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arXiv · 2605.08753

Simultaneous Monitoring of Shape and Surface Color via 4D Point Clouds: A Registration-free Approach

Mariafrancesca Patalano·Giovanna Capizzi·Kamran Paynabar
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Abstract

Advanced manufacturing technologies allow for the production of intricate parts featuring high shape complexity and spatially-varying material composition. Data fusion of point clouds with chromatic attributes provides 4D point clouds, a compact and informative representation that encodes both shape and material information. In this paper, we present a registration-free framework for Simultaneous Monitoring of shApe and Color (SMAC) via 4D point clouds. The proposed framework leverages Laplace-Beltrami operator spectral properties to capture and monitor geometric features and the relationship between shape and surface color. A combined monitoring scheme is proposed to effectively detect shape deformations and color anomalies, along with a spatially-aware post-signal diagnostic procedure to determine the source of change and localize color anomalies. Importantly, neither component relies on registration or mesh reconstruction, eliminating error-prone and computationally expensive preprocessing steps. A Monte Carlo simulation study and a case study on functionally graded materials demonstrate that SMAC achieves effective detection performance, particularly for subtle defects, while providing diagnostic capabilities to identify the source and location of anomalies.

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Mariafrancesca Patalano, Giovanna Capizzi, Kamran Paynabar. 2026-08-30. Simultaneous Monitoring of Shape and Surface Color via 4D Point Clouds: A Registration-free Approach. https://arxiv.org/abs/2605.08753

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