Neural Geometry Fields For Meshes
Article No.: 29, Pages 1 - 11
Abstract
Recent work on using neural fields to represent surfaces has resulted in significant improvements in representational capability and computational efficiency. However, to our knowledge, most existing work has focused on implicit representations such as signed distance fields or volumes, and little work has explored their application to discrete surface geometry, i.e., 3D meshes, limiting the applicability of neural surface representations.
We present Neural Geometry Fields, a neural representation for discrete surface geometry represented by triangle meshes. Our idea is to represent the target surface using a coarse set of quadrangular patches, and add surface details using coordinate neural networks by displacing the patches. We then extract a traditional triangular mesh from a neural geometry field instance by sampling the displacement. We show that our representation excels in mesh compression, where it significantly reduces the memory footprint of meshes without compromising on surface details.
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References
[1]
Jonathan T. Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P. Srinivasan. 2021. Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields. In International Conference on Computer Vision. 5855–5864.
[2]
Marcel Campen. 2017. Partitioning Surfaces into Quad Patches. In Eurographics Tutorials.
[3]
Marcel Campen, David Bommes, and Leif Kobbelt. 2012. Dual loops meshing: quality quad layouts on manifolds. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 31, 4, 1–11.
[4]
Nathan A. Carr, Jared Hoberock, Keenan Crane, and John C. Hart. 2006. Rectangular Multi-Chart Geometry Images. In Symposium of Geometry Processing. 181–190.
[5]
E. Catmull and J. Clark. 1978. Recursively generated B-spline surfaces on arbitrary topological meshes. Computer-Aided Design 10, 6 (1978), 350–355.
[6]
Yun-Chun Chen, Vladimir Kim, Noam Aigerman, and Alec Jacobson. 2023. Neural Progressive Meshes. In SIGGRAPH Conference Proceedings. 1–9.
[7]
Paolo Cignoni, Fabio Ganovelli, Enrico Gobbetti, Fabio Marton, Federico Ponchio, and Roberto Scopigno. 2004. Adaptive Tetrapuzzles: Efficient Out-of-Core Construction and Visualization of Gigantic Multiresolution Polygonal Models. ACM Transactions on Graphics (TOG) 23, 3 (2004), 796–803.
[8]
Jonathan Cohen, Marc Olano, and Dinesh Manocha. 1998. Appearance-Preserving Simplification. In SIGGRAPH. 115–122.
[9]
Michael Deering. 1995. Geometry compression. In SIGGRAPH. 13–20.
[10]
Alexandros Doumanoglou, Petros Drakoulis, Nikolaos Zioulis, Dimitrios Zarpalas, and Petros Daras. 2019. Benchmarking Open-Source Static 3D Mesh Codecs for Immersive Media Interactive Live Streaming. IEEE Journal on Emerging and Selected Topics in Circuits and Systems 9, 1 (2019), 190–203.
[11]
Nira Dyn, David Levine, and John A. Gregory. 1990. A Butterfly Subdivision Scheme for Surface Interpolation with Tension Control. ACM Transactions on Graphics (TOG) 9, 2 (1990), 160–169.
[12]
Frank Galligan, Michael Hemmer, Ondrej Stava, Fan Zhang, and Jamieson Brettle. 2018. Google/draco: a library for compressing and decompressing 3D geometric meshes and point clouds.https://github.com/google/draco.
[13]
William Gao, April Wang, Gal Metzer, Raymond A Yeh, and Rana Hanocka. 2022. TetGAN: A Convolutional Neural Network for Tetrahedral Mesh Generation. In Proceedings British Machine Vision Conference.
[14]
Michael Garland and Paul S. Heckbert. 1997. Surface Simplification Using Quadric Error Metrics. In SIGGRAPH. 209–216.
[15]
Xianfeng Gu, Steven J. Gortler, and Hugues Hoppe. 2002. Geometry Images. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 21, 3 (2002), 355–361.
[16]
Stefan Gumhold and Wolfgang Straßer. 1998. Real Time Compression of Triangle Mesh Connectivity. In SIGGRAPH. 133–140.
[17]
Rana Hanocka, Amir Hertz, Noa Fish, Raja Giryes, Shachar Fleishman, and Daniel Cohen-Or. 2019. MeshCNN: a network with an edge. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 38, 4 (2019).
[18]
Jon Hasselgren, Jacob Munkberg, Jaakko Lehtinen, Miika Aittala, and Samuli Laine. 2021. Appearance-Driven Automatic 3D Model Simplification. In Eurographics Symposium on Rendering. 85–97.
[19]
Hugues Hoppe. 1996. Progressive Meshes. In SIGGRAPH. 99–108.
[20]
Hugues Hoppe, Tony DeRose, Tom Duchamp, Mark Halstead, Hubert Jin, John McDonald, Jean Schweitzer, and Werner Stuetzle. 1994. Piecewise smooth surface reconstruction. In SIGGRAPH. 295–302.
[21]
Shi-Min Hu, Zheng-Ning Liu, Meng-Hao Guo, Jun-Xiong Cai, Jiahui Huang, Tai-Jiang Mu, and Ralph R Martin. 2022. Subdivision-based mesh convolution networks. ACM Trans. Graph. 41, 3 (2022), 25:1–25:16.
[22]
Benjamin T Jones, Michael Hu, Milin Kodnongbua, Vladimir G Kim, and Adriana Schulz. 2023. Self-supervised representation learning for CAD. In Computer Vision and Pattern Recognition. 21327–21336.
[23]
Diederick P Kingma and Jimmy Ba. 2015. Adam: A Method for Stochastic Optimization. In International Conference on Learning Representations.
[24]
Samuli Laine, Janne Hellsten, Tero Karras, Yeongho Seol, Jaakko Lehtinen, and Timo Aila. 2020. Modular primitives for high-performance differentiable rendering. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 39, 6, Article 194 (2020), 11-14 pages.
[25]
Aaron Lee, Henry Moreton, and Hugues Hoppe. 2000. Displaced Subdivision Surfaces. In SIGGRAPH. 85–94.
[26]
Eung-Seok Lee and Hyeong-Seok Ko. 2000. Vertex Data Compression for Triangular Meshes. In Pacific Graphics. 225–234.
[27]
Thibault Lescoat, Hsueh-Ti Derek Liu, Jean-Marc Thiery, Alec Jacobson, Tamy Boubekeur, and Maks Ovsjanikov. 2020. Spectral mesh simplification. Comput. Graph. Forum (Proc. Eurographics) 39, 2 (2020), 315–324.
[28]
Zhaoshuo Li, Thomas Müller, Alex Evans, Russell H Taylor, Mathias Unberath, Ming-Yu Liu, and Chen-Hsuan Lin. 2023. Neuralangelo: High-Fidelity Neural Surface Reconstruction. In Computer Vision and Pattern Recognition. 8456–8465.
[29]
Hsueh-Ti Derek Liu, Vladimir G. Kim, Siddhartha Chaudhuri, Noam Aigerman, and Alec Jacobson. 2020b. Neural Subdivision. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 39, 4 (2020), 124:1–124:16.
[30]
Lingjie Liu, Jiatao Gu, Kyaw Zaw Lin, Tat-Seng Chua, and Christian Theobalt. 2020a. Neural Sparse Voxel Fields. In Advances in Neural Information Processing Systems.
[31]
Stephen Lombardi, Tomas Simon, Gabriel Schwartz, Michael Zollhoefer, Yaser Sheikh, and Jason Saragih. 2021. Mixture of volumetric primitives for efficient neural rendering. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 40, 4 (2021), 1–13.
[32]
Charles Loop. 1987. Smooth Subdivision Surfaces Based on Triangles. Master’s thesis. Department of Mathematics, The University of Utah.
[33]
Andrea Maggiordomo, Henry Moreton, and Marco Tarini. 2023. Micro-mesh construction. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 42, 4 (2023), 1–18.
[34]
Adrien Maglo, Guillaume Lavoué, Florent Dupont, and Céline Hudelot. 2015. 3D Mesh Compression: Survey, Comparisons, and Emerging Trends. Comput. Surveys 47, 3 (2015), 44:1–44:41.
[35]
Julien N. P. Martel, David B. Lindell, Connor Z. Lin, Eric R. Chan, Marco Monteiro, and Gordon Wetzstein. 2021. ACORN: Adaptive Coordinate Networks for Neural Scene Representation. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 40, 4 (2021), 58:1–58:13.
[36]
Lars Mescheder, Michael Oechsle, Michael Niemeyer, Sebastian Nowozin, and Andreas Geiger. 2019. Occupancy Networks: Learning 3D Reconstruction in Function Space. In Computer Vision and Pattern Recognition. 4460–4470.
[37]
Ben Mildenhall, Pratul P. Srinivasan, Matthew Tancik, Jonathan T. Barron, Ravi Ramamoorthi, and Ren Ng. 2020. NeRF: Representing Scenes as Neural Radiance Fields for View Synthesis. In European Conference on Computer Vision. 405–421.
[38]
Luca Morreale, Noam Aigerman, Paul Guerrero, Vladimir G. Kim, and Niloy J. Mitra. 2022. Neural Convolutional Surfaces. In Computer Vision and Pattern Recognition.
[39]
Thomas Müller, Alex Evans, Christoph Schied, and Alexander Keller. 2022. Instant Neural Graphics Primitives with a Multiresolution Hash Encoding. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 41, 4 (2022), 102:1–102:15.
[40]
Shinji Ogaki. 2023. Nonlinear Ray Tracing for Displacement and Shell Mapping. In SIGGRAPH Asia Conference Proceedings. Article 93, 10 pages.
[41]
Jeong Joon Park, Peter Florence, Julian Straub, Richard Newcombe, and Steven Lovegrove. 2019. DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation. In Computer Vision and Pattern Recognition. 165–174.
[42]
Nico Pietroni, Stefano Nuvoli, Thomas Alderighi, Paolo Cignoni, Marco Tarini, 2021. Reliable feature-line driven quad-remeshing. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 40, 4 (2021), 1–17.
[43]
Rolandos Alexandros Potamias, Stylianos Ploumpis, and Stefanos Zafeiriou. 2022. Neural Mesh Simplification. In Computer Vision and Pattern Recognition. 18583–18592.
[44]
Ravi Ramamoorthi and Pat Hanrahan. 2001. An efficient representation for irradiance environment maps. SIGGRAPH Conference Proceedings, 497–500.
[45]
P. V. Sander, Z. J. Wood, S. J. Gortler, J. Snyder, and H. Hoppe. 2003. Multi-Chart Geometry Images. In Symposium of Geometry Processing. 146–155.
[46]
Tianchang Shen, Jun Gao, Kangxue Yin, Ming-Yu Liu, and Sanja Fidler. 2021. Deep Marching Tetrahedra: A Hybrid Representation for High-Resolution 3D Shape Synthesis. In Advances in Neural Information Processing Systems, Vol. 34. 6087–6101.
[47]
Vincent Sitzmann, Julien Martel, Alexander Bergman, David Lindell, and Gordon Wetzstein. 2020. Implicit Neural Representations with Periodic Activation Functions. In Advances in Neural Information Processing Systems, Vol. 33. 7462–7473.
[48]
Jos Stam. 1998. Exact Evaluation of Catmull-Clark Subdivision Surfaces at Arbitrary Parameter Values. In SIGGRAPH. 395–404.
[49]
Towaki Takikawa, Joey Litalien, Kangxue Yin, Karsten Kreis, Charles Loop, Derek Nowrouzezahrai, Alec Jacobson, Morgan McGuire, and Sanja Fidler. 2021. Neural geometric level of detail: Real-time rendering with implicit 3D shapes. In Computer Vision and Pattern Recognition. 11358–11367.
[50]
Matthew Tancik, Pratul Srinivasan, Ben Mildenhall, Sara Fridovich-Keil, Nithin Raghavan, Utkarsh Singhal, Ravi Ramamoorthi, Jonathan Barron, and Ren Ng. 2020. Fourier features let networks learn high frequency functions in low dimensional domains. In Advances in Neural Information Processing Systems, Vol. 33. 7537–7547.
[51]
Marco Tarini, Nico Pietroni, Paolo Cignoni, Daniele Panozzo, and Enrico Puppo. 2010. Practical quad mesh simplification. Comput. Graph. Forum (Proc. Eurographics) 29, 2 (2010), 407–418.
[52]
Gabriel Taubin and Jarek Rossignac. 1998. Geometric compression through topological surgery. ACM Trans. Graph. 17, 2 (1998), 84–115.
[53]
Theo Thonat, Francois Beaune, Xin Sun, Nathan Carr, and Tamy Boubekeur. 2021. Tessellation-free displacement mapping for ray tracing. 40, 6 (2021), 282:1–282:16.
[54]
Costa Touma and Craig Gotsman. 1998. Triangle mesh compression. In Graphics Interface. 26–34.
[55]
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Łukasz Kaiser, and Illia Polosukhin. 2017. Attention is All You Need. In Advances in Neural Information Processing Systems. 6000–6010.
[56]
Luiz Velho and Denis Zorin. 2001. 4–8 Subdivision. Computer Aided Geometric Design 18, 5 (2001), 397–427.
[57]
Peng Wang, Lingjie Liu, Yuan Liu, Christian Theobalt, Taku Komura, and Wenping Wang. 2021. NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction. In Advances in Neural Information Processing Systems, Vol. 34. 27171–27183.
[58]
Yiheng Xie, Towaki Takikawa, Shunsuke Saito, Or Litany, Shiqin Yan, Numair Khan, Federico Tombari, James Tompkin, Vincent Sitzmann, and Srinath Sridhar. 2022. Neural fields in visual computing and beyond. Comput. Graph. Forum (Proc. Eurographics STAR) 41, 2 (2022), 641–676.
[59]
Qingnan Zhou and Alec Jacobson. 2016. Thingi10K: A Dataset of 10,000 3D-Printing Models. arXiv preprint arXiv:1605.04797 (2016).
Index Terms
- Neural Geometry Fields For Meshes
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Published: 13 July 2024
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