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<p>Fractal pattern analysis and quantification find wide-ranging applications spanning diverse interdisciplinary research domains. Specifically, within material engineering, the correlation between fractal dimension (FD) values and material properties has evolved into a robust and widely recognized predictive framework. Nevertheless, contemporary fractal analysis methodologies exhibit inherent limitations when applied to real-time characterization of irregular surface topographies. Robust frameworks for analyzing topographical datasets where the measurement unit/scale differs between the X and Y directional axes remain inadequately established. Furthermore, standardized criteria for selecting appropriate fractal dimension estimation techniques tailored to specific measurement scales remain insufficiently established. In this context, three enhanced methodologies are proposed for fractal dimension estimation: the advanced cubic covering method (ACCM), the enhanced box counting method (EBCM), and the profile roughness parameter method (PRPM), specifically developed to analyze topographical data with disparate measurement scales along orthogonal axes. Subsequently, the influence of measurement scale variations on FD estimation accuracy is systematically investigated using Takagi surfaces as benchmark references, comparing the performance of the proposed methodologies against previously established techniques to evaluate their robustness under varying scaling conditions. The real-world utility of these methodologies is assessed through experimental characterization of cement mortar and concrete fracture surface topographies.</p>

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Measurement Scale Influence and Performance Analysis of Advanced Methodologies for Fractal Dimension Characterization of Real-World Irregular Surfaces

  • 期刊论文

  • 发表日期：

    2026年6月20日

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  • S. Pruthviraj,
  • M. H. Prashanth

摘要

Fractal pattern analysis and quantification find wide-ranging applications spanning diverse interdisciplinary research domains. Specifically, within material engineering, the correlation between fractal dimension (FD) values and material properties has evolved into a robust and widely recognized predictive framework. Nevertheless, contemporary fractal analysis methodologies exhibit inherent limitations when applied to real-time characterization of irregular surface topographies. Robust frameworks for analyzing topographical datasets where the measurement unit/scale differs between the X and Y directional axes remain inadequately established. Furthermore, standardized criteria for selecting appropriate fractal dimension estimation techniques tailored to specific measurement scales remain insufficiently established. In this context, three enhanced methodologies are proposed for fractal dimension estimation: the advanced cubic covering method (ACCM), the enhanced box counting method (EBCM), and the profile roughness parameter method (PRPM), specifically developed to analyze topographical data with disparate measurement scales along orthogonal axes. Subsequently, the influence of measurement scale variations on FD estimation accuracy is systematically investigated using Takagi surfaces as benchmark references, comparing the performance of the proposed methodologies against previously established techniques to evaluate their robustness under varying scaling conditions. The real-world utility of these methodologies is assessed through experimental characterization of cement mortar and concrete fracture surface topographies.