Advanced Optimization of Discrete Orthogonal Hahn Moments for Precision Image Reconstruction via the Firefly Algorithm

Abstract

In recent decades, discrete orthogonal moments have frequently been used to represent images in a variety of computer vision and pattern recognition applications. These moments commonly employ discrete orthogonal polynomials as their basis, some of which are parametric and characterized by localization parameters. Optimizing these parameters is crucial for enhancing the efficiency of orthogonal moments in image analysis. This paper takes a new approach for optimizing the discrete Hahn polynomial parameters ($\alpha, \beta$) using the Firefly optimization algorithm, focusing on minimizing the mean square reconstruction error. Where our method identifies the optimal $\alpha$ and $\beta$ values for constructing Hahn polynomials to achieve superior image moments. The results demonstrate that our Firefly algorithm-based method significantly improves image reconstruction quality, yielding lower reconstruction errors, particularly in low orders of Hahn moments. Furthermore, the proposed method outperforms both the artificial bee colony optimization method and the standard parameter selection method. The experiments clearly indicate the advantages of our proposed method, especially in the lower orders of moments.