Evaluation of mathematical fractal analysis approaches on radiological histopathological and atomic force microscopy images of cancerous tissues

The early and accurate diagnosis of cancer is crucial for preventing aggressive treatments and improving the treatment process. This study aims to evaluate healthy, benign, and malignant tissues in mammography, histopathology, and atomic force microscopy (AFM) images using the fractal analysis method. Fractal dimensions calculated using the box-counting technique demonstrated that malignant tissues had significantly higher fractal dimensions compared to benign and healthy tissues, with a p<0.001 significance level within a 95% confidence interval. Similarly, the fractal dimensions of benign tissues were found to be significantly higher than those of healthy tissues. Statistical analyses, including t-tests, one-way ANOVA, and Kruskal-Wallis H tests, confirmed the significance of differences between the groups. Additionally, using statistical features, a subset of data were classified at a fundamental level with decision trees, achieving an accuracy of 85% and a precision rate of 93.3%. The findings reveal that fractal dimensions calculated through fractal analysis provide high discriminative power between different tissue types and have the potential to serve as an objective reference point in cancer diagnosis. This systems engineering study conducted in the health sciences field suggests that the method developed can be utilized as a reliable tool in the diagnostic process.