Exploring the Role of Fractal Geometry in Engineering Image Processing Based on Similarity and Symmetry: A Review

Abstract

Fractal geometry theory has been widely used in engineering image processing. In this work, the basic principles and features of fractal geometry are first introduced and its importance in image processing is explained. The features of the symmetry and asymmetry of images are represented in fractal geometry and symmetry scaling is utilized to deal with image processing problems in engineering applications. Subsequently, specific applications of fractal geometry in engineering image processing are discussed in detail in terms of image compression, edge detection, texture analysis, and image reconstruction and restoration. The exploration of these applications reveals the advantages and usefulness of fractal geometry theory in image processing, and it is found that the image has certain symmetry and self-similarity, which is conducive to the establishment of mathematical models for the statistics of graphic contours and shapes. Finally, the unique value of fractal geometry in engineering image processing is further emphasized by comparing the innovations of fractal geometry with traditional image processing methods, which prompts the in-depth consideration of its potential value in this field. This paper provides new insights and directions for the research of engineering image processing, which is of positive significance for future research.