Image Registration Using Markov Random Coefficient Fields
Image Registration is central to different applications such as medical analysis, biomedical systems, image guidance, etc. In this paper we propose a new algorithm for multi-modal image registration. A Bayesian formulation is presented in which a likeliho
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bstract. Image Registration is central to different applications such as medical analysis, biomedical systems, image guidance, etc. In this paper we propose a new algorithm for multi-modal image registration. A Bayesian formulation is presented in which a likelihood term is defined using an observation model based on linear intensity transformation functions. The coefficients of these transformations are represented as prior information by means of Markov random fields. This probabilistic approach allows one to find optimal estimators by minimizing an energy function in terms of both the parameters that control the affine transformation of one of the images and the coefficient fields of the intensity transformations for each pixel. Keywords: Image Registration, Markov Random Fields, Bayesian Estimation, Intensity Transformation Function.
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Introduction
Image registration is the alignment of images that may come from the same or different source. This task is very important to many applications involving image processing or analysis such as medical analysis, biomedical systems, image guidance, depth estimation, and optical flow. A special kind of registrations is called Multimodal Image Registration, in which two o more images coming from different sources are aligned; this process is very useful in computer aided visualization in the medical field. In the literature, there are basically two classes of methods to register multimodal images: those based on features such as edge locations, landmarks or surfaces [6][7][11], and those based on intensity [1][19][4][16]. Within the intensity methods there are two popular ones. Partitioned Intensity Uniformly (PIU) [19][5], proposed by Woods et al, is one of them. In this method it is assumed that uniform regions in one of the images correspond to regions, also uniform, in the other one. To achieve the registration, a corresponding measure is established based on the statistical characteristics of both images. The goal of this method is to use this measure to minimize the variance of intensity ratios. The other method that has shown good results is the registration based on mutual V.E. Brimkov, R.P. Barneva, H.A. Hauptman (Eds.): IWCIA 2008, LNCS 4958, pp. 306–317, 2008. c Springer-Verlag Berlin Heidelberg 2008
Image Registration Using Markov Random Coefficient Fields
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information (MI), proposed by Viola et al [18]. In this method, statistical dependencies between images are compared, establishing a metric based on the entropy of each image and the join entropy. Even though the method is theoretically robust, it is complicated to implement and requires vast computational resources. Another drawback of MI is that it completely ignores spatial information such as edges or homogenous regions. A method related to the work proposed in this paper is presented in [10]. It focuses only on elastic registration of multimodal images; it uses an iterative scheme that iterates between finding the coefficients of polynomial intensity transformations and registration using the demons method [17].
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