A point cloud-driven multi-feature-constrained fractal dimension method for corrosion morphology reconstruction

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Abstract
Three-dimensional point-cloud measurement can resolve corrosion topography with high spatial fidelity, but converting measured data into reproducible and quantitatively validated surface representations remains challenging. This study proposes a point cloud–driven multi-feature-constrained fractal reconstruction framework for corrosion morphology reconstruction and intermediate-state prediction of weathering steel surfaces. Based on measured point-cloud data, a descriptor system is established by combining ISO 25178 areal parameters, fractal and multifractal descriptors, spatial statistical metrics, and corrosion-pit morphology descriptors. Five key parameters, namely the fractal dimension D, arithmetic mean height Sa, skewness Ssk, kurtosis Sku, and autocorrelation length Sal, are used as core constraints in a multi-objective iterative reconstruction strategy. The framework is benchmarked against the Gaussian random field, Weierstrass–Mandelbrot, spectral synthesis, and Diamond–Square methods. Measured surfaces at different corrosion stages show substantially improved multi-parameter consistency and height-distribution agreement, with Kolmogorov–Smirnov p-values of 0.05–0.69 for reconstructed surfaces. A time-dependent parameter evolution model is further introduced to support morphology prediction at unmeasured intermediate time points, and a Monte Carlo uncertainty-quantification module is used to evaluate reconstruction variability and identify dominant contributors to uncertainty propagation. The proposed framework provides a measurement-oriented route from point-cloud acquisition to descriptor-based reconstruction, statistical validation, and uncertainty-aware intermediate-state estimation.
Funding Information
  • National Natural Science Foundation of China (52278318)
  • National Natural Science Foundation of China (52378316)
  • National Natural Science Foundation of China Regional Innovation Development Joint Fund (2025ZNSFSC0417)
  • National Natural Science Foundation of China Regional Innovation Development Joint Fund (U25A20347)

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