Geometry-Aware Smoothing Selection for Noisy Scattered Surface Reconstruction: Evidence from Synthetic Benchmarks and Water Quality Data
Abstract
Sampling geometry may influence both reconstruction stability and the smoothing needed to control noise. This study distinguishes geometry-dependent failure of exact multiquadric radial basis function (RBF) interpolation from variation in validation-selected smoothing. A synthetic benchmark crossed four response families, four 16-point geometries, three slice levels, five observation regimes, and 24 repeated holdouts, yielding 17,280 method-level evaluations. Clough--Tocher cubic interpolation, exact RBF, and smoothed RBF were compared, followed by a Water Quality Portal pilot with 1,950 complete activities. On the synthetic shared-valid domain, exact RBF achieved the lowest noise-free mean RMSE (0.0206), whereas smoothed RBF performed best under noise (0.1807 versus 0.2414 for cubic and 0.6106 for exact RBF). Clustered-gap support produced the largest noisy exact-RBF RMSE (1.2706). Geometry added little explanatory power for log-transformed smoothing: the combined model had R2=0.4259, compared with 0.4096 for noise alone. Reported failure-regression results suggest a stronger geometry signal, but remain unverified without their original model specification. In the environmental pilot, smoothed RBF achieved mean RMSE 0.9877 with no negative-R2 failures. Conflicting responses at identical predictor coordinates made exact interpolation unsuitable. All environmental smoothed-RBF fits selected the largest candidate, preventing geometry--smoothing correlation analysis. The findings motivate geometry-aware failure screening but do not establish a transferable rule for smoothing magnitude. Independent multisite validation, appropriate coordinate scaling, joint scale--smoothing tuning, and conditioning diagnostics are needed before an adaptive policy can be claimed.
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BibTeX
@misc{sancak2026geometryaware,
title = {{Geometry-Aware Smoothing Selection for Noisy Scattered Surface Reconstruction: Evidence from Synthetic Benchmarks and Water Quality Data}},
author = {Mirkan Emir Sancak},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.14522},
eprint = {2611.14522},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.14522},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Geometry-Aware Smoothing Selection for Noisy Scattered Surface Reconstruction: Evidence from Synthetic Benchmarks and Water Quality Data
AU - Mirkan Emir Sancak
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.14522
UR - https://arxiv.org/abs/2611.14522
AB - Sampling geometry may influence both reconstruction stability and the smoothing needed to control noise. This study distinguishes geometry-dependent failure of exact multiquadric radial basis function (RBF) interpolation from variation in validation-selected smoothing. A synthetic benchmark crossed four response families, four 16-point geometries, three slice levels, five observation regimes, and 24 repeated holdouts, yielding 17,280 method-level evaluations. Clough--Tocher cubic interpolation, exact RBF, and smoothed RBF were compared, followed by a Water Quality Portal pilot with 1,950 complete activities. On the synthetic shared-valid domain, exact RBF achieved the lowest noise-free mean RMSE (0.0206), whereas smoothed RBF performed best under noise (0.1807 versus 0.2414 for cubic and 0.6106 for exact RBF). Clustered-gap support produced the largest noisy exact-RBF RMSE (1.2706). Geometry added little explanatory power for log-transformed smoothing: the combined model had R^2=0.4259, compared with 0.4096 for noise alone. Reported failure-regression results suggest a stronger geometry signal, but remain unverified without their original model specification. In the environmental pilot, smoothed RBF achieved mean RMSE 0.9877 with no negative-R^2 failures. Conflicting responses at identical predictor coordinates made exact interpolation unsuitable. All environmental smoothed-RBF fits selected the largest candidate, preventing geometry--smoothing correlation analysis. The findings motivate geometry-aware failure screening but do not establish a transferable rule for smoothing magnitude. Independent multisite validation, appropriate coordinate scaling, joint scale--smoothing tuning, and conditioning diagnostics are needed before an adaptive policy can be claimed.
ER -