Multiple Constraints Flow for Weakly Observable Defect Detection Based on Defect-Free Samples

Surface defect is a significant issue in real-world manufacturing systems, and vision-based automated inspection systems play a crucial role in ensuring product quality. Due to the scarcity of defect training data, traditional deep learning methods struggle in this context. Therefore, defect detection methods based on defect-free samples have become mainstream and been widely applied. However, these defect detection methods, relying solely on defect-free samples for learning, suffer from issues related to the instability and broadness of the learned anomaly evaluation space boundaries, which are characteristics of image ill-posed problems. This problem manifests as the failure to detect weakly observable defects during algorithm application. To address this challenge, this article introduces multiple constraints for boundary modification in the anomaly evaluation space to enhance the detection capability for weakly observable defects, called multiple constraints flow (MC-Flow). First, we improve the SNR to define the weak observability of defects signal-to-noise ratio (DSNR) and an adaptive simulation module for weakly observable defects. Second, we propose a dual parallel flow model structure to accept multiple constraints. Leveraging weakly observable defects provides additional constraints beyond maximum likelihood learning from normal samples and introducing these constraints into the anomaly evaluation space to modify and refine space boundary. Meanwhile, we design a specialized optimization objective and training strategy to unify the optimization directions of various constraints. Experimental results on 16 different cases demonstrate that our proposed MC-Flow effectively detects weakly observable defects. Compared with state-of-the-art (SOTA) methods, the proposed MC-Flow also achieves superior overall performance.