Adjusted Fireworks Algorithm Applied to Retinal Image Registration

Image registration is an important problem in image processing, especially in medical imaging. It is a hard optimization problem with objective function that is not appropriate for deterministic mathematical optimization. In this paper we propose a bi-resolution algorithm for rigid image registration based on recent fireworks algorithm. We tested our approach on retinal images from standard benchmark datasets and compared the results with other approaches from literature. Our proposed algorithm succeeded in registering images in all cases, and was more accurate than other compared methods. Studies in Informatics and Control, Vol. 26, No. 1, March 2017 http://www.sic. ici.ro 33 optimize the control points collected by directional finding algorithm to retrieve the binary registered result. In [31], particle swarm optimization algorithm was adjusted for optimization of transformation parameters with hybrid mutual information as a similarity measurement. Revised quantum-behaved particle swarm optimization and diversity-controlled quantum PSO were applied to medical image registration in [41]. In [36] a PSO algorithm was combined with sequential quadratic programming for rigid image registration. In [30] the artificial bee colony, more recent stochastic optimization algorithm, was used for rigid image registration. Another relatively new swarm intelligence algorithm, firefly algorithm, was used for searching maximal similarity measurement in [37] and [35]. Paper [5] deals with the time complexity issue by using multithreading parallel processing technique. In this paper we propose to use one of the latest swarm intelligence algorithms, the fireworks algorithm (FWA), for finding optimal parameters of rigid transformation for retinal image registration of 2D images. The resolution of retinal images from the used dataset is 565x584 pixels. This resolution is too large for finding the optimal parameters for wide search range so we proposed one resolution reduction in order to narrow the search range. In this paper the optimal reduction factor for retinal images as well as optimal parameters for the fireworks algorithm were empirically determined. The rest of the paper is organized as follows. A mathematical model for image registration is presented in Section 2. In Section 3 bi-resolution image technique is explained. Section 4 provides details about fireworks algorithm. Our proposed algorithm and para-meter settings are presented in Section 5. Experimental results and comparative analysis are given in Section 6. At the end, in Section 7 conclusions and future work are presented. 2. Mathematical Model for Image Registration Algorithms for image registration start with two images, one labelled as reference and one as floating image. Floating image should be transformed to align with the reference image. Next, it is necessary to choose criterion function that determines the similarity between two images. The last step is to optimize the transformation so that the stopping criteria are satisfied. Stopping criteria can be the number of iterations for optimization algorithm or desired similarity between images. Image registration refers to the mapping that is the best match between two or more images of the same scene taken at different times or taken by different sensors. Assuming that B is a floating image that should to be aligned with the reference image A, mathematically mapping can be defined as: )) , ( ( ( ) , ( y x T B y x A α ζ = (1) where ζ is the intensity calibration function and Tα is transformation function that maps spatial coordinates x and y to new spatial coordinates x’ and y’ with the transformation parameters α: ) , ( ) ' , ' ( y x T y x α = . (2) Image registration determines spatial transformation which maximizes similarity of the reference and floating images. Previous description of image registration can be represented by the following equation: )), ( , ( max arg * B T A O T α = (3) where Tα is one possible transformation and O represents the objective function which is actually the similarity measurement. In this case, represents transformation with parameters α which maximizes the value of the objective function over all possible transformations. For different purposes different transformations are used. One type of transformations T are linear transformations that include translation, rotation, scaling and other affine transformations. Common name for these transformations is rigid transformations. On the other hand, there are non-linear transformations, also called elastic or non-rigid transformations, which include radial basis functions, physical continuum models and large deformation models. Elastic transformations map curve lines to other curve lines. In this paper we used rigid transformations that include translation and rotation. These transformations are defined by two translation parameters tx and ty and angle of rotation θ . Transformation formula can be written in the matrix form: 1 0 0 ) cos( ) sin( ) sin( ) cos(