# New Evolutionary-Based Techniques for Image Registration
## 1 Introduction  
One of the most challenging tasks of image recognition is to align images acquired at different times, by different sensors and from different angles. The registration process consists of finding correspondence between all pixels in two images of a specific scene. Registration methods are applied in various real-world problems, including object detection and recognition, motion analysis, change detection and object tracking. Basically, image registration techniques deal with geometric distortions, the ultimate goal being to find out a set of transformation parameters that maximize the similarity degree between the images to be aligned. The class of perturbation models addressed by registration includes spatial transformations as for instance rigid, affine, projective, and global polynomial perturbation functions. The research reported in our paper involves the most commonly studied geometric degradation model, namely the affine transformation, defined as a mixture of translation, rotation, scale changes, shear and aspect ratio changes. So far, various classes of registration techniques, mainly depending on the perturbation model, have been presented in the literature [1; 2; 3; 4; 5; 6; 7]. The most commonly used classes of registration methods include Principal Axes Transform (PAT), multiresolution registration, boundary registration, model-based registration, adaptive registration and optimization-based registration. PAT method belongs to PCA-based image processing techniques. Basically, the main advantages of using principal components (PCs) in digital signal analysis is that PCs are uncorrelated, with the information encodedin each one of them being the maximum for the whole set [8]. Multiresolution methods align two images using sets of increasingly smaller size representations. Since smaller images reduce geometric differences, a global transformation function successfully registers the images and speeds up the registration process. Boundary registration uses the idea of aligning images using their boundaries. The adaptive registration techniques are developed based on a collection of tools and use information about the geometric and intensity differences between the images to select the right tool for alignment. The model-based methods are applied when traditional dissimilarity measures cannot be used to find an initial registration of the images. In such cases, additional information about the images should guide the alignment process. The techniques proposed in this paper belong to the optimization class and consist of evolutionary computation (EC) approaches. The EC approaches of image registration are usually three stage mechanisms. First, a similarity measure which can be associated to the fitness function has to be defined. In the second stage the initial parameter values that approximately register the images are automatically established by randomly generating them in a certain search space. Finally, an EC-based algorithm that takes the initial variants of registration to the optimal one is applied. The field of EC consists of genetic algorithms (GA), evolution strategies (ES), genetic programming, differential evolution, evolutionary programming and swarm intelligence. So far, the most commonly used EC methods for image registration includes GAs, memetic algorithms and particle swarm optimization [9; 10; 11; 12; 13; 14]. Our research focuses on the development of image registration techniques for signature recognition. In our work we consider the degradation model that combines the rigid transformation with a shear transformation acting along the x axis. We propose and develop several EC registration methods in order to obtain accurate recognition rates and fast algorithms. First, we introduce two variants of the firefly method that proved to have excellent accuracy and fair run times. In order to speed up the computation, we propose two variants of Accelerated Particle Swarm Optimization (APSO) method.