三维点云去噪技术

doi:10.7523/j.ucas.2022.038

摘要/Abstract

摘要： 调研点云去噪的相关研究工作,根据相关算法的实现原理将其划分为基于优化思想的传统算法和基于深度学习思想的去噪算法,论述每类算法的研究进展,并对代表性算法进行详细分析,结合数据集、评估指标、实验结果等对其进行深入比较,在此基础上讨论当前点云去噪技术面临的问题和可能的发展方向及趋势。

关键词: 三维点云, 去噪, 优化思想, 深度学习

Abstract: With the development of 3D data acquisition technology, point cloud wins the favor of researchers for it's simple but effective representation and it is widely used in the fields of remote sensing, scene reconstruction, 3D modeling, etc. Considering that the data acquisition process is easily disturbed by many factors such as equipment, environment and material, raw point cloud is often corrupted with noise and so it is of great significance to explore robust and efficient denoising algorithms. This paper firstly investigates the relevant research works of point cloud denoising and divides them into traditional algorithms based on the optimization idea and denoising algorithms based on the deep learning idea according to the implementation principles. Secondly, the research progress of each kind of algorithm is discussed and a detailed analysis of representative algorithms is presented. Thirdly, the data sets, the evaluation metrics and experimental results are summarized with an in-depth comparison. Finally, the problems and possible development directions and trends of point cloud denoising are prospected.

Key words: three-dimensional point cloud, denoising, optimization strategy, deep learning

中图分类号:

TP391

肖俊, 石光田. 三维点云去噪技术[J]. 中国科学院大学学报, 2023, 40(5): 577-595.

XIAO Jun, SHI Guangtian. Three-dimensional point cloud denoising[J]. Journal of University of Chinese Academy of Sciences, 2023, 40(5): 577-595.

参考文献

[1] Wang Y, Zhang S S, Wan B L, et al. Point cloud and visual feature-based tracking method for an augmented reality-aided mechanical assembly system[J]. The International Journal of Advanced Manufacturing Technology, 2018, 99(9-12):2341-2352. DOI:10.1007/s00170-018-2575-8.
[2] Mahmood B, Han S U, Lee D E. BIM-based registration and localization of 3D point clouds of indoor scenes using geometric features for augmented reality[J]. Remote Sensing, 2020, 12(14):2302. DOI:10.3390/rs12142302.
[3] Zermas D, Izzat I, Papanikolopoulos N. Fast segmentation of 3D point clouds:a paradigm on LiDAR data for autonomous vehicle applications[C]//2017 IEEE International Conference on Robotics and Automation. May 29-June 3, 2017, Singapore. IEEE, 2017:5067-5073. DOI:10.1109/ICRA.2017.7989591.
[4] Yuan W T, Khot T, Held D, et al. PCN:point completion network[C]//2018 International Conference on 3D Vision (3DV). September 5-8, 2018, Verona, Italy. IEEE, 2018:728-737. DOI:10.1109/3DV.2018.00088.
[5] Wen X, Li T Y, Han Z Z, et al. Point cloud completion by skip-attention network with hierarchical folding[C]//2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). June 13-19, 2020, Seattle, WA, USA. IEEE, 2020:1936-1945. DOI:10.1109/CVPR42600.2020.00201.
[6] Huang Z T, Yu Y K, Xu J W, et al. PF-net:point fractal network for 3D point cloud completion[C]//2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). June 13-19, 2020, Seattle, WA, USA. IEEE, 2020:7659-7667. DOI:10.1109/CVPR42600.2020.00768.
[7] Landrieu L, Simonovsky M. Large-scale point cloud semantic segmentation with superpoint graphs[C]//2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition. June 18-23, 2018, Salt Lake City, UT, USA. IEEE, 2018:4558-4567. DOI:10.1109/CVPR.2018.00479.
[8] Hu Q Y, Yang B, Xie L H, et al. RandLA-net:efficient semantic segmentation of large-scale point clouds[C]//2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). June 13-19, 2020, Seattle, WA, USA. IEEE, 2020:11105-11114. DOI:10.1109/CVPR42600.2020.01112.
[9] Wang Y, Sun Y B, Liu Z W, et al. Dynamic graph CNN for learning on point clouds[J]. ACM Transactions on Graphics, 2019, 38(5):1-12. DOI:10.1145/3326362.
[10] Chen W K, Han X G, Li G B, et al. Deep RBFNet:point cloud feature learning using radial basis functions[EB/OL]. arXiv:1812.04302v2(2019-04-06)[2022-03-07]. https://arxiv.org/abs/1812.04302.
[11] Shi S S, Wang X G, Li H S. PointRCNN:3D object proposal generation and detection from point cloud[C]//2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). June 15-20, 2019, Long Beach, CA, USA. IEEE, 2019:770-779. DOI:10.1109/CVPR.2019.00086.
[12] Lang A H, Vora S, Caesar H, et al. PointPillars:fast encoders for object detection from point clouds[C]//2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). June 15-20, 2019, Long Beach, CA, USA. IEEE, 2019:12689-12697. DOI:10.1109/CVPR.2019.01298.
[13] Rusu R B, Cousins S. 3D is here:point cloud library (PCL)[C]//2011 IEEE International Conference on Robotics and Automation. May 9-13, 2011, Shanghai, China. IEEE, 2011:1-4. DOI:10.1109/ICRA.2011.5980567.
[14] Kolluri R. Provably good moving least squares[J]. ACM Transactions on Algorithms, 2008, 4(2):1-25. DOI:10.1145/1361192.1361195.
[15] Guennebaud G, Gross M. Algebraic point set surfaces[J]. ACM Transactions on Graphics, 2007, 26(3):23-es. DOI:10.1145/1239451.1239474.
[16] Öztireli A C, Guennebaud G, Gross M. Feature preserving point set surfaces based on non-linear kernel regression[J]. Computer Graphics Forum, 2009, 28(2):493-501. DOI:10.1111/j.1467-8659.2009.01388.x.
[17] Lipman Y, Cohen-Or D, Levin D, et al. Parameterization-free projection for geometry reconstruction[J]. ACM Transactions on Graphics, 2007, 26(3):22. DOI:10.1145/1276377.1276405.
[18] Huang H, Li D, Zhang H, et al. Consolidation of unorganized point clouds for surface reconstruction[J]. ACM Transactions on Graphics, 2009, 28(5):1-7. DOI:10.1145/1618452.1618522.
[19] Huang H, Wu S H, Gong M L, et al. Edge-aware point set resampling[J]. ACM Transactions on Graphics, 2013, 32(1):1-12. DOI:10.1145/2421636.2421645.
[20] Avron H, Sharf A, Greif C, et al. l₁-sparse reconstruction of sharp point set surfaces[J]. ACM Transactions on Graphics, 2010, 29(5):1-12. DOI:10.1145/1857907.1857911.
[21] Sun Y J, Schaefer S, Wang W P. Denoising point sets via L0 minimization[J]. Computer Aided Geometric Design, 2015, 35/36:2-15. DOI:10.1016/j.cagd.2015.03.011.
[22] Mattei E, Castrodad A. Point cloud denoising via moving RPCA[J]. Computer Graphics Forum, 2017, 36(8):123-137. DOI:10.1111/cgf.13068.
[23] Yadav S K, Reitebuch U, Skrodzki M, et al. Constraint-based point set denoising using normal voting tensor and restricted quadratic error metrics[J]. Computers & Graphics, 2018, 74:234-243. DOI:10.1016/j.cag.2018.05.014.
[24] Liu Z, Xiao X W, Zhong S S, et al. A feature-preserving framework for point cloud denoising[J]. Computer-Aided Design, 2020, 127:102857. DOI:10.1016/j.cad.2020.102857.
[25] Schoenenberger Y, Paratte J, Vandergheynst P. Graph-based denoising for time-varying point clouds[C]//2015 3DTV-Conference:The True Vision-Capture, Transmission and Display of 3D Video (3DTV-CON). July 8-10, 2015, Lisbon, Portugal. IEEE, 2015:1-4. DOI:10.1109/3DTV.2015.7169366.
[26] Gao X, Hu W, Guo Z M. Graph-based point cloud denoising[C]//2018 IEEE Fourth International Conference on Multimedia Big Data (BigMM). September 13-16, 2018, Xi'an, China. IEEE, 2018:1-6. DOI:10.1109/BigMM.2018.8499090.
[27] Roveri R, Öztireli A C, Pandele I, et al. PointProNets:consolidation of point clouds with convolutional neural networks[J]. Computer Graphics Forum, 2018, 37(2):87-99. DOI:10.1111/cgf.13344.
[28] Rakotosaona M J, la Barbera V, Guerrero P, et al. PointCleanNet:learning to denoise and remove outliers from dense point clouds[J]. Computer Graphics Forum, 2020, 39(1):185-203. DOI:10.1111/cgf.13753.
[29] Zhang D B, Lu X Q, Qin H, et al. Pointfilter:point cloud filtering via encoder-decoder modeling[J]. IEEE Transactions on Visualization and Computer Graphics, 2021, 27(3):2015-2027. DOI:10.1109/TVCG.2020.3027069.
[30] Casajus P H, Ritschel T, Ropinski T. Total denoising:unsupervised learning of 3D point cloud cleaning[C]//2019 IEEE/CVF International Conference on Computer Vision (ICCV). October 27-November 2, 2019, Seoul, Korea (South). IEEE, 2019:52-60. DOI:10.1109/ICCV.2019.00014.
[31] Shepard D. A two-dimensional interpolation function for irregularly-spaced data[C]//ACM'68:Proceedings of the 1968 23rd ACM national conference. New York, NY:Association for Computing Machinery, 1968:517-524. DOI:10.1145/800186.810616.
[32] Shen C, O'Brien J F, Shewchuk J R. Interpolating and approximating implicit surfaces from polygon soup[J]. ACM Transactions on Graphics, 2004, 23(3):896-904. DOI:10.1145/1015706.1015816.
[33] Guennebaud G, Germann M, Gross M. Dynamic sampling and rendering of algebraic point set surfaces[J]. Computer Graphics Forum, 2008, 27(2):653-662. DOI:10.1111/j.1467-8659.2008.01163.x.
[34] Huang Z Y, Carr N, Ju T. Variational implicit point set surfaces[J]. ACM Transactions on Graphics, 2019, 38(4):1-13. DOI:10.1145/3306346.3322994.
[35] Liao B, Xiao C X, Jin L Q, et al. Efficient feature-preserving local projection operator for geometry reconstruction[J]. Computer-Aided Design, 2013, 45(5):861-874. DOI:10.1016/j.cad.2013.02.003.
[36] Preiner R, Mattausch O, Arikan M, et al. Continuous projection for fast L₁ reconstruction[J]. ACM Transactions on Graphics, 2014, 33(4):1-13. DOI:10.1145/2601097.2601172.
[37] Lu X Q, Wu S H, Chen H H, et al. GPF:GMM-inspired feature-preserving point set filtering[J]. IEEE Transactions on Visualization and Computer Graphics, 2018, 24(8):2315-2326. DOI:10.1109/TVCG.2017.2725948.
[38] Candès E J, Li X D, Ma Y, et al. Robust principal component analysis?[J]. Journal of the ACM, 2011, 58(3):1-37. DOI:10.1145/1970392.1970395.
[39] Chen H H, Wei M Q, Sun Y X, et al. Multi-patch collaborative point cloud denoising via low-rank recovery with graph constraint[J]. IEEE Transactions on Visualization and Computer Graphics, 2020, 26(11):3255-3270. DOI:10.1109/TVCG.2019.2920817.
[40] Deutsch S, Ortega A, Medioni G. Manifold denoising based on spectral graph wavelets[C]//2016 IEEE International Conference on Acoustics, Speech and Signal Processing. March 20-25, 2016, Shanghai, China. IEEE, 2016:4673-4677. DOI:10.1109/ICASSP.2016.7472563.
[41] Dinesh C, Cheung G, Bajic I V, et al. Fast 3D point cloud denoising via bipartite graph approximation & total variation[EB/OL]. arXiv:1804.10831v1(2018-04-28)[2022-03-07]. https://arxiv.org/abs/1804.10831.
[42] Zeng J, Cheung G, Ng M, et al. 3D point cloud denoising using graph Laplacian regularization of a low dimensional manifold model[J]. IEEE Transactions on Image Processing, 2020, 29:3474-3489. DOI:10.1109/TIP.2019.2961429.
[43] Hu W, Gao X, Cheung G, et al. Feature graph learning for 3D point cloud denoising[J]. IEEE Transactions on Signal Processing, 2020, 68:2841-2856. DOI:10.1109/TSP.2020.2978617.
[44] Levin D. The approximation power of moving least-squares[J]. Mathematics of Computation, 1998, 67(224):1517-1531. DOI:10.1090/s0025-5718-98-00974-0.
[45] Levin D. Mesh-independent surface interpolation[C]//Geometric Modeling for Scientific Visualization. Berlin, Germany:Springer-Verlag, 2004:37-49. DOI:10.1007/978-3-662-07443-5_3.
[46] Alexa M, Behr J, Cohen-Or D, et al. Computing and rendering point set surfaces[J]. IEEE Transactions on Visualization and Computer Graphics, 2003, 9(1):3-15. DOI:10.1109/TVCG.2003.1175093.
[47] Amenta N, Kil Y J. The domain of a point set surfaces[C]//SPBG '04:Proceedings of the First Eurographics conference on Point-Based Graphics. Goslar, Germany:Eurographics Association, 2004:139-147. DOI:10.2312/SPBG/SPBG04/139-147.
[48] Fleishman S, Cohen-Or D, Silva C T. Robust moving least-squares fitting with sharp features[J]. ACM Transactions on Graphics, 2005, 24(3):544-552. DOI:10.1145/1073204.1073227.
[49] Alliez P, Cohen-Steiner D, Tong Y, et al. Voronoi-based variational reconstruction of unoriented point sets[C]//SGP'07:Proceedings of the fifth Eurographics symposium on Geometry processing, July 4-6, 2007, Barcelona, Spain. Goslar, Germany:Eurographics Association, 2007:39-48.
[50] Walder C, Chapelle O, Schölkopf B. Implicit surface modelling as an eigenvalue problem[C]//ICML'05:Proceedings of the 22nd international conference on Machine learning. New York, NY:Association for Computing Machinery, 2005:936-939. DOI:10.1145/1102351.1102469.
[51] Hoppe H, DeRose T, Duchamp T, et al. Surface reconstruction from unorganized points[C]//Proceedings of the 19th annual conference on Computer graphics and interactive techniques-SIGGRAPH'92. Not Known. New York:ACM Press, 1992:71-78. DOI:10.1145/133994.134011.
[52] Jones T R, Durand F, Zwicker M. Normal improvement for point rendering[J]. IEEE Computer Graphics and Applications, 2004, 24(4):53-56. DOI:10.1109/MCG.2004.14.
[53] Myronenko A, Song X B. Point set registration:coherent point drift[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2010, 32(12):2262-2275. DOI:10.1109/TPAMI.2010.46.
[54] Candès E J, Romberg J, Tao T. Robust uncertainty principles:exact signal reconstruction from highly incomplete frequency information[J]. IEEE Transactions on Information Theory, 2006, 52(2):489-509. DOI:10.1109/TIT.2005.862083.
[55] Donoho D L, Elad M, Temlyakov V N. Stable recovery of sparse overcomplete representations in the presence of noise[J]. IEEE Transactions on Information Theory, 2006, 52(1):6-18. DOI:10.1109/TIT.2005.860430.
[56] Chan T F, Osher S, Shen J. The digital TV filter and nonlinear denoising[J]. IEEE Transactions on Image Processing:a Publication of the IEEE Signal Processing Society, 2001, 10(2):231-241. DOI:10.1109/83.902288.
[57] Xu L, Lu C W, Xu Y, et al. Image smoothing via L₀ gradient minimization[J]. ACM Transactions on Graphics (TOG), 2011, 30(6):1-12. DOI:10.1145/2070781.2024208.
[58] He L, Schaefer S. Mesh denoising via L₀ minimization[J]. ACM Transactions on Graphics, 2013, 32(4):1-8. DOI:10.1145/2461912.2461965.
[59] Candès E J, Recht B. Exact matrix completion via convex optimization[J]. Foundations of Computational Mathematics, 2009, 9(6):717-772. DOI:10.1007/s10208-009-9045-5.
[60] Candès E J, Tao T. The power of convex relaxation:Near-optimal matrix completion[J]. IEEE Transactions on Information Theory, 2010, 56(5):2053-2080. DOI:10.1109/TIT.2010.2044061.
[61] Hotelling H. Analysis of a complex of statistical variables into principal components[J]. Journal of Educational Psychology, 1933, 24(6):417-441. DOI:10.1037/h0071325.
[62] Wold S, Esbensen K, Geladi P. Principal component analysis[J]. Chemometrics and Intelligent Laboratory Systems, 1987, 2(1/2/3):37-52. DOI:10.1016/0169-7439(87)80084-9.
[63] Mateos G, Giannakis G B. Robust PCA as bilinear decomposition with outlier-sparsity regularization[J]. IEEE Transactions on Signal Processing, 2012, 60(10):5176-5190. DOI:10.1109/TSP.2012.2204986.
[64] Li B, Liu R S, Cao J J, et al. Online low-rank representation learning for joint multi-subspace recovery and clustering[J]. IEEE Transactions on Image Processing, 2018, 27(1):335-348. DOI:10.1109/TIP.2017.2760510.
[65] Xie X Y, Wu J L, Liu G C, et al. Matrix recovery with implicitly low-rank data[J]. Neurocomputing, 2019, 334:219-226. DOI:10.1016/j.neucom.2019.01.030.
[66] Yan H, Paynabar K, Shi J J. Image-based process monitoring using low-rank tensor decomposition[J]. IEEE Transactions on Automation Science and Engineering, 2015, 12(1):216-227. DOI:10.1109/TASE.2014.2327029.
[67] Tsuchie S, Higashi M. Surface mesh denoising with normal tensor framework[J]. Graphical Models, 2012, 74(4):130-139. DOI:10.1016/j.gmod.2012.03.010.
[68] Wei M Q, Liang L M, Pang W M, et al. Tensor voting guided mesh denoising[J]. IEEE Transactions on Automation Science and Engineering, 2017, 14(2):931-945. DOI:10.1109/TASE.2016.2553449.
[69] Park M K, Lee S J, Lee K H. Multi-scale tensor voting for feature extraction from unstructured point clouds[J]. Graphical Models, 2012, 74(4):197-208. DOI:10.1016/j.gmod.2012.04.008.
[70] Zhang J, Cao J J, Liu X P, et al. Point cloud normal estimation via low-rank subspace clustering[J]. Computers & Graphics, 2013, 37(6):697-706. DOI:10.1016/j.cag.2013.05.008.
[71] Zhang J, Cao J J, Liu X P, et al. Multi-normal estimation via pair consistency voting[J]. IEEE Transactions on Visualization and Computer Graphics, 2019, 25(4):1693-1706. DOI:10.1109/TVCG.2018.2827998.
[72] Yadav S K, Reitebuch U, Polthier K. Mesh denoising based on normal voting tensor and binary optimization[J]. IEEE Transactions on Visualization and Computer Graphics, 2018, 24(8):2366-2379. DOI:10.1109/TVCG.2017.2740384.
[73] Liu Z, Zhong S S, Xie Z, et al. A novel anisotropic second order regularization for mesh denoising[J]. Computer Aided Geometric Design, 2019, 71:190-201. DOI:10.1016/j.cagd.2019.04.013.
[74] Zheng Y L, Li G Q, Xu X M, et al. Rolling normal filtering for point clouds[J]. Computer Aided Geometric Design, 2018, 62:16-28. DOI:10.1016/j.cagd.2018.03.004.
[75] Hammond D K, Vandergheynst P, Gribonval R. Wavelets on graphs via spectral graph theory[J]. Applied and Computational Harmonic Analysis, 2011, 30(2):129-150. DOI:10.1016/j.acha.2010.04.005.
[76] Osher S, Shi Z Q, Zhu W. Low dimensional manifold model for image processing[J]. SIAM Journal on Imaging Sciences, 2017, 10(4):1669-1690. DOI:10.1137/16m1058686.
[77] Deutsch S, Ortega A, Medioni G. Robust denoising of piece-wise smooth manifolds[C]//2018 IEEE International Conference on Acoustics, Speech and Signal Processing. April 15-20, 2018, Calgary, AB, Canada. IEEE, 2018:2786-2790. DOI:10.1109/ICASSP.2018.8462113.
[78] Verdoja F, Thomas D, Sugimoto A. Fast 3D point cloud segmentation using supervoxels with geometry and color for 3D scene understanding[C]//2017 IEEE International Conference on Multimedia and Expo. July 10-14, 2017, Hong Kong, China. IEEE, 2017:1285-1290. DOI:10.1109/ICME.2017.8019382.
[79] dal Mutto C, Zanuttigh P, Cortelazzo G M. Fusion of geometry and color information for scene segmentation[J]. IEEE Journal of Selected Topics in Signal Processing, 2012, 6(5):505-521. DOI:10.1109/JSTSP.2012.2194474.
[80] Irfan M A, Magli E. Joint geometry and color point cloud denoising based on graph wavelets[J]. IEEE Access, 2021, 9:21149-21166. DOI:10.1109/ACCESS.2021.3054171.
[81] Irfan M A, Magli E. 3D point cloud denoising using a joint geometry and color k-NN graph[C]//2020 28th European Signal Processing Conference (EUSIPCO). January 18-21, 2021, Amsterdam, Netherlands. IEEE, 2021:585-589. DOI:10.23919/Eusipco47968.2020.9287341.
[82] Zhang X, Cheung G, Pang J H, et al. Graph-based depth denoising & dequantization for point cloud enhancement[EB/OL]. arXiv:2111.04946v1(2021-11-09)[2022-03-07]. https://arxiv.org/abs/2111.04946.
[83] Pistilli F, Fracastoro G, Valsesia D, et al. Learning graph-convolutional representations for point cloud denoising[C]//ECCV 2020:16th European Conference, August 23-28, 2020, Glasgow, UK. Berlin, Heidelberg:Springer-Verlag, 2020:103-118. DOI:10.1007/978-3-030-58565-5_7.
[84] Luo S T, Hu W. Differentiable manifold reconstruction for point cloud denoising[C]//MM'20:Proceedings of the 28th ACM International Conference on Multimedia, October 12-16, 2020, Seattle, WA, USA. New York, NY:Association for Computing Machinery, 2020:1330-1338. DOI:10.1145/3394171.3413727.
[85] Luo S T, Hu W. Score-based point cloud denoising[C]//2021 IEEE/CVF International Conference on Computer Vision (ICCV). October 10-17, 2021, Montreal, QC, Canada. IEEE, 2021:4563-4572. DOI:10.1109/ICCV48922.2021.00454.
[86] Yu L Q, Li X Z, Fu C W, et al. Ec-net:an edge-aware point set consolidation network[EB/OL]. arXiv:1807.06010v1(2018-07-16)[2022-03-07]. https://arxiv.org/abs/1807.06010.
[87] Regaya Y, Fadli F, Amira A. Point-Denoise:Unsupervised outlier detection for 3D point clouds enhancement[J]. Multimedia Tools and Applications, 2021, 80(18):28161-28177. DOI:10.1007/s11042-021-10924-x.
[88] Zhang Z W, Cui P, Zhu W W. Deep learning on graphs:a survey[J]. IEEE Transactions on Knowledge and Data Engineering, 2022, 34(1):249-270. DOI:10.1109/TKDE.2020.2981333.
[89] Zhou J, Cui G Q, Hu S D, et al. Graph neural networks:a review of methods and applications[J]. AI Open, 2020, 1:57-81. DOI:10.1016/j.aiopen.2021.01.001.
[90] Simonovsky M, Komodakis N. Dynamic edge-conditioned filters in convolutional neural networks on graphs[C]//2017 IEEE Conference on Computer Vision and Pattern Recognition. July 21-26, 2017, Honolulu, HI, USA. IEEE, 2017:29-38. DOI:10.1109/CVPR.2017.11.
[91] Hyvärinen A. Estimation of non-normalized statistical models by score matching[J]. Journal of Machine Learning Research, 2005, 6:695-709.
[92] Vincent P. A connection between score matching and denoising autoencoders[J]. Neural Computation, 2011, 23(7):1661-1674. DOI:10.1162/NECO_a_00142.
[93] Song Y, Ermon S. Generative modeling by estimating gradients of the data distribution[EB/OL]. arXiv:1907.05600v3(2020-10-10)[2022-03-07]. https://arxiv.org/abs/1907.05600.
[94] Cai R J, Yang G D, Averbuch-Elor H, et al. Learning gradient fields for shape generation[EB/OL]. arXiv:2008.06520v2(2020-08-18)[2022-03-07]. https://arxiv.org/abs/2008.06520.
[95] Yu L Q, Li X Z, Fu C W, et al. PU-net:Point cloud upsampling network[C]//2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition. June 18-23, 2018, Salt Lake City, UT, USA. IEEE, 2018:2790-2799. DOI:10.1109/CVPR.2018.00295.
[96] Lehtinen J, Munkberg J, Hasselgren J, et al. Noise2Noise:learning image restoration without clean data[EB/OL]. arXiv:1803.04189v3(2018-10-29)[2022-03-07]. https://arxiv.org/abs/1803.04189.
[97] Krull A, Buchholz T O, Jug F. Noise2Void:learning denoising from single noisy images[C]//2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). June 15-20, 2019, Long Beach, CA, USA. IEEE, 2019:2124-2132. DOI:10.1109/CVPR.2019.00223.
[98] Batson J, Royer L. Noise2Self:blind denoising by self-supervision[EB/OL]. arXiv:1901.11365v2(2019-06-08)[2022-03-07]. https://arxiv.org/abs/1901.11365.
[99] Hermosilla P, Ritschel T, Vázquez P P, et al. Monte Carlo convolution for learning on non-uniformly sampled point clouds[J]. ACM Transactions on Graphics, 2018, 37(6):1-12. DOI:10.1145/3272127.3275110.
[100] Chang A X, Funkhouser T, Guibas L J, et al. ShapeNet:an information-rich 3D model repository[EB/OL]. arXiv:1512.03012v1(2015-12-09)[2022-03-07]. https://arxiv.org/abs/1512.03012.
[101] Wu Z R, Song S R, Khosla A, et al. 3D ShapeNets:a deep representation for volumetric shapes[C]//2015 IEEE Conference on Computer Vision and Pattern Recognition. June 7-12, 2015, Boston, MA, USA. IEEE, 2015:1912-1920. DOI:10.1109/CVPR.2015.7298801.