Estimation of Urban Fractal Dimension Using a Convolutional Neural Network

A deep learning approach to estimate the urban fractal dimension Df using high-resolution WorldView-2 (WV-2) imagery is proposed. The networks are trained on fractal Brownian Motion (FBM) surfaces generated through computational models to simulate natural textures with varying degrees of roughness. Each surface is characterized by the Hurst exponent (H) related to the fractal dimension as Df=2-H. For the classification task, the images are divided into nine distinct classes, each corresponding to a defined range of H values. The regression task uses the same dataset for training and predicts the value of the fractal dimension. The CNNs learn to detect spatial patterns that reflect differences in the fractal geometry of the surfaces. Trained on a large dataset of synthetic images, the models can accurately estimate the urban fractal dimension Df from unseen satellite data. Our CNN-based predictions are compared against well-established methods for estimating the fractal dimension using real-world satellite data.