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Registration of Brain Images Using Fast Walsh Hadamard Transform (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 2, May 2010 Registration of Brain Images using Fast Walsh Hadamard Transform D.Sasikala 1 and R.Neelaveni 2 1 Research Scholar, Assistant Professor, Bannari Amman Institute of Technology, Sathyamangalam. Tamil Nadu-638401. Email address : [email protected] 2 Assistant Professor, PSG College of Technology, Coimbatore, Tamil Nadu -641004. Email address : [email protected] Abstract various parameters. This step determines the success or failure A lot of image registration techniques have been developed with of image analysis. This technique may be classified based on great significance for data analysis in medicine, astrophotography, four different aspects given as follows: (i) the feature selection satellite imaging and few other areas. This work proposes a method for (extracting features from an image) using their similarity medical image registration using Fast Walsh Hadamard transform. measures and a correspondence basis, (ii) the transformation This algorithm registers images of the same or different modalities. function, (iii) the optimization procedure, and (iv) the model for Each image bit is lengthened in terms of Fast Walsh Hadamard basis functions. Each basis function is a notion of determining various processing by interpolation. aspects of local structure, e.g., horizontal edge, corner, etc. These Amongst the numerous algorithms developed for image coefficients are normalized and used as numerals in a chosen number registration so far, methods based on image intensity values are system which allows one to form a unique number for each type of particularly excellent as they are simple to automate as local structure. The experimental results show that Fast Walsh solutions to optimization problems. Pure translations, for Hadamard transform accomplished better results than the conventional example, can be calculated competently, and universally, as the Walsh transform in the time domain. Also Fast Walsh Hadamard maxima of the cross correlation function between two images transform is more reliable in medical image registration consuming [11] [15] [17]. Additional commands such as rotations, less time. combined with scaling, shears, give rise to nonlinear functions Keywords: Walsh Transform, Fast Walsh Hadamard Transform, which must be resolved using iterative nonlinear optimization Local Structure, Medical Image Registration, Normalization. methods [11]. I. INTRODUCTION In the medical imaging field, image registration is regularly used to combine the complementary and synergistic Digital image processing is developing the ultimate information of images attained from different modalities. A machine that could perform the visual functions of all. It is a problem when registering image data is that one does not have rapidly evolving field with growing applications in many areas direct access to the density functions of the image intensities. of science and engineering. The main criterion of registration is They must be estimated from the image data. A variety of to fuse the sets of data with the variations if any or with their image registration techniques have been used for successfully similarities into a single data. These sets of data are acquired by registering images that are unoccluded and generally practiced sampling the same scene or object at different times or from with the use of Parzen windows or normalized frequency different perspectives, in different co-ordinate systems. The histograms [12]. purpose of registration is to visualize a single data merged with The work proposed in this paper uses Fast Walsh all the details about these sets of data obtained at different times Hadamard Transform (FWHT) [18, 19] for image registration. or perspectives or co-ordinate systems. Such data is very The coefficients obtained are normalized to determine a unique essential in medicine for doctors to plan for surgery. The most number which in turn represents the digits in a particular range. common and important classes of image analysis algorithm The experiments conducted on clinical images show that with medical applications [1,3] are image registration and proposed algorithm performed well than the conventional image segmentation. In Image analysis technique, the same Walsh Transform (WT) method in medical image registration. input gives out somewhat detail description of the scene whose In addition, this paper provides a comparative analysis of image is being considered. Hence the image analysis algorithms FWHT and WT in Medical image registration. perform registration as a part of it towards producing the The remainder of the paper is ordered as follows. Section 2 description. In single subject analysis, the statistical analysis is provides an overview on the related work for image done either before or after registration. But in group analyses, it registration. Section 3 explains WT in image registration. is done after registration. Section 4 describes the proposed approach for image Generally registration is the most difficult task, as aligning registration using FWHT. Section 5 illustrates the experimental images to overlap the common features and differences if any results to prove the efficiency of the proposed approach in are to be emphasized for immediate visibility to the naked eye. image registration and Section 6 concludes the paper with a There is no general registration [1-17] algorithm, which can discussion. work reasonably well for all images. A suitable registration algorithm for the particular problem must be chosen or II. Related Work Many discussions have been carried out previously on Image developed, as they are adhoc in nature. The algorithms can be Registration. This section of paper provides a quick look on the incorporated explicitly or implicitly or even in the form of relevant research work in image registration. 96 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 2, May 2010 An automatic scheme using global optimization technique for information. Construct a unique number out of eight numbers retinal image registration was put forth by Matsopoulos et al. in using these numbers as the digits of the unique number. The [1]. A robust approach that estimates the affine transformation number of levels depends on the number system adopted. For parameters necessary to register any two digital images decimal system, the normalized coefficients are quantized that misaligned due to rotation, scale, shear, and translation was taking integer values in the range [0, 9]. proposed by Wolberg and Zokai in [2]. Zhu described an approach by cross-entropy optimization in [3]. Jan Kybic and Michael Unser together put forth an approach for fast elastic multidimensional intensity-based image registration with a (a) parametric model of the deformation in [4]. Bentoutou et al. in [5] (a). WTs basis images for a 3X3 images offered an automatic image registration for applications in remote a00 a01 a02 sensing. A novel approach that addresses the range image a10 a11 a12 registration problem for views having low overlap and which may a20 a21 a22 (b). Nine coefficients in matrix form include substantial noise for image registration was described by Figure 1. Walsh Transformation Silva et al. in [6]. Matungka et al. proposed an approach that In Figure 1(a) the coefficients along the first row and the involved Adaptive Polar Transform (APT) for Image registration first column are of equal importance, as they measure the in [7, 10]. A feature-based, fully non supervised methodology presence of a vertical or a horizontal edge, respectively. The dedicated to the fast registration of medical images was described remaining four coefficients measure the presence of a corner. by Khaissidi et al. in [8]. Wei Pan et al. in [9] proposed a The following ordering of coefficients are used in images, technique for image registration using Fractional Fourier Ordering IA α01, α 10, α 20, α 02, α 11, α 21, α 12, α 22 Transform (FFT). Ordering IB α 10, α 01, α 02, α 20, α 11, α 12, α 21, α 22 Ordering IIA α , α , α α , α , α , α , α I. WALSH TRANSFORM 22 21 12, 11 02 20 10 01 Ordering IIB α 22, α 12, α 21, α 11, α 20, α 02, α 01, α 10 Orthogonal transforms expand an image into sets of orthogonal basis images each of which represents a type of II. PROPOSED APPROACH local structure. Examples are the Walsh, Haar [13], etc. The A. Fast Walsh Hadamard Transform coefficients of such an extension point toward the effectiveness of the occurrence of the similar structure at the particular A fast transform algorithm is seen as a sparse factorization position. If these coefficients are normalized by the dc of the transform matrix, and refers to each factor as a stage. The coefficient of the expansion, i.e., the local average gray value of proposed algorithms have a regular interconnection pattern the image, then they measure purely the local structure between stages, and consequently, the inputs and outputs for independent of modality. Walsh basis functions correspond to each stage are addressed from or to the same positions, and the local structure, in the form of positive or negative going factors of the decomposition, the stages, have the property of horizontal or vertical edge, corner of a certain type, etc. being equal between them. The 2X2 Hadamard matrix is Registration schemes based on wavelet coefficient matching do defined as H2 is given in equation (3) not present a general mechanism of combining the matching 11 results across different scales. H 2 = (3) −11 Two images I1 and I2, I1 is assumed as reference image whereas I2 represent an image that has to be deformed to match A set of radix-R factorizations in terms of identical sparse I1. First, consider around each pixel, excluding border pixels, a matrices rapidly obtained from the WHT property that relates 3X3 neighborhood and compute from it, the nine Walsh the matrix H with its inverse and is given in coefficients (3X3 WT of a 3X3 image patch).
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