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

TL;DR

This paper introduces a registration-free framework called SMAC for simultaneous monitoring of shape and surface color in 4D point clouds, effectively detecting and localizing subtle defects without requiring registration or mesh reconstruction.

Contribution

The novel SMAC framework leverages spectral properties of the Laplace-Beltrami operator to monitor geometric and color changes simultaneously without registration, improving defect detection accuracy.

Findings

SMAC effectively detects subtle shape and color anomalies.

The framework localizes the source of detected anomalies.

Simulation and case studies validate SMAC's high detection performance.

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.