Advances in Digital Multimedia 4 Vol. 1, No. 1, March 2012 Copyright © World Science Publisher, United States www.worldsciencepublisher.org Rigid Image Registration by PSOSQP Algorithm Yudong Zhang, Lenan Wu (School of Information Science and Engineering, Southeast University, Nanjing, China, 210096) zhangyudongnuaa@gmail.com , wuln@seu.edu.cn Abstract: Image registration is a hot topic in the field of image processing, and it can be simplified as an optimization problem. The particle swam optimization (PSO) technique is an effective global convergence method, but its local search speed is slow. The sequential quadratic programming (SQP) method can solve a nonlinear programming problem quickly, but may be trapped into a local minimum. Therefore, we combined the two individual algorithms into a new PSOSQP algorithm. The digital experiments on 18 images demonstrate that the proposed method can achieve the closest solution to the true spatial transformation parameter, and it costs the least computation of only 1.0423s compared to GA, PSO, and ABC algorithms. Keywords: Image Registration; Normalized Cross Correlation; Particle Swarm Optimization; Sequential Quadratic Programming; Genetic Algorithm; Artificial Bee Colony. 1 Introduction Image registration is the process of transforming different sets of data into one coordinate system. Data may be acquired from different sensors, times, or viewpoints. Many common minimization strategies have been applied to image registration problems, including exhaustive search, gradient descent, simplex method, simulated annealing [1], genetic algorithms [2], Powell’s minimization, and artificial bee colony [3]. First task of image registration is to determine the similarity function[4]. An image similarity measure quantifies the degree of similarity between intensity patterns in two images [5]. The choice of an image similarity measure depends on the modality of the images to be registered. Common examples of image similarity measures include cross-correlation [6], mutual information [7], sum of squared intensity differences, and ratio image uniformity. Mutual information and normalized mutual information are the most popular image similarity measures for registration of multimodality images. Cross-correlation, sum of squared intensity differences and ratio image uniformity are commonly used for registration of images in the same modality [8]. The second task is to solve the similarity function. In order to overcome the shortcomings of being trapped in local minima, global optimization technique is chosen in recent years. Zhang et al. [9] proposed a bacterial multiple colony chemotaxis to realize the multi-resolution rigid image registration. Chalermwat et al. [10] presented a two-phase sequential and coarse-grained parallel image registration algorithm using genetic algorithm (GA) as optimization mechanism. Janko et al. [2] presented a successful application of GA to the registration of uncalibrated optimal images. Dreo et al. [11] employed Nelder-Mead local search and the HCIAC ant colony metaheuristic for robust rigid registration of retinal angiograms. Wang et al. [3] adopted the artificial bee colony and tested their algorithms on three images. Unfortunately, aforementioned optimization techniques all demand expensive computational costs, and are easy to get misled into local minima. The particle swam optimization (PSO) technique is an effective global convergence method, but its local search speed is slow [12]. The sequential quadratic programming (SQP) method is effective in local search, but may be trapped into a local minimum [13]. Therefore, the combined algorithm PSOSQP is able to conduct both global search and local search in each iteration, and as a result the probability of finding the optimal is significantly increased, which effectively avoid local optima to a large extent [14]. The structure of the paper is organized as follows: next section 2 gives brief introduction of the model of image registration; and presents the normalized cross correlation criterion; Section 3 combines the PSO and SQP, and lists the detailed pseudo codes of PSOSQP; Experiments in section 4 shows the dataset of 18 pairs of reference image and input image, and compare our algorithm to GA, PSO, and ABC with respect to error rate and computation time. Final section 5 is devoted to conclusions and discussions. 2 Model If A is the reference image and B is input image, the object of image registration is to bring the input image into alignment with the reference image by applying a spatial transformation to the input image [15-16], namely, * arg max {, [ ]} T T SATB  (1) Here, S represents the measurement of similarity, T represents the transformation matrix. In this study we focus on the rigid transform, which consists of two translation parameters (t x and t y ) and one rotation parameter (θ). The translation matrix T trans and rotation matrix T rot can be expressed as follows. 1 0 0 0 1 0 1 trans x y T t t            (2)