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Mutual Information based Medical Image Registration using Extremal Optimization

Image Registration (IR) is a challenge that arises in many image processing applications when several images must be aligned. In this work we address the registration of medical images which can be of different modalities. In this context, one of the most popular approaches is the Mutual Information based methods [2], [3]. In general, the basic input data for the registration process are two images: one is referred as the fixed image f (X) and the other as the moving image m(X), where X represents a position in N-dimensional space. The transform component T(X) represents the spatial mapping of points from the fixed image space to points in the moving image space. To determine the quality of the matching process, i.e. how well the fixed image is matched by the transformed moving image, a metric component S(f,m◦T) is usually defined, providing a measure which forms the quantitative criterion to be optimized by the optimizer over the search space defined by the parameters [4]. As noted in the paragraph above, IR is treated as an optimization problem with the goal of finding the spatial mapping that will bring the moving image into alignment with the fixed image [4]. Deterministic optimization algorithms are mostly used to compute the cost function. They are fast and accurate but in some cases, especially in multimodal IR, these approaches may stuck in a local optima when the number of transformation parameters increases. This work is aimed to overcome this disadvantage using heuristic optimization algorithms. In order to facilitate the portability of the software, we use the Insight Segmentation and Registration Toolkit (ITK), which is a set of libraries in C++ designed for the development of registration methods [4]. One of the advantages of this library consists in the possibility of compare different methods and implementations. As an example of how a local optima can introduce errors in the solution of the algorithm, let consider the “Mean Squares” as a metric and the “Regular Step Gradient Descent” as the optimizer. The results are presented at Figure 1 where images (a) and (b) are input images of different modalities, the first one being the fixed image and the second one the moving image. At (c) both images are superimposed before the registration process while (d) is the result of applying the method. It can be clearly seen that the scale was not corrected, thus, the registration was not performed successfully.