Abstract: Surface anomaly can lead to defects in the appearance, quality, and performance of industrial products, thereby reducing production efficiency and increasing safety risks, ultimately resulting in economic and reputational losses for manufacturing enterprises. Therefore, accurate identification and detection of surface anomalies in industrial products is of paramount importance. With the rapid development of artificial intelligence, computer vision techniques based on deep neural networks (DNNs) have emerged quickly and are extensively used in surface anomaly detection for industrial products. However, due to the scarcity of surface anomalies, uncertainty in defect types, and high cost of manual labeling, the recognition accuracy of DNNs remains suboptimal. To address this issue, this paper proposes a distributionally robust optimization generative (DRO-G) model with label smoothing (LS). This model operates in two phases. In the first phase, the regularization effect of LS is extended and demonstrated to be able to generate new images. In the second phase, the generated images are used to train DNNs for anomaly detection. Moreover, this paper constructs a label smoothing-stochastic gradient (LS-SG) algorithm to approximately solve the model. In the first phase, gradient ascent is used to incorporate the LS regularization effect into existing images and generate new ones. In the second phase, gradient descent is employed to train DNNs to identify anomalous images. Furthermore, this paper conducts simulation experiments using multiple types of surface anomaly data from four products categories: grid, carpet, wood, and screw, in the MVTecAD dataset. The results demonstrate that the proposed algorithm can effectively expand the surface anomaly dataset and improve the recognition accuracy of DNNs for certain product anomalies, while also exhibiting a degree of noise resistance. This approach not only assists enterprises in improving product quality and production efficiency but also offers an innovative solution for anomaly recognition and detection in industrial imaging. This approach not only aids enterprises in enhancing product quality and production efficiency but also provides an innovative solution for anomaly recognition and detection in industrial imaging.

Key words: distributionally robust optimization, label smoothing (LS), industrial image anomaly recognition

摘要： 表面异常可能会导致工业产品在外观、质量及性能等方面出现缺陷，降低生产效率及增加安全风险，给生产企业带来经济与信誉损失。因此，工业产品表面异常的识别与检测至关重要。随着人工智能的快速发展，基于深度神经网络（DNNs）的计算机视觉识别方法迅速兴起，被广泛应用于工业产品的表面异常检测中。然而，由于表面异常数量稀少、类型多样且标注成本高昂，DNNs的识别准确率常受限制。针对上述问题，提出了应用标签平滑（label smoothing，LS）的分布鲁棒优化生成式（DRO-G）模型。该模型分为两个阶段：第1阶段中拓展LS的正则化效应，证明了该正则化项可用于生成新图像；第2阶段利用生成的图像训练DNNs进行异常识别。进一步地，构建标签平滑-随机梯度（LS-SG）算法对模型近似求解：该算法第1阶段通过梯度上升法将LS的正则化效应添加到现有图像并生成新样本；第2阶段则通过梯度下降法训练DNNs以识别异常图像。以MVTecAD数据集（涵盖grid、carpet、wood和screw 4种产品）上的多种表面异常数据进行仿真实验表明，所提LS-SG算法能够有效扩大产品表面异常图像数据集的规模，并在一定程度上提高DNNs对特定产品异常的识别准确率，同时展现出一定的抗噪能力。本研究不仅有助于企业提高产品质量与生产效率，也为工业图像异常识别与检测提供了创新性解决方案。

关键词: 分布鲁棒优化, 标签平滑, 工业图像异常识别