Surface Defect Identification using Bayesian Filtering on a 3D Mesh

TL;DR

This work addresses automated surface defect detection by marrying a CAD-derived dense 3D mesh with measurements from commercial stereo cameras through a Bayesian filtering framework. By assigning a per-face state that quantifies dissimilarity to the nominal CAD model and fusing multi-sensor point clouds via recursive weighted least squares (and its information-filter variant), the method localizes defects with sub-millimeter precision under favorable sensing conditions. Key contributions include a robust measurement model based on ray casting, a scalable information-form update for large meshes, and an empirical demonstration using RealSense and Zed2 cameras that validates the approach under practical industrial-like setups. The findings indicate significant potential for low-cost, CAD-guided quality control, while highlighting avenues for bias compensation, parallel computation, and active sensing to enable near-online inspection in manufacturing environments.

Abstract

This paper presents a CAD-based approach for automated surface defect detection. We leverage the a-priori knowledge embedded in a CAD model and integrate it with point cloud data acquired from commercially available stereo and depth cameras. The proposed method first transforms the CAD model into a high-density polygonal mesh, where each vertex represents a state variable in 3D space. Subsequently, a weighted least squares algorithm is employed to iteratively estimate the state of the scanned workpiece based on the captured point cloud measurements. This framework offers the potential to incorporate information from diverse sensors into the CAD domain, facilitating a more comprehensive analysis. Preliminary results demonstrate promising performance, with the algorithm achieving convergence to a sub-millimeter standard deviation in the region of interest using only approximately 50 point cloud samples. This highlights the potential of utilising commercially available stereo cameras for high-precision quality control applications.

Figures (6)

• Figure 1: Example of polygonal mesh with $n_v = 5$ vertices and $n_f = 3$ faces.
• Figure 2:
• Figure 3: RMSE of the algorithm computed on a $5$ mm as function of the iterations and relative distances between object and camera for the two compared devices.
• Figure 4: Estimation error $\boldsymbol{e}_{50} = \hat{\boldsymbol{x}}_{50} - \boldsymbol{x}$, in the region of interest, for the Realsense (a) and Zed2 (b) cameras at the $50$-th iteration. Measurements have been taken at $50$ cm, and the mesh has size of $5$ mm. Drawn isolines mark the barrier at each whole integer step of error. The reported triangular grid is the one of the mesh actually used to carry out the estimation.
• Figure 5: State estimate $\hat{\boldsymbol{x}}_{50}$, in the region of interest, for the Realsense camera and location of the spherical defect (dashed green line). Experiment setup as in Fig. \ref{['fig:state-error']}.The reported triangular grid is the one of the mesh actually used to carry out the estimation.