Fractal dimension of RGB color images

Abstract Fractal Dimension (FD) is a very useful feature in fractal geometry for analysis of digital images. For estimating FD, several existing algorithms are, (i) box-counting, (ii) probability box-counting, (iii) differential box-counting (DBC), (iv) relative DBC (RDBC), and (v) improved DBC (IDBC) for gray-scale images. For color images the existing methods are, (i) extended version of probability box-counting method, (ii) box merging method and (iii) improved version of IDBC method. However, the accuracy of an algorithm for estimation of FD in RGB color domain is still a challenging issue! In this article, we have attempted to estimate FD of RGB color images by extending the DBC algorithm into a color domain. To validate this new approach, we have generated gradient images with known FD along with experimentally controlled images. The experimental work were carried out by three sets of color images; one set of color brodatz database, one set of smooth color images from SGA color checker, and one set of generated gradient images. The experimental results are found to be more precise and time saving in case of the proposed method. From the t -test results, it was found to be more efficient to compute the FDs that distinguish the surface roughness of RGB color images as compared to existing methods.