**5. Conclusions**

In this work, we propose a distribution-aware pseudo labeling for small defect detection (DAP-SDD) when limited labeled data are available. We first applied bootstrapping for the available labeled data to approximate the distribution of the whole labeled dataset. Then, we used it to guide pseudo label propagation. Our proposed method incorporates t-distribution confidence interval and adaptive training strategies, and thus can effectively generate more pseudo labels with high confidence while reducing confirmation bias. The extensive experimental evaluation on various datasets with various types of defects has demonstrated that our proposed DAP-SDD consistently outperforms the state-of-the-art techniques with above 0.9 of average precision and up to 0.99. Our in-depth analysis of the ablation studies clearly shows how each component employed in our approach effectively utilizes the limited labeled data.

**Author Contributions:** Conceptualization, X.Z. (Xiaoyan Zhuo); methodology, X.Z. (Xiaoyan Zhuo) and W.R.; evaluation, X.Z. (Xiaoyan Zhuo), W.R., and X.Z. (Xiaoqian Zhang); formal analysis, X.Z. (Xiaoyan Zhuo) and W.R.; writing—original draft preparation, X.Z. (Xiaoyan Zhuo); writing—review and editing, X.Z. (Xiaoyan Zhuo), W.R., and S.W.S.; supervision, T.D. and S.W.S. All authors have read and agreed to the published version of the manuscript.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** DAGM dataset: https://hci.iwr.uni-heidelberg.de/content/weaklysupervised-learning-industrial-optical-inspection (accessed on 7 April 2022). PCB dataset: http: //robotics.pkusz.edu.cn/resources/dataset/ (accessed on 7 April 2022).

**Acknowledgments:** The Titan X Pascal used for this research was donated by the NVIDIA Corporation. The authors acknowledge the MIT SuperCloud and Lincoln Laboratory Supercomputing Center for providing (HPC, database, consultation) resources that have contributed to the research results reported within this paper.

**Conflicts of Interest:** The authors declare no conflict of interest.
