Analysing roughness of surface through fractal dimension: A review

Abstract In last three decades, fractal geometry (FG) has been the focus of attention by several researchers owing to it exhibiting excellent properties and robust application with respect to current research scenario. Fractal Dimension (FD) plays a vital role in order to analyse complex objects that are found in nature which was failed to be analysed by Euclidian geometry. FD is an imperative aspect of FG to provide indicative application in different areas of research including image processing, pattern recognition, computer graphics and many more. Analysis of an image is an important technique of image processing to describe image features like texture, roughness, smoothness etc., and is only possible through FG. Due to this reason many more technique were evolved to estimate the fractal dimension. The main aim of this article is to give a comprehensive review, which summarizes recent research progress on analysis of surface roughness and an overview of different concepts, and the way they work and their benefits and their limitations, and also we deliver how the different concepts taken into consideration to estimate FD depend upon different algorithms. This article also discusses several factors affecting FD estimation; types of similarity property, spatial resolution, sampling process, region of interest, spectral band and box-height criteria are discussed. Furthermore, we have tried to present the application area oriented versus core area of FG. There are several contradictory results found in many kinds of literature on the influence of different parameters while conducting FD analysis. Mainly it has been observed that the FD estimation will be affected by texture property, gray scale range, color property, color distance and the other parameters which are already mentioned. Hence this article will be beneficial for researchers in order to select precise FD estimation. However different algorithms lead to different results even with the use of the same kind of database images, so selection of appropriate technique is a major challenge for accurate estimation. Therefore an in-depth and proper understanding is required in order to choose the appropriate algorithm and also a robust algorithm for analysing roughness in better and precise way needs to be developed.

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