AI framework with computational box counting and Integer programming removes quantization error in fractal dimension analysis of optical images

Abstract

Because many Chemical Engineering phenomena and processes involve distinctive shapes and structures, fractal dimension (FD) analysis is of great interest to the Chemical Engineering community due to its utility in providing a statistical index of shape complexity, which not only quantifies image structure but also helps explain functional properties. Past box counting (BC) methods for estimation of FDs are inconsistent due to quantization error (QE) introduced from image rotation and translation. In this work, we propose a systematic and automatic artificial intelligence (AI) framework that consistently estimates FDs of relevance to different fields of Chemical Engineering without QE by integrating image preprocessing, set-covering optimization-based BC, and regression analysis. As a result of the deterministic optimization technique, FD estimations remain consistent for all images regardless of image rotation and translation. The results of image datasets obtained from fields such as interfacial science, biomedical engineering, human anatomy, among others, demonstrate efficient box size specification to maximize regression effectiveness and FD calculation accuracy for a variety of images. Overall, the proposed AI framework offers a new means of estimating FD accurately and efficiently for optical images of interest to the Chemical Engineering community.