research-article

Learning modified indicator functions for surface reconstruction▪

Authors:

Bin WangAuthors Info & Claims

Volume 102, Issue C

Pages 309 - 319

https://doi.org/10.1016/j.cag.2021.10.017

Published: 01 February 2022 Publication History

Abstract

Surface reconstruction is a fundamental problem in 3D graphics. In this paper, we propose a learning-based approach for implicit surface reconstruction from raw point clouds without normals. Our method is inspired by Gauss Lemma in potential energy theory, which gives an explicit integral formula for the indicator functions. We design a novel deep neural network to perform surface integral and learn the modified indicator functions from un-oriented and noisy point clouds. We concatenate features with different scales for accurate point-wise contributions to the integral. Moreover, we propose a novel Surface Element Feature Extractor to learn local shape properties. Experiments show that our method generates smooth surfaces with high normal consistency from point clouds with different noise scales and achieves state-of-the-art reconstruction performance compared with current data-driven and non-data-driven approaches.

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Highlights

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A learning-based approach for surface reconstruction from raw point clouds.

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A novel Surface Element Feature Extractor to learn local shape properties.

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Aggregating the point-wise contributions of Gauss Lemma in the network.

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Generating smooth surfaces with high normal consistency.

References

[1]

Berger M., Tagliasacchi A., Seversky L.M., Alliez P., Guennebaud G., Levine J.A., Sharf A., Silva C.T., A survey of surface reconstruction from point clouds, Comput Graph Forum 36 (1) (2017) 301–329.

Digital Library

[2]

Kazhdan M.M., Reconstruction of solid models from oriented point sets, in: Desbrun M., Pottmann H. (Eds.), Third eurographics symposium on geometry processing, Vienna, Austria, July 4-6, 2005, in: ACM international conference proceeding series, vol. 255, Eurographics Association, 2005, pp. 73–82.

[3]

Kazhdan MM, Bolitho M, Hoppe H. Poisson surface reconstruction. In: Sheffer A, Polthier K, editors. Proceedings of the fourth eurographics symposium on geometry processing, Cagliari, Sardinia, Italy, June 26-28, 2006, Vol. 256. 2006; p. 61–70.

[4]

Calakli F., Taubin G., SSD: smooth signed distance surface reconstruction, Comput Graph Forum 30 (7) (2011) 1993–2002.

[5]

Kazhdan M.M., Hoppe H., Screened poisson surface reconstruction, ACM Trans Graph 32 (3) (2013) 29:1–29:13.

Digital Library

[6]

Kazhdan M., Chuang M., Rusinkiewicz S., Hoppe H., Poisson surface reconstruction with envelope constraints, Comput Graph Forum 39 (5) (2020) 173–182.

[7]

Lu W., Shi Z., Sun J., Wang B., Surface reconstruction based on the modified Gauss formula, ACM Trans Graph 38 (1) (2019) 2:1–2:18.

Digital Library

[8]

Erler P., Guerrero P., Ohrhallinger S., Mitra N.J., Wimmer M., Points2Surf: Learning implicit surfaces from point clouds, in: Vedaldi A., Bischof H., Brox T., Frahm J. (Eds.), Computer vision - ECCV 2020 - 16th European conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part V, Vol. 12350, 2020, pp. 108–124.

[9]

Qi C.R., Su H., Mo K., Guibas L.J., PointNet: Deep learning on point sets for 3D classification and segmentation, in: 2017 IEEE conference on computer vision and pattern recognition, CVPR 2017, Honolulu, HI, USA, July 21-26, 2017, 2017, pp. 77–85.

[10]

Qi C.R., Yi L., Su H., Guibas L.J., PointNet++: Deep hierarchical feature learning on point sets in a metric space, in: Guyon I., von Luxburg U., Bengio S., Wallach H.M., Fergus R., Vishwanathan S.V.N., Garnett R. (Eds.), Advances in neural information processing systems 30: Annual conference on neural information processing systems 2017, December 4-9, 2017, Long Beach, CA, USA, 2017, pp. 5099–5108.

[11]

Li Y., Bu R., Sun M., Wu W., Di X., Chen B., PointCNN: Convolution on X-Transformed points, in: Bengio S., Wallach H.M., Larochelle H., Grauman K., Cesa-Bianchi N., Garnett R. (Eds.), Advances in neural information processing systems 31: Annual conference on neural information processing systems 2018, NeurIPS 2018, December 3-8, 2018, Montréal, Canada, 2018, pp. 828–838.

[12]

Wu W., Qi Z., Li F., PointConv: Deep convolutional networks on 3D point clouds, in: IEEE conference on computer vision and pattern recognition, CVPR 2019, Long Beach, CA, USA, June 16-20, 2019, 2019, pp. 9621–9630.

[13]

Guerrero P., Kleiman Y., Ovsjanikov M., Mitra N.J., PCPNet: Learning local shape properties from raw point clouds, Comput Graph Forum 37 (2) (2018) 75–85.

[14]

Groueix T, Fisher M, Kim VG, Russell B, Aubry M. AtlasNet: A Papier-Mâché approach to learning 3D surface generation. In: Proceedings IEEE conf. on computer vision and pattern recognition (CVPR). 2018.

[15]

Mescheder L.M., Oechsle M., Niemeyer M., Nowozin S., Geiger A., Occupancy networks: Learning 3D reconstruction in function space, in: IEEE conference on computer vision and pattern recognition, CVPR 2019, Long Beach, CA, USA, June 16-20, 2019, 2019, pp. 4460–4470.

[16]

Peng S., Niemeyer M., Mescheder L.M., Pollefeys M., Geiger A., Convolutional occupancy networks, in: Vedaldi A., Bischof H., Brox T., Frahm J. (Eds.), Computer vision - ECCV 2020 - 16th European conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part III, in: Lecture notes in computer science, vol. 12348, 2020, pp. 523–540.

[17]

Park J.J., Florence P., Straub J., Newcombe R.A., Lovegrove S., DeepSDF: Learning continuous signed distance functions for shape representation, in: IEEE conference on computer vision and pattern recognition, CVPR 2019, Long Beach, CA, USA, June 16-20, 2019, 2019, pp. 165–174.

[18]

Dai A., Nießner M., Scan2Mesh: From unstructured range scans to 3D meshes, in: IEEE conference on computer vision and pattern recognition, CVPR 2019, Long Beach, CA, USA, June 16-20, 2019, 2019, pp. 5574–5583.

[19]

Folland G.B., Introduction to partial differential equations, in: Texts in applied mathematics, 1995.

[20]

Wendland W.L., On the double layer potential, Birkhäuser Basel, 2009.

[21]

Hoppe H, DeRose T, Duchamp T, McDonald JA, Stuetzle W. Surface reconstruction from unorganized points. In: Thomas JJ, editor. Proceedings of the 19th annual conference on computer graphics and interactive techniques, SIGGRAPH 1992, Chicago, IL, USA, July 27-31. 1992; p. 71–8.

[22]

Fuhrmann S., Goesele M., Floating scale surface reconstruction, ACM Trans Graph 33 (4) (2014) 46:1–46:11.

[23]

Huang Z., Carr N., Ju T., Variational implicit point set surfaces, ACM Trans Graph 38 (4) (2019) 124:1–124:13.

[24]

Chabra R., Lenssen J.E., Ilg E., Schmidt T., Straub J., Lovegrove S., Newcombe R.A., Deep local shapes: Learning local SDF priors for detailed 3D reconstruction, in: Computer vision - ECCV 2020 - 16th European conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part XXIX, Vol. 12374, 2020, pp. 608–625.

[25]

Atzmon M., Lipman Y., SAL: sign agnostic learning of shapes from raw data, in: 2020 IEEE/CVF conference on computer vision and pattern recognition, CVPR 2020, Seattle, WA, USA, June 13-19, 2020, IEEE, 2020, pp. 2562–2571.

[26]

Zhao W., Lei J., Wen Y., Zhang J., Jia K., Sign-agnostic implicit learning of surface self-similarities for shape modeling and reconstruction from raw point clouds, 2020, CoRR abs/2012.07498. URL: https://arxiv.org/abs/2012.07498. arXiv:2012.07498.

[27]

Jaderberg M., Simonyan K., Zisserman A., Kavukcuoglu K., Spatial transformer networks, in: Cortes C., Lawrence N.D., Lee D.D., Sugiyama M., Garnett R. (Eds.), Advances in neural information processing systems 28: Annual conference on neural information processing systems 2015, December 7-12, 2015, Montreal, Quebec, Canada, 2015, pp. 2017–2025.

[28]

Huang H., Li D., Zhang H., Ascher U.M., Cohen-Or D., Consolidation of unorganized point clouds for surface reconstruction, ACM Trans Graph 28 (5) (2009) 176.

Digital Library

[29]

Lorensen WE, Cline HE. Marching cubes: A high resolution 3D surface construction algorithm. In: Stone MC, editor. Proceedings of the 14th annual conference on computer graphics and interactive techniques, SIGGRAPH 1987, Anaheim, California, USA, July 27-31, 1987. 1987; p.163–9.

[30]

Lewiner T., Lopes H., Vieira A.W., Tavares G., Efficient implementation of marching cubes’ cases with topological guarantees, J Graph GPU Game Tools 8 (2) (2003) 1–15.

[31]

Koch S., Matveev A., Jiang Z., Williams F., Artemov A., Burnaev E., Alexa M., Zorin D., Panozzo D., ABC: A big CAD model dataset for geometric deep learning, in: IEEE conference on computer vision and pattern recognition, CVPR 2019, Long Beach, CA, USA, June 16-20, 2019, 2019, pp. 9601–9611.

[32]

Albertina V., Museum V.K., Museum V.T., Paris Musée Guimet and Paris Musée des Monuments français C., des sculptures de la Ville de P., et al., Three d scans, 2021, Accessed: 2021, URL: https://threedscans.com.

[33]

Dawson Haggerty V., et al., Trimesh 3.9, 2021, URL: https://trimsh.org/.

[34]

Chang AX, Funkhouser TA, Guibas LJ, Hanrahan P, Huang Q, Li Z, Savarese S, Savva M, Song S, Su H, Xiao J, Yi L, Yu F. ShapeNet: An Information-Rich 3D Model Repository CoRR abs/1512.03012. URL: https://arxiv.org/abs/1512.03012. arXiv:1512.03012.

[35]

Peethambaran J., Muthuganapathy R., Reconstruction of water-tight surfaces through Delaunay sculpting, Comput Aided Des 58 (2015) 62–72.

[36]

Dey T.K., Li K., Ramos E.A., Wenger R., Isotopic reconstruction of surfaces with boundaries, Comput Graph Forum 28 (5) (2009) 1371–1382.

[37]

Thayyil S.B., Yadav S.K., Polthier K., Muthuganapathy R., Local delaunay-based high fidelity surface reconstruction from 3D point sets, Comput Aided Geom Design 86 (2021).

[38]

Cignoni P., Callieri M., Corsini M., Dellepiane M., Ganovelli F., Ranzuglia G., MeshLab: an open-source mesh processing tool, in: Scarano V., Chiara R.D., Erra U. (Eds.), Eurographics Italian chapter conference 2008, Salerno, Italy, 2008, Eurographics, 2008, pp. 129–136.

Cited By

Xiao DShi ZLi SDeng BWang B(2023)Point normal orientation and surface reconstruction by incorporating isovalue constraints to Poisson equationComputer Aided Geometric Design10.1016/j.cagd.2023.102195103:COnline publication date: 1-Jun-2023
https://dl.acm.org/doi/10.1016/j.cagd.2023.102195
Biasotti SLiu YZhu B(2022)Foreword to the Special Issue on Shape Modeling International 2021 (SMI2021)Computers and Graphics10.1016/j.cag.2022.03.001103:C(A7-A9)Online publication date: 1-Apr-2022
https://dl.acm.org/doi/10.1016/j.cag.2022.03.001

Index Terms

Learning modified indicator functions for surface reconstruction▪
1. Computing methodologies
2. Theory of computation
  1. Randomness, geometry and discrete structures

Index terms have been assigned to the content through auto-classification.

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Published In

cover image Computers and Graphics

Computers and Graphics Volume 102, Issue C

Feb 2022

670 pages

ISSN:0097-8493

Issue’s Table of Contents

Elsevier Ltd.

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Pergamon Press, Inc.

United States

Publication History

Published: 01 February 2022

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Cited By

Xiao DShi ZLi SDeng BWang B(2023)Point normal orientation and surface reconstruction by incorporating isovalue constraints to Poisson equationComputer Aided Geometric Design10.1016/j.cagd.2023.102195103:COnline publication date: 1-Jun-2023
https://dl.acm.org/doi/10.1016/j.cagd.2023.102195
Biasotti SLiu YZhu B(2022)Foreword to the Special Issue on Shape Modeling International 2021 (SMI2021)Computers and Graphics10.1016/j.cag.2022.03.001103:C(A7-A9)Online publication date: 1-Apr-2022
https://dl.acm.org/doi/10.1016/j.cag.2022.03.001

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