Deep Subspace Learning for Surface Anomaly Classification Based on 3D Point Cloud Data

TL;DR

This work tackles surface anomaly classification on 3D point clouds by explicitly modeling each anomaly class as a subspace to capture intra-class variation while enforcing inter-class separation. It combines a lightweight encoder with a subspace classifier that computes distances to class subspaces, enabling both accurate known-class classification and detection of new, out-of-distribution anomalies. A novel loss, including a subspace deviation term, and an SVD-based subspace initialization drive efficient training with limited anomalous data. Empirical results on synthetic and real datasets show superior classification accuracy and robust new-anomaly detection (AUROC near 1) compared with established backbones, demonstrating practical potential for manufacturing fault diagnosis and quality control. The approach also offers reduced parameter count and better generalization than conventional MLP-based classifiers.

Abstract

Surface anomaly classification is critical for manufacturing system fault diagnosis and quality control. However, the following challenges always hinder accurate anomaly classification in practice: (i) Anomaly patterns exhibit intra-class variation and inter-class similarity, presenting challenges in the accurate classification of each sample. (ii) Despite the predefined classes, new types of anomalies can occur during production that require to be detected accurately. (iii) Anomalous data is rare in manufacturing processes, leading to limited data for model learning. To tackle the above challenges simultaneously, this paper proposes a novel deep subspace learning-based 3D anomaly classification model. Specifically, starting from a lightweight encoder to extract the latent representations, we model each class as a subspace to account for the intra-class variation, while promoting distinct subspaces of different classes to tackle the inter-class similarity. Moreover, the explicit modeling of subspaces offers the capability to detect out-of-distribution samples, i.e., new types of anomalies, and the regularization effect with much fewer learnable parameters of our proposed subspace classifier, compared to the popular Multi-Layer Perceptions (MLPs). Extensive numerical experiments demonstrate our method achieves better anomaly classification results than benchmark methods, and can effectively identify the new types of anomalies.

Figures (13)

• Figure 1: The motivations of proposed deep subspace model for anomaly classification. (i) Different samples of the same class can be located widely in the same subspace, which allows for intra-class variation. (ii) The subspaces are promoted to be discrepant so that similar samples across different classes can be distinguished. (iii) The new type of anomaly is far away from all established subspaces and thus able to be detected.
• Figure 2: Our proposed deep subspace learning framework for anomaly classification and the new type of anomaly detection.
• Figure 3: The architecture of the adopted encoder when $p=128$. The shared MLP is the 1D convolution used in PointNet qi2017pointnet, BN is batch normalization operation, and ReLU is the activation function.
• Figure 4: Interpretation of different dimensions of subspaces. (a) 0-dimensional subspace. The subspace degrades to a singleton. (b) 1-dimensional subspace. The subspace is a line. (c) n-dimensional subspace. The subspace is a hyperplane that allows representations distributed along various directions.
• Figure 5: Projection of representation $\boldsymbol{f}_i$ on the subspace of class $c$.