## 5 Conclusions  
This paper introduces an innovative approach for the identification and extraction of rock discontinuities, leveraging an enhanced Naive Bayes classifier. The key conclusions can be summarized as follows:  
Figure 18: Extraction results of two methods: (**a**) proposed method; (**b**) FCM.  
In response to the arduous and time-intensive process of manually selecting training point sets, fraught with challenges such as randomness that could compromise classification accuracy, this paper introduces an innovative approach to generating training sets around the selected training points, streamlining the selection process and elevating the precision of the training sets. Tailored to meet the demands of point cloud classification tasks, the Naive Bayes classifier is enhanced to effectively filter out noise points during the point cloud classification process by incorporating a logarithmic probability threshold, thereby improving the accuracy of discontinuity set extraction. The HDBSCAN algorithm is employed for the swift extraction of individual discontinuities, while the PCA algorithm is employed to compute the normal vectors of these discontinuities, facilitating accurate positioning.  
The proposed novel methodology has been applied to two cases located near Colorado and Kingston, respectively. Leveraging case A, the study explains the principles and procedures of the new method, validating its reliability through comparative analysis with previous research results. Case B is employed to discuss the optimal parameter selection, showcasing the reliable results obtained by the new method through comparisons with prior research outcomes and highlighting its advantages in the realm of noise reduction.  
The innovative method proposed in this study for generating training point sets not only minimizes the manual selection of samples but also reduces the likelihood of errors in the training point set. In contrast to existing methods, the use of an improved Naive Bayes classifier for extracting discontinuity sets ensures the removal of noise points while preserving efficiency and reliability, leading to more trustworthy results.  
Furthermore, the method proposed in this study operates under the assumption that the features used for classification are independent of each other, but many of the features may not be completely independent of each other, and thus subsequent research could further improve the Naive Bayes classifier in this direction to give it a better performance in terms of discontinuity extraction.  
Conceptualization, G.L.; methodology, X.Z.; software, X.Z.; validation, Y.L. and Z.Y.; formal analysis, G.L.; investigation, X.Z. and B.C.; resources, G.L.; data curation, X.Z. and B.C.; writing--original draft preparation, X.Z.; writing--review and editing, X.Z. and B.C.; visualization, X.Z.; supervision, C.T.; project administration, X.Z.; funding acquisition, G.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Science and Technology Research and Development Project of China Railway Co., Ltd. (Grant No. 2022-Special-07-02), the National Natural Science Foundation of China (Grant No. 41974148), the Natural Resources Science and Technology Project of Hunan Province (Grant No. 2022-01), and the Research Foundation of the Department of Natural Resources of Hunan Province (Grant No. 20230101 DZ).  
Not applicable.  
The data and materials that support the findings of this study are available from the author, [PERSON], upon reasonable request.  
Thanks to [PERSON] for sharing the point clouds of case A. The raw data of case B was obtained from the Rockbench repository. The authors kindly appreciated [PERSON], [PERSON], [PERSON], and [PERSON] for establishing the Rockbench repository. The authors' special appreciation goes to Editors and anonymous reviewers for valuable comments.  
The authors declare no conflicts of interest.