Examining the Source of Defects from a Mechanical Perspective for 3D Anomaly Detection

TL;DR

This work reframes 3D anomaly detection as a mechanics problem, modeling anomalies as damaging forces $F_D(\mathbf{p})=F_E(\mathbf{p})+F_I(\mathbf{p})$ and seeking corrective forces $F_C(\mathbf{p})=-F_D(\mathbf{p})$ to restore normal geometry. It introduces the Mechanics Complementary Model for 3D-AD (MC4AD) with three components: Diverse Anomaly-Generation (DA-Gen) to synthesize defects, Corrective Force Prediction Network (CFP-Net) to infer per-point corrective forces ($F_C=\text{MLPs}(F_9')$, decomposed into $F_E'$ and $F_I'$), and a Combined Loss $\mathcal{L}_{\text{comb}}$ enforcing symmetry and directional constraints. An HQC strategy simulates cost-limited industrial detection and a new Anomaly-IntraVariance dataset assesses intra-class variance under realistic conditions. Extensive experiments across five datasets show nine state-of-the-art results with minimal parameters and fast inference, demonstrating robust anomaly detection and segmentation. The approach advances practical 3D-AD by linking defect origins to corrective actions, while highlighting future work to incorporate explicit physical constraints.)

Abstract

In this paper, we explore a novel approach to 3D anomaly detection (AD) that goes beyond merely identifying anomalies based on structural characteristics. Our primary perspective is that most anomalies arise from unpredictable defective forces originating from both internal and external sources. To address these anomalies, we seek out opposing forces that can help correct them. Therefore, we introduce the Mechanics Complementary Model-based Framework for the 3D-AD task (MC4AD), which generates internal and external corrective forces for each point. We first propose a Diverse Anomaly-Generation (DA-Gen) module designed to simulate various types of anomalies. Next, we present the Corrective Force Prediction Network (CFP-Net), which uses complementary representations for point-level analysis to simulate the different contributions from internal and external corrective forces. To ensure the corrective forces are constrained effectively, we have developed a combined loss function that includes a new symmetric loss and an overall loss. Notably, we implement a Hierarchical Quality Control (HQC) strategy based on a three-way decision process and contribute a dataset titled Anomaly-IntraVariance, which incorporates intraclass variance to evaluate our model. As a result, the proposed MC4AD has been proven effective through theory and experimentation. The experimental results demonstrate that our approach yields nine state-of-the-art performances, achieving optimal results with minimal parameters and the fastest inference speed across five existing datasets, in addition to the proposed Anomaly-IntraVariance dataset. The source is available at https://github.com/hzzzzzhappy/MC4AD

Figures (9)

• Figure 1: Overview of our MC4AD. Compared with existing methods, the proposed MC4AD demonstrates excellent performance, low memory, and more efficiency. We examine for the first time the source of anomalies from a mechanical perspective and use it as a motivation to design models.
• Figure 2: Overview of MC4AD. The proposed MC4AD contains three important parts: 1) Diverse Anomaly-Generation (DA-Gen) transfers training normal samples into pseudo-anomaly point clouds. 2) Corrective Force Prediction Network (CFP-Net) extracts the potential damage forces in the input point cloud and generates the corresponding corrective forces. 3) Combined loss is used to constrain CFP-Net to generate corrective forces that conform to mechanical constraints correctly.
• Figure 3: The distribution of anomaly detection scores on class "vase9", compared between External, Internal, and Internal+External. Red and blue represent abnormal and normal points, respectively.
• Figure 4: Localization results.
• Figure 5: Visualization of the training and test sets on Group 1 and Group 2.

Theorems & Definitions (1)

• proof