Resolution Effect on the Fractal Dimension of Simulated Fracture Surfaces

Objectives: We aimed to migrate our fracture surface measuring protocol to an open source image analysis application that runs on a wide variety of platforms, to develop an unbiasing (accuracy correction) factor for each algorithm that will be used to analyze atomic force microscope scans of dental ceramic specimens in the future, to determine which of the algorithms will provide the best precision in measuring dimensionality after unbiasing, and to determine whether resolution affects the accuracy and precision.
Methods: 40 Brownian interpolation surfaces having known dimensionality of D=2.1, 2.2, 2.3, and 2.4 (n=10) were generated in two resolutions (2048x2048 and 256x256) using MatLab. Gwyddion image analysis software was used to analyze each surface by 4 different algorithms (partitioning, cube counting, triangulation, and power spectrum). An unbiasing factor was determined by plotting the known D values versus the means of the fractal dimensions estimated by each algorithm. Linear models were used to correct the fractal dimension values and to determine the algorithm with the greatest precision (lowest standard deviation).
Results: All algorithms except for power spectrum could be corrected for bias using linear models for the 2048x2048 resolution, and all algorithms could be corrected for 256x256 resolution (R²≥0.99). Increasing resolution increased precision but did not affect accuracy.
Conclusions: The migration to a new software platform and unbiasing operations were successful. The cube counting algorithm had the best precision and accuracy after bias correction of the 4 algorithms investigated, so it will be used in future studies on clinically retrieved failed dental prostheses and implants.