Fig. 1. Aero-engine. (a) Photograph; (b) measured point clouds

Fig. 2. Shape characteristics of aero-engine profile point cloud

Fig. 3. Feature segmentation method

Fig. 4. Feature segmentation network

Fig. 5. Local information coding unit

Fig. 6. Features learned by encoder unit. (a) Small patch; (b) global feature from DGCNN^[31]; (c) medium patch; (d) large patch

Fig. 7. Spatial transform network

Fig. 8. EdgeConvmlp(a1,a2,…,an) network

Fig. 9. Casing point cloud comparison. (a) Original model; point clouds obtained by algorithms (b) with and (c) without density equalization algorithm

Fig. 10. Feature segmentation dataset

Fig. 11. Flow chart of density equalization algorithm

Fig. 12. Shape characteristics of aero-engine profile point clouds. (a) Irregular shape; (b) rich details; (c) irregular distribution

Fig. 13. Multi-scale local patches. (a) Size difference among different structural features; (b) rich detail shapes from the same structural feature

Fig. 14. Comparison of IFPS and random sampling

Fig. 15. Flowchart of IFPS algorithm

Fig. 16. Comparison of segmentation results of different methods

Fig. 17. Comparison of segmentation results of different learning-based methods

Fig. 18. Feature segmentation results of aero-engine profile point cloud. (a) Input point cloud; (b) training set only has single casing; (c) training set has both single casing and casing assembly

Fig. 19. Feature segmentation results of noisy point cloud

Fig. 20. Segmentation network with single-scale surface patches as input

Fig. 21. Coding units using only high-level feature vectors