Affine-based registration of CT and MR modality ... - Semantic Scholar

Neural Comput & Applic DOI 10.1007/s00521-010-0374-8

ORIGINAL ARTICLE

Affine-based registration of CT and MR modality images of human brain using multiresolution approaches: comparative study on genetic algorithm and particle swarm optimization Arpita Das • Mahua Bhattacharya

Received: 15 August 2009 / Accepted: 21 April 2010  Springer-Verlag London Limited 2010

Abstract We present a non-linear 2-D/2-D affine registration technique for MR and CT modality images of section of human brain. Automatic registration is achieved by maximization of a similarity metric, which is the correlation function of two images. The proposed method has been implemented by choosing a realistic, practical transformation and optimization techniques. Correlation-based similarity metric should be maximal when two images are perfectly aligned. Since similarity metric is a non-convex function and contains many local optima, choice of search strategy for optimization is important in registration problem. Many optimization schemes are existing, most of which are local and require a starting point. In present study we have implemented genetic algorithm and particle swarm optimization technique to overcome this problem. A comparative study shows the superiority and robustness of swarm methodology over genetic approach. Keywords Affine transformation  Correlation function  Multiresolution registration  Genetic algorithm  Particle swarm optimization

A. Das Department of Radio Physics & Electronics, University of Calcutta, 92 A.P.C. Road, Kolkata 700009, India e-mail: [email protected] M. Bhattacharya (&) Indian Institute of Information Technology and Management, Morena Link Road, Gwalior 474010, India e-mail: [email protected]

1 Introduction The term ‘registration’ [1] manifests the fact of finding a correspondence between the two images. Registration is used to describe the geometric transformations such that the generated image should be registered or aligned with some standard or reference image. Registration is a crucial prior step for fusion of two image data sets to obtain an integrated display. The registration procedure has immense importance in the case of multimodal medical image processing for clinical interest [2–10]. In radio therapeutic planning, the computed tomography (CT) data is very useful for imaging of bony structure whereas magnetic resonance imaging (MRI) provides the details of soft tissue regions. Functional imaging is becoming increasingly important for medical research. Positron emission tomography (PET) and single photon computed tomography (SPECT) imaging provide information on blood flow and metabolic processes. As recommended by the physicians, areas of interest of the body are imaged with different modalities. These images are used in a complimentary manner to gain additional insights into the shape, size and spatial relationships among anatomical structures. Registration is also used in treatment planning, brain mapping and image-guided therapies. We have already done experiment of registration using MR (both T1 and T2 weighted) and CT imaging modalities of ventricular region of brain as the region of interest (ROI) for patients having Alzheimer’s diseases using shape theoretic approach [2]. The control points on the concavities present in the contours are chosen to re-project ROI from the respective modalities in a reference frame [2]. All types of sensors are not expected to perform equally well for all types of structures, but it should be possible to find some features that are defined by two relevant sensors in a

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Neural Comput & Applic

particular case for the purpose of registration. Earlier works [2, 6–9, 11, 12] depict the registration of images along with medical images like CT and MR by a semiautomatic method where the local and global transformations are used depending on the number of structures of interest. We may also refer the comparison and evaluation of retrospective intermodality brain image registration techniques as it is described in [10]. A target registration error (TRE) has been defined as a true representation of the distance between the actual and estimated positions of targets within the cranial cavity. A complete evaluation of retrospective techniques based on their TRE at different landmark locations with in the brain has been performed using fiducial markers as a gold standard [10]. The two registration tasks have been evaluated between CT and MR and other between PET and MR. In our earlier study on medical image registration, we have suggested mutual information measure along with Parzen window estimator for optimization [13]. The optimization criteria of mutual information measure can be successfully used for multiresolution image registration [5, 13–15]. There are many approaches for biomedical image registration. The gold standard utilizes markers placed on the region of interest [16]. Other approaches include correlation of geometrical features [17–19]. More works are recently focused on intensity-based approaches, in which the intensity values (color or gray level) are used to compute similarity measures between the images. The quality of medical image registration depends on the choices involve transformation technique, interpolation, estimation of similarity metric and optimization. Gray value correlation can be applied to use all the information in the images to determine the best match. The resulting matching is fully automatic and assumed to be maximal if both images are geometrically aligned [17, 19–22]. Proposed algorithm starts with the 2D/2D registration of MR and CT modalities of section of human brain. The objective of the present work is to introduce a robust and global search strategy (optimization) for maximization of the similarity metric for the process of registration. The similarity metric is generally not a smooth function and contains many local optima [23]. Choice of optimization routine plays an important role in registration process. In present study, we have suggested search strategy for maximization of the similarity metric using multiresolution approaches where both the techniques genetic algorithm (GA) and particle swarm optimization (PSO) have been implemented to achieve optimization. GA is based on natural survival-of-the-fittest principle and selecting the global best of the new generation by crossover and mutation operators [24–27]. The optimization scheme is initialized with a population of random solutions and searches for optima by updating the generations. PSO was

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discovered through the simulation of simplified social– psychological principles, more specifically the collective behaviors of simple individuals interacting with their environment and with each other. Movement of each individual through the search space is controlled by social influence and social network, and by end of trial, flock can find out the best success. In theory, at least individual members of the flock can profit from the discoveries and previous experience of all other members of the flock during the search for food. This statement suggests that social sharing of information among individuals offers an evolutionary advantage. This hypothesis was fundamental of the development of PSO [8, 28–31]. The vital parameters of swarm intelligence are inertia and acceleration coefficients that are adapted with the iterations and making the algorithm capable of handling optimization problems. Present article considers both optimization schemes in a multiresolution manner to decrease the sensitivity of the registration procedure to local maxima, and a comparative study analyzes the results. The rough idea of the initial orientation of the images to be registered can be achieved from the reduced resolution [32, 33]. The term ‘multiresolution’ can be used with respect to the images in the sense that the images are downscaled to a number of resolution levels.

2 Overview of the proposed methodology Proposed methodology implements affine transformationbased correlation function of floating images as similarity metric and maximizes it to achieve appropriate registration of images. To validate the importance of the optimization method in registration problem, we have implemented both the meta-heuristic search strategies—GA and PSO techniques in multiresolution domain. The Fig. 1 demonstrates an overview of our present work.

Fig. 1 Brief overview of the proposed method

Neural Comput & Applic

The values of f (T(x)) are calculated by affine transformation followed by bilinear interpolation of the gray values of the floating image f. If there is a match between r(x) and f(x), the correlation of the two images will be maximum.

3 Image registration process 3.1 Transformation The transformation techniques applied to align the images can be categorized according to the degrees of freedom. Although elastic transformations are more realistic (as most body tissues are deformable to some degree), rigid body registration is performed in most of the articles [28]. Rigid body registration used initially to determine the global alignment, followed by local elastic registration described in [34]. Other non-linear registration methods align small blocks of the floating image to the reference image in a linear manner [35]. Application of non-linear affine transformation on the whole floating images is a newer approach and having much more practical implementation [14, 36]. The affine transformation preserves the parallelism of lines, but not their lengths or their angles. It extends the degrees of freedom of the rigid transformation with a scaling factor for each image dimension and additionally a shearing option in each dimension. Let T denote the spatial transformation that maps features or coordinates from one image to another image. For 2-D affine registration, the transformation matrix is: x0 ¼ a  x þ b  y þ c 0

y ¼dxþeyþf or in matrix notation: 2 3 " # x x0 6 7 ¼ T 4 y5 y0 1 where T is a 2 9 3 matrix of coefficients:   a b c T¼ d e f

ð1Þ ð2Þ

ð3Þ

3.3 Multiresolution approach The fundamental theory of multiresolution imaging is to study the images at more than one resolution. A powerful but simple structure for representing the images at more than one resolution is the image pyramid. An image pyramid is a collection of decreasing resolution images arranged in the shape of a pyramid as shown in Fig. 2. The base of the pyramid contains the highest resolution representation of the image, and the apex contains a lowestresolution approximation. With moving up the pyramid, both size and resolution of the images decrease. In recent problem, we have used Haar wavelet transform to achieve multiresolution approach. With moving up the pyramid, both size and resolution decrease. The base level J is size 2J 9 2J or N 9 N, intermediate level j is size 2j 9 2j, where 0 B j B J. Fully populated pyramids are composed of J ? 1 resolution levels from 2J 9 2J to 20 9 20, but in practice most pyramids are truncated to P ? 1 levels, where j = J - P, …, J - 2, J - 1, J and 1 B P B J, since a 1 9 1 pixel image is of little value. As shown in Fig. 3, any image of level j can be approximated to level j - 1 by applying Haar wavelet transform. It will contain only the gross structure of level j. The size of level j - 1 image is just half of level j image. The level j - 1 approximation output is used to create approximation pyramid. The level j prediction residual output is used to build prediction residual pyramid. This pyramid contains a low-resolution approximation of the

ð4Þ

3.2 Computation of similarity metric (objective function) Correlation function: we are matching multimodal images, which are similar in some respects but dissimilar in other parts. But as long as there are sufficient similar structures in images, the matching algorithm performs well even with some dissimilarity present in either image. For affine transformation (T) of floating image f, the correlation measure CT of image f and the reference image r is calculated using the formula, XX r ðx Þ  f ðT ðx ÞÞ ð5Þ CT ¼ where r(x) denotes the intensity of the coordinates (x, y) in reference image r.

Fig. 2 A pyramidal image structure

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Neural Comput & Applic

 T¼

a d

b e

c f

 ð6Þ

These parameters are optimized by GA/PSO, so that the image formed with optimized parameters is perfectly registered with the reference image (Image A). 3.4.1 Optimization based on GA

Fig. 3 System for constructing image pyramids

original image at level J - P and information for the construction of P higher resolution approximations at the other levels. The information at level j is the difference between the level j approximation of the corresponding approximation pyramid and an estimate of that approximation based on the level j - 1 prediction residual. In present work, we have applied two-level Haar wavelet transform and initial information of the affine transformation parameters are acquired from level j - 1 approximate image. 3.4 Optimization The optimum similarity function is assumed to correspond to the transformation that correctly registers the images. In medical image registration, the similarity metric is not a smooth function and contains many local optima. Local maxima occur as a result of interpolation or because of changes in the overlapping part of the images. Due to the existence of local maxima, the choice of optimization routine is very much important. It influences the results of the registration methodology, particularly determines the robustness with respect to the initial transformation. Evolutionary algorithms (EAs) have shown to be a promising approach to solve complex constrained optimization problems. The evolutionary techniques, which have been demonstrated to be the promising approaches for solving constrained optimization problems, are GA and particle swarm optimization. In present work, the search strategy for maximizing of the similarity function is based on multiresolution approaches for GA and PSO. In the registration problem, it is considered that the multimodality images to be registered are Image A and Image B. Image A is termed as reference image and Image B is the transformed image by affine transformation technique such that it will be correctly registered with Image A. Now for 2D affine transformation, six parameters are required to transform the image.

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GA is search/optimization algorithm based on the mechanics of natural selection and natural genetics. In GA, a collection of possible chromosomes forms a population, which produces another generation through a natural search process. The search process adopts ‘‘the fittest survives’’ rule after a structured yet randomized information exchange within the existing generation to yield a new generation. Basically, GA uses three operators—selection (or reproduction), crossover and mutation to achieve the goal of evolution. GA is not just simple random walk; it efficiently exploits the information to speculate on new search points with expected improved performance. This method is allowed to make escapes from local optima, and the chromosomes will approach the global optimum point. To apply GA in our registration problem, we encode the transformation matrix and optimize the six parameters (described in (4)) to achieve the best possible result. The steps of GA are summarized in Fig. 4. 3.4.2 Mathematical approach of GA Let us suppose that at a given time step t, there are m examples of schema (chromosome) H within the population A(t), where we may write M ¼ mðH; tÞ ð7Þ During reproduction, a chromosome will mate according to its fitness, given by , X pi ¼ fi f ð8Þ i

where fi ? fitness value of ith chromosome. After picking a non-overlapping population of size (n) with replacement from the population A(t), we obtain m(H, t ? 1) examples in the population at time (t ? 1). mðH; tÞ  n  f ðHÞ P mðH; t þ 1Þ ¼ ð9Þ if where f(H) is the average fitness of the population representing the chromosome H at time t. If we write the average fitness of the entire population as P f 0 ð10Þ f ¼ i n then,

Neural Comput & Applic Fig. 4 Schematic flow of genetic algorithm

mðH; t þ 1Þ ¼

mðH; tÞ  f ðHÞ f0

ð11Þ

In words, chromosome with fitness value above the population average will receive an increasing number of samples in the next generation, while chromosome with fitness value below the population average will receive a decreasing number of samples. Thus, the effect of reproduction on the number of chromosome is clear: above-average chromosomes grow and below-average chromosomes die off. On the other hand, reproduction alone does nothing to promote exploration of new regions of the search space, since no new points are searched if we copy old structures without change. This is where crossover comes into play. Crossover is a structured yet randomized information exchange between chromosomes. It creates new structures with minimum disruption to the allocation strategy dictated by reproduction alone. This results an exponential decrease or increase in chromosomes in a population. Let us consider two different chromosomes H1 and H2 with length (l) 7, exchange information between them. H1 ¼  1 j    0

ð12Þ

H2 ¼    j 10  

ð13Þ

The asterisks are do not care symbols which match either 0 or 1 at a particular position. Here, the crossing site has been marked with separator symbol |.

If the crossover site is selected uniformly at random among the l – 1 = 7 – 1 = 6 possible sites, then chromosome H1 is destroyed with probability dð Þ 5 pd ¼ H1 ¼ ð14Þ ðl  1Þ 6 Or survival probability 1 - pd = 1/6 (the defining length d(H1) of chromosome H1 is the first and last specific string position). Similarly, the chromosome H2 will be destroyed with probability, dð Þ 1 pd ¼ H2 ¼ ð15Þ ðl  1Þ 6 The survival probability of a chromosome under simple crossover is 1  dðHÞ ps ¼ ð16Þ ðl  1Þ Since the chromosome is likely to be disrupted whenever a crossover site within the length l - 1. If the crossover is itself performed by uniformly random way, say with probability pc at particular mating, the survival probability may be given by the expression 1  ps dðHÞ ps  ð17Þ ðl  1Þ Considering the combined effect of reproduction and crossover, we obtain the estimate:

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mðH; t þ 1Þ 

mðH; tÞ  f ðHÞ h i ps dðHÞ f 0 1 l1

obtain the probability of surviving mutation, (1 - pm)o(H). For small values of pm (pm  1), the chromosome survival probability may be approximated by 1 - o(H)*pm. We therefore conclude that a particular chromosome H receives an expected number of copies in the next generation under reproduction, crossover and mutation as given by the following equation,

ð18Þ

With both crossover and reproduction, chromosome growing or decaying depends on two factors: whether the chromosome is above or below the population average and whether the chromosome has relatively short or long defining length. Those chromosomes with both aboveaverage fitness and short defining length are growing at exponential rate. The last operator to consider is mutation. Mutation is the random alteration of a single position with probability pm. Therefore, since a single bit survives with probability (1 - pm) and since each of the mutations is statistically independent, a particular chromosome survives when each of the o(H) (order of chromosome denoted as o(H) ? states the number of fixed positions) fixed positions within the chromosome survives. Multiplying the survival probability (1 - pm) by itself o(H) times, we

mðH; tÞ  f ðHÞ i mðH; t þ 1Þ  h 1ps dðHÞ f 0 ðl1 ÞoðHÞpm

ð19Þ

Thus with addition of mutation, our final conclusion on the survival of chromosome is low-order, above-average chromosomes receive exponentially increasing trials in subsequent generations. 3.4.3 Optimization algorithm 1.

Generate 20 (between 0 and 1) random number for each parameters a, b, c, d, e, f.

Table 1 Registration of MR T2 and MR T1 images Correlation of MR T2 and MR T1 images before registration

Correlation of MR T2 and MR T1 after GA-based registration

Correlation value of MR T2 and MR T1 after PSO-based registration

SET-I

0.5147

0.4994

0.5289

SET-II

0.4811

0.4867

0.5012

SET-I

Reference Image

Floating Image

Registration using GA

Registration using PSO

SET-II

Reference Image

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Floating Image

Registration using GA

Registration using PSO

Neural Comput & Applic

2.

3.

4.

5.

6.

7.

With these new set of values of a, b, c, d, e, f, each transforms the Image B using affine transformation and achieve 20 new transformed Image B(T). Calculate similarity metric (SM) between the reference image (Image A) and above obtained 10 new transformed images (denoted as Image B(T1)). These 10 values of SM act as the fitness/objective function of GA. Find the maximum SM value and denote it as ‘max SM1’. Now encode the values of a, b, c, d, e, f by simple binary numbers to form the population of chromosomes in GA. Perform three genetic operations—reproduction, crossover and mutation (ref. Fig. 4) for each encoded parameters like a, b, c, d, e, f. After mutation, new generation of chromosomes is formed. These chromosomes are now decoded to obtain the new values of a, b, c, d, e, f. Transform Image B using affine transformation with the new set of values of a, b, c, d, e, f found from new

8.

9.

generation of GA (let denote these images as Image B(T2)). Compute 10 new values of SM between the reference image (Image A) and the transformed image B(T2). Among these 10 SM values, find out the maximum SM value and denote it as ‘max SM2’. If the difference between ‘max SM1’ and ‘max SM2’ is less than a predefined threshold value (T), stop iteration otherwise replace the value of ‘max SM1’ by ‘max SM2’ and go to step 4.

3.4.4 Particle swarm optimization (PSO) The application of a relatively new meta-heuristic strategy, called PSO, to the registration problem is presented in our study. The registration results show significant improvements compared to the currently used genetic registration techniques, as well as techniques involving other meta-heuristic optimization strategy, such as tabu

Table 2 Registration of MR T1 and MR T2 images Correlation value of MR T1 and MR T2 images before registration

Correlation value of MR T1 and MR T2 after GA-based registration

Correlation value of MR T1 and MR T2 after PSO-based registration

SET-I

0.5098

0.5519

0.5715

SET-II

0.5602

0.5736

0.5791

SET-I

Reference Image

Floating Image

Registration using GA

Registration using PSO

SET-II

Reference Image

Floating Image

Registration using GA

Registration using PSO

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Neural Comput & Applic Table 3 Registration of MR T1 and CT images Correlation value of MR T1 and CT images before registration

Correlation value of MR T1 and CT after GA-based registration

Correlation value of MR T1 and CT after PSO-based registration

SET-I

0.3773

0.3461

0.5865

SET-II

0.3780

0.3913

0.5721

SET-III

0.4104

0.5679

0.5738

SET-I

Reference Image

Floating Image

Registration using GA Registration using PSO SET-II

Reference Image

Floating Image

Registration using GA Registration using PSO SET-III

Reference Image

Floating Image

search method [37]. The PSO algorithm as proposed in [31] simulates the social behavior of a school of fish or a flock of birds, called the swarm. The individual swam members are called particles. Particles benefit from experiences and discoveries of others when searching for food. Each particle remembers its own best position called the individual best or ‘pbest’, as well as the best

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Registration using GA Registration using PSO

position found by the whole swarm, and called the global best or ‘gbest’ [6]. A global best is known to all and immediately updated when a new best position is found by any particle in the swarm. The ith particle position (xi) and velocity (vi) update equations in the simplest form that govern the PSO are given by

Neural Comput & Applic Table 4 Registration of MR T2 and CT images Correlation value of MR T2 and CT images before registration

Correlation value of MR T2 and CT after GA-based registration

Correlation value of MR T2 and CT after PSO-based registration

SET-I

0.3235

0.3278

0.3476

SET-II

0.3185

0.3561

0.3577

SET-I

Reference Image

Floating Image

Registration using GA Registration using PSO SET-II

Reference Image

Floating Image

rand vi ¼ c0 vi þ crand 1 ðÞðpbest  xi Þ þ c2 ðÞðgbest  xi Þ

xi

xi þvi

ð20Þ ð21Þ

where c0, c1, c2 C 0. c0 is the inertia coefficient, c1 and c2 are the acceleration coefficients and rand() is random numbers, generated uniformly in the range [0, 1], responsible for imparting randomness to the flight of the swarm. The values of c1 and c2 allow the particle to tune the cognition and the social terms, respectively, in the velocity update equation. In fact, these two parameters affects how much the particle’s ‘pbest’ and flock’s ‘gbest’ influence the movement of the swarm. A larger value of c1 allows exploration, while a larger value of c2 encourages exploitation. In this study, values of c1, c2 are set to 2 and c0 with slightly less than 1 to lead medium convergence rate of the algorithm. Initially, the algorithm is allowed to perform a very diverse search exploring a broad range of possible solutions. A satisfying simulation was relied on two propositions:

Registration using GA Registration using PSO

nearest-neighbor velocity matching and craziness determined by inertial coefficient. If the inertial coefficient of the velocity is small, all particles could slow down until they approach to zero velocity at the global best. The selection of coefficients in the velocity update equation affects the convergence and the ability of the swarm to find the optimum. A population of individuals was randomly initialized with a position for each on a torus pixel grid with different velocities. At each iteration, a loop in the program determined for each particle with other particle was its nearest neighbor and then assigned that particle’s velocities to the particle in focus. This simple rule created a synchrony of movement. Unfortunately, the population is quickly settled on a unanimous unchanging direction. Therefore, a stochastic variable called craziness was introduced. At each iteration, some change was added to randomly chosen velocities. This has introduced enough variation into the system to give the simulation an interesting and lifelike appearance.

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Neural Comput & Applic Table 5 Registration of CT and MR T2 images Correlation value of CT and MR T2 images before registration

Correlation value of CT and MR T2 after GA-based registration

Correlation value of CT and MR T2 after PSO-based registration

SET-I

0.7220

0.7019

0.7308

SET-II

0.7239

0.7282

0.7363

SET-I

Reference Image

Floating Image

Registration using GA Registration using PSO SET-II

Reference Image

Floating Image

Registration using GA

3.4.5 Proposed PSO algorithm The six parameters for 2-D affine transformation required to transform are optimized by PSO, so that the Image B transformed with the optimized parameters is perfectly registered with the Reference image (Image A). In each iteration, six transformation parameters to be optimized as described in (4) are updated by following two best values. The first one is ‘pbest’—the best value achieved so far by the particle. Another best value is ‘gbest’—obtained so far by any particle in the population. 1.

2.

Generate 20 (between 0 and 1) random numbers for each parameters a, b, c, d, e, f of affine transform in the reduced resolution. Transform Image B with these set of values of a, b, c, d, e, f. Then calculate the similarity metric (objective function/fitness value) values of Image A and transformed Image B. Search the maximum similarity metric (SM) value and corresponding transformation

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3.

4. 5.

Registration using PSO

parameters a, b, c, d, e, f. These values used as ‘pbest’ values of each of 6 transformation parameters.(Reduced resolution images are used to obtain the rough idea of ‘pbest’ value of each transform parameters a, b, c, d, e, f). In actual resolution domain, each of the transform parameters (a, b, c, d, e, f) again randomly initialized to form a population in PSO algorithm. Transform Image B with these new set of values of parameters. Then calculate the SM of Image A and transformed Image B. Find out maximum SM value and corresponding transform parameters a, b, c, d, e, f. These values are treated as ‘gbest’ values of each parameter in the present population. Now update the transform parameters according to (20) and (21). Transform Image B with the set of updated parameter values obtained from (1) and calculate SM between Image A and Image B.

Neural Comput & Applic Table 6 Registration of CT and MR T1 images Correlation value of CT and MR T1 images before registration

Correlation value of CT and MR T1 after GA-based registration

Correlation value of CT and MR T1 after PSO-based registration

SET-I

0.4623

0.4497

0.4659

SET-II

0.4578

0.4132

0.4631

SET-I

Reference Image

Floating Image

Registration using GA Registration using PSO SET-II

Reference Image

6.

7.

Floating Image

If the objective function/fitness value f(xi) (SM here) is better than the best fitness value in the previous history, consider the current values of the parameters as updated ‘pbest’ values of a, b, c, d, e, f. Stop when maximum iterations attained, otherwise go to step 3.

In the registration problem, it is obtained that after 30 iterations, the parameters to be optimized converges to a particular direction and updating of objective function between to successive population is less than a particular threshold value (T).

Registration using GA Registration using PSO

of ventricular region is an indication of degeneracy/disorder of brain tissues. The dataset contains CT and MR (both T1 and T2) brain images. Tables 1, 2, 3, 4, 5 and 6 exhibit the correlation value before and after the registration process utilizing both GA and PSO. Tables 7 and 8 show the result of registration of section of brain of two patients considering the MR T1 and MR T2 images of preoperative and postoperative conditions. Each of the optimization algorithm runs for 30 iterations. The figures of the experimental results exhibit GA- and PSO-based registered sample images.

4 Experimental results

5 Conclusions

4.1 Registration of different modality (CT and MR) images

We have presented a non-linear registration technique for MR and CT modality images of section of human brain by maximization of a similarity measure, which is the correlation function of two images. The proposed method is based on a more realistic and practical transformation and

In present problem, we have registered the ventricular region of the brain images since any deformation of shape

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Neural Comput & Applic Table 7 Postoperative MRI T2 versus postoperative MRI T1 registration using PSO for patient 1 Correlation value of postoperative MR T2 and MR T1 images before registration

Correlation value of postoperative MR T2 and MR T1 after GA-based registration

Correlation value of postoperative MR T2 and MR T1 after PSO-based registration

SET-I

0.4242

0.4723

0.4782

SET-II

0.3961

0.4567

0.4696

SET-III

0.3970

0.4489

0.4816

SET-I

Reference Image

Floating Image

Registration using GA

Registration using PSO

SET-II

Reference Image

Registration using GA

Floating Image

Registration using PSO

SET-III

Reference Image

Floating Image

optimization techniques using multiresolution approach. Registration process performs the integration of information from the multimodality imaging to a single reference frame and provides more accuracy in diagnostics procedure. We have considered similarity measuring functions that are real valued, irregular and often characterized by many local optima. Most of the optimization techniques are accurate when the initial orientation is much close to the transformation and yields the best registration. The approach that addresses this issue uses multiresolution

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Registered Image

techniques when images are registered at increasing resolutions with initial orientations from preceding lower resolution. Another important issue of optimization technique is the efficiency of the method. For this purpose, the number of iterations required to achieve accurate registration result must be as low as possible. EAs have shown to be a promising approach to solve non-convex-constrained optimization problems. The focus of the current study is to compare the performance of optimization techniques for maximizing similarity metric.

Neural Comput & Applic Table 8 Preoperative MRI T1 versus postoperative MRI T2 registration using PSO for patient 2 Correlation value of preoperative MR T1 and MR T2 images before registration

Correlation value of preoperative MR T1 and MR T2 after GA-based registration

Correlation value of preoperative MR T1 and MR T2 after PSO-based registration

SET-I

0.2520

0.2799

0.3238

SET-II

0.2586

0.2848

0.3226

SET-III

0.2527

0.2571

0.3081

SET-I

Reference Image

Floating Image

Registration using GA

Registration using PSO

SET-II

Reference Image

Floating Image

Registration using GA

Registration using PSO

SET-III

Reference Image

Floating Image

Specifically, PSO is proposed as an accurate global optimization approach for medical image registration. A relatively new meta-heuristic strategy like PSO implemented for biomedical image registration is noticeably more accurate and efficient than GA and other evolutionary techniques. PSO in its basic form is best suited for continuous variables; thus, the objective function may be evaluated for the tiniest increment. The results obtained from PSO are compared with a well-known genetic optimization technique. GA is naturally better suited to discrete search spaces, so in this application PSO outperforms than GA. The considerable adaptability through stochastic exploration and exploitation of the swarm strengthens PSO

Registered Image

over other robust optimization techniques. It is assumed that both optimization techniques implemented here start with 20 random particles is large enough to obtain good convergence result. Incorporation of multiresolution strategy also improves the performance of optimization technique. Both the optimization methods have no prior knowledge of the location of global optimum. Performance analysis including accuracy has been described in the experiment. One aspect that we would like to explore in future is to analyze exhaustively the evaluation indices of the system like mutation rate in GA or inertial coefficient and acceleration coefficients of PSO to acquire an efficient performance.

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Neural Comput & Applic Acknowledgement Authors are thankful to the National Brain Research Center, Gurgao, Govt. of India. Authors also like to thank to Dr. S. K. Sharma of EKO X-ray and Imaging Institute, Kolkata.

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