GPU-Accelerated Fractal Compression Dimension Estimation

Fractal dimension is widely used as a quantitative descriptor of structural complexity in digital images. However, its practical implementation often involves methodological and computational trade-offs. The compression-based estimator provides an information-theoretic formulation that operates directly on grayscale images without mandatory binarization. Although the method is theoretically grounded and has been applied in real-world scenarios, its implementation-level behavior and computational characteristics have not been systematically analyzed under controlled conditions. To address this gap, this work presents a structured GPU-enabled validation framework for this estimator using synthetic Julia sets with known theoretical fractal dimensions. By focusing on their planar boundaries, which enable direct ground-truth comparison across multiple resolutions, numerical accuracy, statistical stability, and execution time are jointly evaluated across CPU and GPU implementations. Furthermore, additional experiments assess sensitivity to progressive Gaussian blur and exploratory behavior on grayscale textures from the Brodatz dataset, revealing that boundary-dominated fractals consistently yield dimensions between 1 and 2, whereas volumetric textures produce values greater than 2 without modifying the estimation framework. Performance profiling identifies distinct computational regimes and highlights a trade-off between robustness and execution time in the double-compression GPU configuration. This approach establishes a reproducible evaluation framework that supports the practical deployment of compression-based fractal dimension estimation in large-scale and time-constrained image analysis systems.