A Study of Using Convolutional Neural Networks in Fractal Dimension Estimation of Grayscale and Color Images

Abstract

Fractal dimension (FD) estimation is widely used to characterize image complexity and self-similarity in image analysis and texture characterization. Traditional FD estimators such as Box-Counting (BC) and Differential Box-Counting (DBC) are simple and efficient but can be sensitive to scale selection, resolution, and noise. This paper investigates the effectiveness of using convolutional neural network (CNN) in FD estimation compared to traditional methods. To this end, we have developed a CNN-based method for FD estimation under a fair and reproducible evaluation design. First, we have included an analytic-fractals benchmark (such as Sierpinski and Koch families) with closed-form FD values for independent evaluation. Second, for large-scale Julia/Mandelbrot images, FD labels are treated as reference estimates computed from multiple BC/DBC parameter settings and reported as mean ± standard deviation to quantify label uncertainty. We additionally assess behavior on an external natural-texture dataset and evaluate robustness under controlled degradations (noise, blur, compression, and downsampling). Performance is reported on large test sets using MAE/RMSE with 95% confidence intervals (bootstrap), together with per-image inference time under clearly specified hardware settings. Results indicate that the proposed CNN-based method provides stable FD estimation and fast inference, particularly under noise and resolution variations.