A Grayscale Segmentation Approach Using the Firefly Algorithm and the Gaussian Mixture Model

In this article, the author proposes an unsupervised grayscale image segmentation method based on a combination of the Firefly Algorithm and the Gaussian Mixture Model. Firstly, the Firefly Algorithm has been applied in a histogram-based research of cluster centroids. The Firefly Algorithm is a stochastic global optimization technique, centred on the flashing characteristics of fireflies. In this histogram-based segmentation approach, it is employed to determine the number of clusters and to select the gray levels for grouping pixels into homogeneous regions. Successively these gray values are used in the initialization step for the parameter estimation of a Gaussian Mixture Model. The parametric probability density function of a Gaussian Mixture Model is represented as a weighted sum of Gaussian components, whose parameters are evaluated applying the iterative Expectation-Maximization technique. The coefficients of the linear super-position of Gaussians can be thought as prior probabilities of each component. Applying the Bayes rule, the posterior probabilities of the grayscale intensities have been evaluated, therefore their maxima are used to assign each pixel to the clusters, according to their gray levels.