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

arXiv: https://arxiv.org/abs/2605.08753 · HTML: https://mlsanity.com/paper/2605.08753/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 61 references that are in the map.
- First posted on arXiv 9 May 2026.

## Builds on (most cited first, 5 of 5)

- [General, Single-shot, Target-less, and Automatic LiDAR-Camera Extrinsic Calibration Toolbox](https://mlsanity.com/paper/2302.05094/) (2023)
- [Laplacian Canonization: A Minimalist Approach to Sign and Basis Invariant Spectral Embedding](https://mlsanity.com/paper/2310.18716/) (2023)
- [Review of Machine Learning Methods for Additive Manufacturing of Functionally Graded Materials](https://mlsanity.com/paper/2309.16571/) (2023)
- [Implicit Modeling for 3D-printed Multi-material Computational Object Design via Python](https://mlsanity.com/paper/2509.15562/) (2025)
- [Registration-Free Monitoring of Unstructured Point Cloud Data via Intrinsic Geometrical Properties](https://mlsanity.com/paper/2511.05623/) (2025)

## Abstract (arXiv)

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.