Fractal dimension of synthesized and natural color images in Lab space

Chinmaya Panigrahy, Ayan Seal, Nihar Kumar Mahato

Abstract: Fractal dimension (FD) is a useful metric for the analysis of natural images that exhibit a high degree of complexity, randomness and irregularity in color and texture. Several approaches exist in the literature to measure FD of gray-scale images. The aim of this study is to introduce a FD estimation method for color images with color proximity in Lab space. The proposed method uses a xy-plane partitioning–shifting mechanism, where the divisors of image size are used as grid sizes. The proposed method simulates on synthesized color fractal Brownian motion (FBM) images, publicly available Brodatz database, Google color fractal images and noisy Brodatz database. The random midpoint displacement algorithm for the formation of gray-scale images is extended in this work to synthesize color FBM images. Noisy Brodatz database is obtained by adding salt-and-pepper noise with different noise densities to understand the behavior of FD. The experimental results illustrate that the proposed method is effective and efficient and outperforms the three state-of-the-art methods by observing the values of two proposed metrics, namely average error and average computed FD. A new mathematical expression for estimating FD of a color image is demonstrated, which relies on the number of edge pixels of individual color channel using multiple linear regression.