An Instantaneous Memetic Algorithm for Illumination Correction Elsa Femandez, Manuel Grafia @to. de Ciencias zyxwvutsrq de la Computacibn e Inteligencia Artificial, Facultad de Informitica de San Sebastian, zyxwvuts UPV/EHU, Paseo Manuel de Lardizabal,l, CP. 20003, San Sebastih, Spain zyxwvutsr { ccafegoe,ccpgrrom) @sc.ehu.es Abstract Memetic algorithms are hybrid evolutionary algorithms that combine local optimizationwith evolutionarysearch operators. In this paper we describe an instance ofthis paradigm designed for the zyxwvutsrqpo correction zyxwvutsrqpon of illumination inhomogeneities in images. The algorithm uses the gradient information of an error function embedded in the mutation operator. Moreover, the algorithm is a single-solution population algorithm, which makes it computationallyLight. The fitness function is defined assuming that the image intensity is piecewise constant and that the illumination bias may be approximated by a linear combination of ZD Legendre polynomials. We call the algorithm Instantaneous Memetic Illumination Correction (IMIC). 1. INTRODUCTION Illumination inhomogeneity correction is a key problem in several domains, above all in medical imaging and Magnetic Resonance Imaging (MRI). The correction is critical in many cases to obtain meaningful image segmentations. The contribution of the illumination to the image formation is multiplicative, therefore its consequences can not be removed easily through traditional linear filtering algorithms. In this paper we will not consider specific noise contributions that appear in MRI zyxwvutsrqpon [6]. The classic approach to solve this problem is the homomorphic filtering [3] that filters out the low frequency components of the logarithm image in the Fourier transform domain. Illumination gradients arc usually smooth functions, therefore it is expected that the lowest components of the logarithm image will correspond to the illumination bias. The basic approach of working on the logarithm image hying to isolate the ilumination components of the image is common to many other algorithms that estimate the logarithm of the illumination bias and perform the correction subtracting it from the corrupted image logarithm. Few algorithms perform the correction computing the division of the corrupted image by the estimated bias. A coarse taxonomy of illumination correction algorithms distinguishes between parametric and non-parametric methods. Non-parametric algorithms include Bayesian image nodelling of the image logarithm, using some minimization method to estimate the most likely illumination bias logiarithm. For this estimation task [IO] applies an EM algorithm, while [4] applies a minimization of an entropy criterion. These works hy to isolate the bias field, on the other hand [I] introduces the effect of the Jesds Ruiz Cabello Unidad de Resonancia Magnttica Universidad Complutense, Paseo Juan XXIII, 1, Madrid, Spain bias field inside the classification adding a bias term into the fuzzy omeans procedure that they apply to the image pixels classification in order to obtain image segmentations. On the whole, non parametric methods arc computer intensive and require huge amounts of memory in some cases. Another non- parametric approach that gives good results based on the iterative deconvolution with gaussian kernels is described in [SI. Parametric methods assume some mathematical model of the illumination field. In [5] these models arc second and fourth order polynomials. In [9] they are linear combinations of Legendre polynomials. The estimation of the model parameters is done through minimization of some criterion function. In [SI the criterion is the minimization of the information of the restored image, preserving the image statistics. In [9] the fitting of the model is done minimizing the classification err01 of the restored image, analogous to the classification error in [l]. The Memetic Algorithms [SI arc inspired by the notion of a meme, which is defined as a unit of information that modifies itself while people are exchange ideas. A meme is modified (optimized) by a person before passing it to the next person. The Memetic Algorithms are hybrid between the population-based global search algorithms and local search algorithms. They have been applied in a variety of problems (i.e.:[7, 11, 121. In the present work we consider Evolution Strategies [Z] as the evolutionary paradigm. The figure 1 shows a general pseudocode of a memetic algorithm. The approach proposed in this paper is an instantaneous approach that uses gradient information of the fitness function to drive the search for the next generation individuals. Random population creation. Local optimization of each individual. Compute fitness. Repeat Select parents. Perform crossover and mutation, Compute fitness. Select new population, Local optimization of each individual. Compute fitness. Until convergence. Figure 1. Pseudocode of a Memetic Algorithm. 0-7803-85 15-2/04/$20.00 02004 IEEE 1105