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

2026-05-09

AI Summary

This work addresses the significant challenge in advanced manufacturing of simultaneously monitoring complex geometries and spatially varying surface colors, a task hindered by conventional approaches that rely on point cloud registration or mesh reconstruction—processes prone to error accumulation and high computational cost. To overcome these limitations, the authors propose SMAC, a novel framework that enables joint shape–color monitoring without requiring registration or reconstruction. SMAC leverages 4D point cloud modeling and exploits spectral features derived from the Laplace–Beltrami operator to capture intrinsic correlations between geometry and color. Furthermore, it incorporates a spatially aware diagnostic mechanism to localize anomaly sources. Experimental results demonstrate that SMAC effectively detects subtle deformations and color anomalies in both Monte Carlo simulations and functional graded material case studies, accurately identifying their types and spatial locations.

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.

Problem

• 4D point clouds
• shape deformation
• color anomaly
• registration-free
• simultaneous monitoring

Innovation

• 4D point clouds
• registration-free
• Laplace-Beltrami operator
• simultaneous shape-color monitoring
• anomaly localization