An improved method to estimate the fractal dimension of colour images

Abstract

Summary Fractal dimension (FD) is an important feature of fractal geometry has many applications in various fields including image processing, image analysis, texture segmentation, shape classification and identifying the image features such as roughness and smoothness of an image. There are many techniques to estimate the dimension of fractal surface. The famous technique to calculate fractal dimension is the grid dimension method, which is popularly known as box counting method and some of the other improved methods like differential box counting and improved differential box counting method are used to estimate fractal dimension of grayscale images. The usual way of estimating the roughness or FD of color image involves two steps: (i) converting color image to grayscale and (ii) finding the roughness of generated grayscale image. But due to this conversion, significant color information is lost and leads to inaccurate roughness estimation. To avoid such inaccuracy this paper proposes the development and study of novel technique for estimating fractal dimension of color images. In this study, the improved differential box counting method is applied to the 24 bit representation of RGB color images to extract the roughness of color images. The validation of the proposal is performed by generating twelve different synthesized color images in terms of small variation of intensity value in RGB space and compared with previously three well defined existing methods that are weighted sum, average and desaturation method. The results showed that our proposed method is able to capture the accurate sharp variation of roughness as compared to the existing methods.