCS 6145, pp. 160–166, 2010. © Springer-Verlag Berlin Heidelberg 2010
Medical Image Registration Algorithm with Generalized Mutual Information
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Renyi entropy. At first the PSO algorithm was used to find the local extreme of this measure function, which is use of the feature removing unwanted local optimum and smoothing out optimal curve. Then the Powell optimization algorithm was used to locate the global optimal solution which is use of the characteristic that has the depth of the basin of attraction, make the registration function easier to be optimized. The objective function can be located fast and accuracy through the mixed optimization algorithm and measure function. The registration tests proven that this algorithm and measure function can overcome the local extreme of the mutual information measure function, make registration results up to a sub-pixel level, and also have better robust and accuracy.
，
，
2 Methods 2.1 Generalized Mutual Information Based on Renyi Entropy According to Renyi entropy’s definition, the Renyi entropy of an image is defined as: N
Rq ( X ) = (1 − q ) −1 ln(∑ Pi ), q ∈ R, q ≠ 1 q
(1) . It is important that the Renyi entropy tends to the Shannon entropy as q→1. In analogy to Shannon entropy normalized mutual information, the generalized normalized mutual information of the two images based on Renyi entropy is given by i =1
I(A,B) =
R(A) + R(B) R(A,B) .
(2)
An image is selected as reference image. The floating image can be get by translating the reference image along x axis. The normalized mutual information of the two images can be computed, which is based on Renyi entropy and Shannon entropy, when Parameter q of the Renyi entropy is 2, 1.5, 1.25, 1.1, 0.9, 0.5, 0.25 respectively. The results are shown in Fig.1[7].
Fig. 1. They are the translation curves of normalized MI based on different entropy
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According to Fig.1, Renyi entropy is more approximate to the Shannon entropy when q is more near one. The normalized mutual information curve based on Renyi entropy is most approximate to normalized mutual information curve based on Shannon entropy as q is 1.1. But at the same time the normalized mutual information curve based on Renyi entropy remove unwanted local optimum, smooth out optimal curve than curve based on Shannon entropy. 2.2 Hybrid Optimization Algorithm Based on PSO and Powell PSO [8] is a stochastic population based optimization algorithm, firstly introduced by Kennedy and Eberhart in 1995. It is a global optimization algorithm. But in the end it is difficult to decide whether the solution we got is global optimum value in solution space, furthermore, whether it is located next to global optimization value. However, the Powell algorithm has a good performance in finding out local extreme. Thus the Powell algorithm could combine with the PSO Algorithm, and different optimization algorithms are used in different searching process. At first the PSO global optimization algorithm was used to find the local extreme of generalized mutual information measure based on Renyi entropy as q is equal to 1.1, which is use of the feature that remove unwanted local optimum, smooth out optimal curve. Then the Powell local optimization algorithm was used to locate the global optimal solution by searching the current local optimal extreme which is use of the characteristic that has the depth of the basin of attraction as q is 0.99, make the registration function easier to be optimized. The PSO-Powell hybrid optimization algorithm in this paper solved searching the registration parameters process described as follows.
，
，
，
(1) Select a point T in three-dimensional solution space randomly, and Initialize a particle swarm in the solution space with the center of point. As a three-dimensional vector, the displacement of x, y and the rotational angle z. (2) Do a certain number of iteration using PSO algorithm, then we can get the current local optimal solution T1, when parameter q in objective measure function is equal to 1.1 in this process. (3) Calculate the objective measure functional value MI and MI1 in point T and T1 respectively. If MI is less than MI1, go to (4), otherwise go to (6). (4) Taking T1 as initial point and use Powell optimization algorithm to get the optimal point in the neighbor region, when parameter q in objective measure function is equal to 0.99 in this process. (5) Initialized the Particle Swarm with the initial point T=T2, then go to (2). (6) Output the optimal solution and corresponding objective measure functional value as the optimal transformation parameters. The initial strategy of PSO algorithm are improved in the searching process after the first search, in short the last searching result of the Powell optimization algorithm is as the current initial optimal point of PSO algorithm. Thus the algorithm performance would be improved because it not only makes full used of the previous calculated results but also decreases possibility falling into the local extreme.
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3 Experimental Results The generalized mutual information measure function and mixed optimization algorithm are used in single-modality and multi-modality image registration. Single-modality image registration is using three different medical images and three floating images which are got form the former after a certain degree of rotation and translation transformation. Multi-modality image registration is using two different modality medical images, at the same time the performances of PSO algorithm, Powell algorithm and mixed algorithm are compared in the same computer. 3.1 Single-Modality Medical Image Registration Selecting two medical images as reference images, the first image is translated 9 pixels to the right along x axis, 4 pixels downward along y axis and rotated 7.5 degrees along counter-clockwise. The second image is translated 6 pixels to the right along x axis, 8 pixels downward along y axis and rotated 4.7 degrees along counter-clockwise. Then we can get two floating images. Using the two reference images and two floating images, single-modality image registration experiments are made with the algorithm in this paper. The results are shown in Table.1. Table 1. They are the results of the single-modality medical image registration experiment. The RMS is Root-mean-square of the 50 registration results. The mean is average of the 50 registration results.
15th 30th Image 45th A mean RMS 15th 30th Image 45th B mean RMS
x 9.0012 9.0061 9.0109 9.0040 9.0040 6.0169 6.0086 6.0147 6.0170 6.0170
y 4.0051 4.0031 3.9972 4.0009 4.0009 8.0006 7.9986 7.9892 8.0039 8.0039
z 7.4982 7.4988 7.5012 7.5008 7.5008 4.6976 4.7014 4.7009 4.7026 4.7026
△
△
x y 0.0012 0.0051 0.0061 0.0031 0.0109 -0.0028 0.0040 0.0009 0.0000 0.0000 0.0169 0.0006 0.0086 -0.0014 0.0147 -0.0108 0.0170 0.0039 0.0001 0.0001
△
z -0.0018 -0.0012 0.0012 0.0008 0.0000 -0.0024 0.0014 0.0009 0.0026 0.0000
GMI 1.4450 1.4450 1.4450 1.4450 1.4450 1.4212 1.4213 1.4212 1.4212 1.4212
T 74.810 100.386 69.277 103.692 109.386 146.793 139.386 146.776 110.338 117.120
According to the table, in the registration results of image A the horizontal offset error of the 45th results between theoretical value and registration result is 0.0109, it is more than 0.01. And the other parameters selected are all less than 0.01. While in the registration results of image B it is only that the parameter errors of the 30th registration results are all less than 0.01, and the others are not all less than 0.01. So the registration results of image B are slightly inferior to image A. However, the single-modality image registration results are all a high accuracy. At last, using the 15th registration results as registration parameters, and with bilinear transformation, image A is used for registration simulation. The Fig.2 could get form the simulation. The effect of the methods adopted in this paper is proved to be effective and better precision.
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Fig. 2. It is the simulation experiment of the single-modality medical image registration
3.2 Multi-modality Medical Image Registration We choose two groups of CT/MRI images. The two groups of CT/MRI images are used for multi-modality medical image registration, the registration optimization algorithm are Powell algorithm, PSO algorithm and PSO-Powell mixed algorithm Respectively, and the objective measure function is adopted generalized mutual information measure function based on Renyi entropy. The results of multi-modality medical image registration are shown in Table.2. According to the table, in the three algorithms the experimental time of the Powell algorithm and PSO algorithm are less than the hybrid optimization algorithm. While not only the average measure function values got by hybrid algorithm are the largest, but also that measure function values and registration parameters in every time got by hybrid algorithm are more concentrated in distribution than the other algorithm. General speaking, the registration results are up to a good precision by this hybrid algorithm and generalized measure function measure function in this paper. Table 2. They are the results of the Multi-modality medical image registration experiment. The mean is average of the 50 registration results. First group images Second group images x y z GMI T x y z GMI T 15th 11.302 -5.695 4.807 1.1202 56.124 31.026 -11.380 -7.704 1.0941 72.812 Powell 30th 10.332 -6.548 7.066 1.1205 44.017 34.250 -12.906 -2.980 1.0947 16.618 method 45th 11.531 -5.888 3.575 1.1207 37.875 32.395 -13.228 -6.330 1.0944 35.333 mean 10.797 -6.123 5.701 1.1206 34.896 32.306 -12.646 -5.715 1.0943 37.629 15th 10.614 -5.320 6.738 1.1253 23.189 33.804 -11.779 -4.736 1.0956 36.313 30th 8.904 -5.091 6.682 1.1251 49.801 33.791 -11.769 -4.750 1.0957 42.225 PSO 45th 9.142 -5.471 4.472 1.1247 23.768 33.548 -11.482 -4.801 1.0954 31.145 method mean 9.977 -5.607 5.632 1.1248 25.213 33.041 -11.874 -5.863 1.0953 32.807 15th 11.253 -5.618 4.757 1.1256 42.168 33.873 -11.432 -4.672 1.0959 97.020 Powell 30th 11.136 -5.533 4.711 1.1257 131.71 33.815 -11.332 -4.741 1.0959 84.559 +PSO method 45th 11.134 -5.672 4.709 1.1255 116.30 32.636 -11.145 -4.233 1.0958 68.079 mean 11.169 -5.586 4.708 1.1256 101.46 33.574 -11.394 -4.652 1.0958 65.669
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Fig. 3. It is the simulation experiment of the multi-modality medical image registration
At last, we choose one group of CT/MRI images to make registration experiment. Method used for registration is the method adopted in this paper. Then we can get the Fig. 3. The effect of the methods adopted in this paper is proved to be better.
4 Conclusions Though registration results of MMI have the advantages of high accuracy and independence from any image pretreatments there are still a few shortcomings. The registration images would exist better local matching, the interpolation algorithm would bring in errors. Thus objective measure function will produce a lot of local extreme, which has a large influence on optimization. The generalized mutual information measure function based on Renyi entropy and PSO-Powell mixed optimization algorithm have been adopted in this paper. At first the PSO optimization algorithm was used to find the local extreme of generalized mutual information measure based on Renyi entropy. Then the Powell optimization algorithm was used to locate the global optimal solution by searching the current local optimal extreme. The registration results have proven that this algorithm and measure function can make them up to a sub-pixel level, and also have better robust and accuracy.
，
，
，
References 1. Zitova, B., Flusser, J.: Image registration methods: A survey. J. Image and Vision Computing 21, 977–1000 (2003) 2. Ardizzone, E., Gambino, O., La Cascia, M., Lo Presti, L., Pirrone, R.: Multimodal non-rigid registration of medical images based on mutual information maximization. In: 14th IEEE International Conference on Image Analysis and Processing (2007) 3. Liu, Y., Fedorov, A., Kikinis, R., Chrisochoides, N.: Real-time Non-rigid Registration of Medical Images on a Cooperative Parallel Architecture. In: IEEE International Conference on Bioinformatics and Biomedicine (2009) 4. Andronache, A., von Siebenthal, M., Szekely, G., Cattin, P.: Non-rigid registration of multimodal images using both mutual information and cross-correlation. J. Medical Image Analysis 12(1), 3–15 (2008)
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J. Zhang et al.
5. Yang, F., Zhang, H.: Multiresolution 3D Image Registration Using Hybrid Ant Colony Algorithm and Powell’s Method. J. Journal of Electronics & Information Technology 3 29(3), 622–625 (2007) 6. Feng, L., Yan, L., Huang, D., He, M., Teng, H.: A Study of PSO and Powell Hybrid Algorithm Applied in Medical Image Registration. J. Beijing Biomedical Engineering 4 4(1), 8–12 (2005) 7. Zhang, H., Zhang, J., Sun, J.: Medical Image Registration Method Based on Mixed Mutual Information. J. Computer Applications 10 26(10), 2351–2353 (2006) 8. Chen, Y., Lin, C., Mimori, A.: Multimodal Medical Image Registration Using Particle Swarm Optimization. In: Eighth International Conference on Intelligent Systems Design and Applications, pp. 127–131 (2008)
Abstract. The medical image registration algorithm uses the mutual information measure function that has many local extremes. Therefore, we propose our medical image registration algorithm that combines generalized mutual information with PSO-Powell hybrid algorithm and uses the objective measure function based on Renyi entropy. The Renyi entropy can remove the local extremes. We use the particle swarm optimization (PSO) algorithm to locate the measure function near the local extremes. Then we take the local extremes as initial point and use the Powell optimization algorithm to search for the global optimal solution. Section 2.2 of the paper presents the six-step procedure of our registration algorithm. We simulate medical image data with the registration algorithm; the simulation results, given in Table. 2 and 3, show preliminarily that the registration algorithm can eliminate the local extremes of objective measure function and accelerate the convergence rate, thus obtaining accurate and better registration results. Keywords: Medical image registration, Generalized mutual information, Measure function, Optimization algorithm.
1 Introduction Image registration is the process of overlaying two or more images of the same scene taken at different times, from different viewpoints, and/or by different sensors. It geometrically aligns two images—the reference and sensed images [1]. Ever since the concept of mutual information was introduced into the region of image registration has the validity of this new approach been widely accepted. Recently the registration based on mutual information has been widely used in occasions of image registration[2-4]. The registration algorithm based on maximization of mutual information(MMI) only uses statistical performance of gray values whereas neglects the image anatomical characteristics, so it is more robust and accuracy than traditional based on feature [5]. However, a few shortcomings still exist in the MMI registration algorithm, the objective measure function based on mutual information will lead to produce some local optimum in searching process, it would lead that the optimization process end in local optimum rather than global optimum [6]. Through the analysis of Renyi entropy [7], we found that mutual information based on Renyi entropy can not only remove unwanted local optimum but also has the depth of the basin of attraction. A new generalized mutual information measure function based on Renyi entropy has been given in this paper on the basis of the two characteristics of Y. Tan, Y. Shi, and K.C. Tan (Eds.): ICSI 2010, Part I, LNCS 6145, pp. 160–166, 2010. © Springer-Verlag Berlin Heidelberg 2010
Medical Image Registration Algorithm with Generalized Mutual Information
，
161
Renyi entropy. At first the PSO algorithm was used to find the local extreme of this measure function, which is use of the feature removing unwanted local optimum and smoothing out optimal curve. Then the Powell optimization algorithm was used to locate the global optimal solution which is use of the characteristic that has the depth of the basin of attraction, make the registration function easier to be optimized. The objective function can be located fast and accuracy through the mixed optimization algorithm and measure function. The registration tests proven that this algorithm and measure function can overcome the local extreme of the mutual information measure function, make registration results up to a sub-pixel level, and also have better robust and accuracy.
，
，
2 Methods 2.1 Generalized Mutual Information Based on Renyi Entropy According to Renyi entropy’s definition, the Renyi entropy of an image is defined as: N
Rq ( X ) = (1 − q ) −1 ln(∑ Pi ), q ∈ R, q ≠ 1 q
(1) . It is important that the Renyi entropy tends to the Shannon entropy as q→1. In analogy to Shannon entropy normalized mutual information, the generalized normalized mutual information of the two images based on Renyi entropy is given by i =1
I(A,B) =
R(A) + R(B) R(A,B) .
(2)
An image is selected as reference image. The floating image can be get by translating the reference image along x axis. The normalized mutual information of the two images can be computed, which is based on Renyi entropy and Shannon entropy, when Parameter q of the Renyi entropy is 2, 1.5, 1.25, 1.1, 0.9, 0.5, 0.25 respectively. The results are shown in Fig.1[7].
Fig. 1. They are the translation curves of normalized MI based on different entropy
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J. Zhang et al.
According to Fig.1, Renyi entropy is more approximate to the Shannon entropy when q is more near one. The normalized mutual information curve based on Renyi entropy is most approximate to normalized mutual information curve based on Shannon entropy as q is 1.1. But at the same time the normalized mutual information curve based on Renyi entropy remove unwanted local optimum, smooth out optimal curve than curve based on Shannon entropy. 2.2 Hybrid Optimization Algorithm Based on PSO and Powell PSO [8] is a stochastic population based optimization algorithm, firstly introduced by Kennedy and Eberhart in 1995. It is a global optimization algorithm. But in the end it is difficult to decide whether the solution we got is global optimum value in solution space, furthermore, whether it is located next to global optimization value. However, the Powell algorithm has a good performance in finding out local extreme. Thus the Powell algorithm could combine with the PSO Algorithm, and different optimization algorithms are used in different searching process. At first the PSO global optimization algorithm was used to find the local extreme of generalized mutual information measure based on Renyi entropy as q is equal to 1.1, which is use of the feature that remove unwanted local optimum, smooth out optimal curve. Then the Powell local optimization algorithm was used to locate the global optimal solution by searching the current local optimal extreme which is use of the characteristic that has the depth of the basin of attraction as q is 0.99, make the registration function easier to be optimized. The PSO-Powell hybrid optimization algorithm in this paper solved searching the registration parameters process described as follows.
，
，
，
(1) Select a point T in three-dimensional solution space randomly, and Initialize a particle swarm in the solution space with the center of point. As a three-dimensional vector, the displacement of x, y and the rotational angle z. (2) Do a certain number of iteration using PSO algorithm, then we can get the current local optimal solution T1, when parameter q in objective measure function is equal to 1.1 in this process. (3) Calculate the objective measure functional value MI and MI1 in point T and T1 respectively. If MI is less than MI1, go to (4), otherwise go to (6). (4) Taking T1 as initial point and use Powell optimization algorithm to get the optimal point in the neighbor region, when parameter q in objective measure function is equal to 0.99 in this process. (5) Initialized the Particle Swarm with the initial point T=T2, then go to (2). (6) Output the optimal solution and corresponding objective measure functional value as the optimal transformation parameters. The initial strategy of PSO algorithm are improved in the searching process after the first search, in short the last searching result of the Powell optimization algorithm is as the current initial optimal point of PSO algorithm. Thus the algorithm performance would be improved because it not only makes full used of the previous calculated results but also decreases possibility falling into the local extreme.
Medical Image Registration Algorithm with Generalized Mutual Information
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3 Experimental Results The generalized mutual information measure function and mixed optimization algorithm are used in single-modality and multi-modality image registration. Single-modality image registration is using three different medical images and three floating images which are got form the former after a certain degree of rotation and translation transformation. Multi-modality image registration is using two different modality medical images, at the same time the performances of PSO algorithm, Powell algorithm and mixed algorithm are compared in the same computer. 3.1 Single-Modality Medical Image Registration Selecting two medical images as reference images, the first image is translated 9 pixels to the right along x axis, 4 pixels downward along y axis and rotated 7.5 degrees along counter-clockwise. The second image is translated 6 pixels to the right along x axis, 8 pixels downward along y axis and rotated 4.7 degrees along counter-clockwise. Then we can get two floating images. Using the two reference images and two floating images, single-modality image registration experiments are made with the algorithm in this paper. The results are shown in Table.1. Table 1. They are the results of the single-modality medical image registration experiment. The RMS is Root-mean-square of the 50 registration results. The mean is average of the 50 registration results.
15th 30th Image 45th A mean RMS 15th 30th Image 45th B mean RMS
x 9.0012 9.0061 9.0109 9.0040 9.0040 6.0169 6.0086 6.0147 6.0170 6.0170
y 4.0051 4.0031 3.9972 4.0009 4.0009 8.0006 7.9986 7.9892 8.0039 8.0039
z 7.4982 7.4988 7.5012 7.5008 7.5008 4.6976 4.7014 4.7009 4.7026 4.7026
△
△
x y 0.0012 0.0051 0.0061 0.0031 0.0109 -0.0028 0.0040 0.0009 0.0000 0.0000 0.0169 0.0006 0.0086 -0.0014 0.0147 -0.0108 0.0170 0.0039 0.0001 0.0001
△
z -0.0018 -0.0012 0.0012 0.0008 0.0000 -0.0024 0.0014 0.0009 0.0026 0.0000
GMI 1.4450 1.4450 1.4450 1.4450 1.4450 1.4212 1.4213 1.4212 1.4212 1.4212
T 74.810 100.386 69.277 103.692 109.386 146.793 139.386 146.776 110.338 117.120
According to the table, in the registration results of image A the horizontal offset error of the 45th results between theoretical value and registration result is 0.0109, it is more than 0.01. And the other parameters selected are all less than 0.01. While in the registration results of image B it is only that the parameter errors of the 30th registration results are all less than 0.01, and the others are not all less than 0.01. So the registration results of image B are slightly inferior to image A. However, the single-modality image registration results are all a high accuracy. At last, using the 15th registration results as registration parameters, and with bilinear transformation, image A is used for registration simulation. The Fig.2 could get form the simulation. The effect of the methods adopted in this paper is proved to be effective and better precision.
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J. Zhang et al.
Fig. 2. It is the simulation experiment of the single-modality medical image registration
3.2 Multi-modality Medical Image Registration We choose two groups of CT/MRI images. The two groups of CT/MRI images are used for multi-modality medical image registration, the registration optimization algorithm are Powell algorithm, PSO algorithm and PSO-Powell mixed algorithm Respectively, and the objective measure function is adopted generalized mutual information measure function based on Renyi entropy. The results of multi-modality medical image registration are shown in Table.2. According to the table, in the three algorithms the experimental time of the Powell algorithm and PSO algorithm are less than the hybrid optimization algorithm. While not only the average measure function values got by hybrid algorithm are the largest, but also that measure function values and registration parameters in every time got by hybrid algorithm are more concentrated in distribution than the other algorithm. General speaking, the registration results are up to a good precision by this hybrid algorithm and generalized measure function measure function in this paper. Table 2. They are the results of the Multi-modality medical image registration experiment. The mean is average of the 50 registration results. First group images Second group images x y z GMI T x y z GMI T 15th 11.302 -5.695 4.807 1.1202 56.124 31.026 -11.380 -7.704 1.0941 72.812 Powell 30th 10.332 -6.548 7.066 1.1205 44.017 34.250 -12.906 -2.980 1.0947 16.618 method 45th 11.531 -5.888 3.575 1.1207 37.875 32.395 -13.228 -6.330 1.0944 35.333 mean 10.797 -6.123 5.701 1.1206 34.896 32.306 -12.646 -5.715 1.0943 37.629 15th 10.614 -5.320 6.738 1.1253 23.189 33.804 -11.779 -4.736 1.0956 36.313 30th 8.904 -5.091 6.682 1.1251 49.801 33.791 -11.769 -4.750 1.0957 42.225 PSO 45th 9.142 -5.471 4.472 1.1247 23.768 33.548 -11.482 -4.801 1.0954 31.145 method mean 9.977 -5.607 5.632 1.1248 25.213 33.041 -11.874 -5.863 1.0953 32.807 15th 11.253 -5.618 4.757 1.1256 42.168 33.873 -11.432 -4.672 1.0959 97.020 Powell 30th 11.136 -5.533 4.711 1.1257 131.71 33.815 -11.332 -4.741 1.0959 84.559 +PSO method 45th 11.134 -5.672 4.709 1.1255 116.30 32.636 -11.145 -4.233 1.0958 68.079 mean 11.169 -5.586 4.708 1.1256 101.46 33.574 -11.394 -4.652 1.0958 65.669
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Fig. 3. It is the simulation experiment of the multi-modality medical image registration
At last, we choose one group of CT/MRI images to make registration experiment. Method used for registration is the method adopted in this paper. Then we can get the Fig. 3. The effect of the methods adopted in this paper is proved to be better.
4 Conclusions Though registration results of MMI have the advantages of high accuracy and independence from any image pretreatments there are still a few shortcomings. The registration images would exist better local matching, the interpolation algorithm would bring in errors. Thus objective measure function will produce a lot of local extreme, which has a large influence on optimization. The generalized mutual information measure function based on Renyi entropy and PSO-Powell mixed optimization algorithm have been adopted in this paper. At first the PSO optimization algorithm was used to find the local extreme of generalized mutual information measure based on Renyi entropy. Then the Powell optimization algorithm was used to locate the global optimal solution by searching the current local optimal extreme. The registration results have proven that this algorithm and measure function can make them up to a sub-pixel level, and also have better robust and accuracy.
，
，
，
References 1. Zitova, B., Flusser, J.: Image registration methods: A survey. J. Image and Vision Computing 21, 977–1000 (2003) 2. Ardizzone, E., Gambino, O., La Cascia, M., Lo Presti, L., Pirrone, R.: Multimodal non-rigid registration of medical images based on mutual information maximization. In: 14th IEEE International Conference on Image Analysis and Processing (2007) 3. Liu, Y., Fedorov, A., Kikinis, R., Chrisochoides, N.: Real-time Non-rigid Registration of Medical Images on a Cooperative Parallel Architecture. In: IEEE International Conference on Bioinformatics and Biomedicine (2009) 4. Andronache, A., von Siebenthal, M., Szekely, G., Cattin, P.: Non-rigid registration of multimodal images using both mutual information and cross-correlation. J. Medical Image Analysis 12(1), 3–15 (2008)
166
J. Zhang et al.
5. Yang, F., Zhang, H.: Multiresolution 3D Image Registration Using Hybrid Ant Colony Algorithm and Powell’s Method. J. Journal of Electronics & Information Technology 3 29(3), 622–625 (2007) 6. Feng, L., Yan, L., Huang, D., He, M., Teng, H.: A Study of PSO and Powell Hybrid Algorithm Applied in Medical Image Registration. J. Beijing Biomedical Engineering 4 4(1), 8–12 (2005) 7. Zhang, H., Zhang, J., Sun, J.: Medical Image Registration Method Based on Mixed Mutual Information. J. Computer Applications 10 26(10), 2351–2353 (2006) 8. Chen, Y., Lin, C., Mimori, A.: Multimodal Medical Image Registration Using Particle Swarm Optimization. In: Eighth International Conference on Intelligent Systems Design and Applications, pp. 127–131 (2008)
