三维建筑模型的低模网格生成

doi:10.11996/JG.j.2095-302X.2023040764

图学学报 ›› 2023, Vol. 44 ›› Issue (4): 764-774.DOI: 10.11996/JG.j.2095-302X.2023040764

• 计算机图形学与虚拟现实 • 上一篇下一篇

三维建筑模型的低模网格生成

岳明宇¹(), 高希峰², 毕重科¹()

1.天津大学智能与计算学部，天津 300350
2.腾讯科技有限公司光子游戏工作室群，华盛顿贝尔维尤 98004

收稿日期:2022-11-24 接受日期:2022-12-26 出版日期:2023-08-31 发布日期:2023-08-16
通讯作者: 毕重科(1982-)，男，副教授，博士。主要研究方向为可视化与高性能计算。E-mail：bichongke@tju.edu.cn
作者简介:
岳明宇(1999-)，男，硕士研究生。主要研究方向为三维模型处理。E-mail：yuemingyu@tju.edu.cn
基金资助:
国家重点研发计划项目(2021YFE0108400);国家自然科学基金项目(62172294)

3D low-poly mesh generation for building models

YUE Ming-yu¹(), GAO Xi-feng², BI Chong-ke¹()

1. College of Intelligence and Computing, Tianjin University, Tianjin 300350, China
2. LightSpeed Studios, Tencent Technology Company Limited, Bellevue WA 98004, USA

Received:2022-11-24 Accepted:2022-12-26 Online:2023-08-31 Published:2023-08-16
Contact: BI Chong-ke (1982-), associate professor, Ph.D. His main research interests cover visualization and high performance computing. E-mail：bichongke@tju.edu.cn
About author:
YUE Ming-yu (1999-), master student. His main research interest covers 3D model processing. E-mail：yuemingyu@tju.edu.cn
Supported by:
National Key Research and Development Program of China(2021YFE0108400);National Natural Science Foundation of China(62172294)

摘要/Abstract

摘要：

三维虚拟场景中，低模网格(三角面数较少的网格)在多细节层次等方面的运用对实时运算效率提升有着重要的作用。然而，给定高精度的建筑模型(高模网格)，现有方法所生成的低模网格很难在达到极低简化率的同时依旧与原高模网格保持良好的视觉相似性，仍需人工调整以修正缺陷。为此提出了一个新的方法，用户仅需提供少量鲁棒的参数，就能生成具有良好视觉相似性和满足水密性、流形等良好几何特性的低模建筑网格。首先，为了从高模网格中捕获重要的几何特征，需通过逆渲染的方法对另一个新网格变形，使其与高模网格有相似的外观且仅保留大尺度的外观特征。为保持网格拓扑在变形过程中的一致性，可将高模网格体素化后的外包(The outer hull)作为被变形网格的初始化。之后，为处理变形过程中带来的相交三角形，还设计了参数自适应模型拓扑的alpha wrapping算法。通过保证变形后网格体素化后的外包和结果网格的亏格数一致，该算法能够生成变形后网格的近似网格，且保证近似网格无相交三角形、满足水密性和二流形。最后，部署了一个改进的边收缩算法将alpha wrapping算法生成的网格简化到用户的目标面数，该算法对平面上点对合并过程进行了数值优化。在一个建筑模型的数据集上测试了本文方法并将其与最流行和最先进的方法进行了比较，证明了其稳健性和有效性。

关键词: 网格简化, 三角形网格, 低模网格生成, 细节层次, 建筑模型

Abstract:

Within the domain of 3D virtual scenes, the usage of low-poly meshes (meshes comprised of few triangles) used in levels of detail play a pivotal role in improving the efficiency of real-time rendering. However, given detailed building models (high-poly meshes), it is difficult for the low-poly meshes generated by the existing methods to maintain good visual similarity with the high-poly meshes while achieving extremely low simplification rates, requiring the manual correction of defects. We proposed a novel method in which the user only needed to provide a few robust parameters to generate low-poly building meshes with good visual similarity and satisfying benign geometric properties such as watertightness and two-manifold. Firstly, new meshes were morphed by inverse rendering, enabling the capture of important geometric features from the high-poly meshes, so that they could have similar appearances to the high-poly meshes and retain only the large-scale appearance features. Additionally, to maintain the consistency of the mesh topology during the morphing process, we leveraged the outer hull of the voxelized high-poly meshes as the initialization of the new meshes. Secondly, to address the intersecting triangles that arose during the morphing process, we designed the alpha wrapping algorithm with topology-adaptive parameters. The algorithm ensured that the genus of the outer hull of the voxelized morphed meshes and the genus of the results remained the same, generating approximate meshes from the morphed meshes with no intersecting triangles, satisfying watertightness and two-manifold. Finally, an improved edge collapse algorithm was applied and generated meshes that were simplified to users’ target facet count. The algorithm optimized the contraction of vertex pairs on planes. We evaluated our method’s robustness and effectiveness against a dataset of building models and compared it against popular and state-of-the-art methods.

Key words: mesh simplification, triangle mesh, low-poly mesh generation, level of detail, building model

中图分类号:

TP391

岳明宇, 高希峰, 毕重科. 三维建筑模型的低模网格生成[J]. 图学学报, 2023, 44(4): 764-774.

YUE Ming-yu, GAO Xi-feng, BI Chong-ke. 3D low-poly mesh generation for building models[J]. Journal of Graphics, 2023, 44(4): 764-774.

图/表 7

图1 高模网格和不同方法生成的简化结果((a)高精度模型10 081个面；(b) QEM 402个面；(c) Simplygon 402个面；(d)本文方法290个面)

Fig. 1 A high-poly mesh and simplified results generated by different methods ((a) The high-poly mesh with 10 081 triangles; (b) QEM with 402 triangles; (c) Simplygon with 402 triangles; (d) Our method with 290 triangles)

图2 方法概览((a)原始模型，逆渲染框架的参考网格；(b)逆渲染框架的基网格，模型的体素化网格外包；(c)变形后的网格；(d)变形后的网格的体素化网格外包；(e) Alpha wrapping算法处理后的网格；(f)简化后的网格)

Fig. 2 An overview of our method ((a) The original model, also the reference mesh of the inverse rendering framework; (b) The base mesh of the inverse rendering framework, also the outer hull of the voxelized original model; (c) The mesh after being morphed; (d) The outer hull of the voxelized morphed model; (e) The mesh generated by alpha wrapping algorithm; (f) The simplified mesh)

图3 基网格的不同初始化及其得到的变形结果之间的比较((a)球体网格；(b)球体网格变形结果；(c)模型体素化网格外包；(d)外包网格变形结果)

Fig. 3 Comparison between different initial base meshes and the morphed results obtained from them ((a) The sphere mesh; (b) The mesh morphed from the sphere; (c) The outer hull of the voxelized mesh; (d) The mesh morphed from the outer hull)

图4 ??取不同值的结果((a)变形后网格的体素化网格的外包，亏格为8；(b) α=d/190，δ=d/10000，亏格为8；(c) α=d/200，δ=d/10000，亏格为10；(d) α=d/210，δ=d/10000，亏格为10。d是网格的包围盒的对角线长度)

Fig. 4 The result of the different values of ?? ((a) The outer hull of the voxelized morphed mesh; (b) The result with α=d/190 & δ=d/10000, and the genus is 8; (c) The result with α=d/200 & δ=d/10000, and the genus is 10; (d) The result with α=d/210 & δ=d/10000, and the genus is 10. d is the diagonal length of the bounding box of the mesh)

图5 结果比较，每个网格下的数据分别表示三角面数、简化率和相似度误差((a)输入；(b) QEM；(c) PolyFit；(d) Simplygon reduction；(e) Simplygon remeshing；(f)本文方法)

Fig. 5 The comparison between results, and the data under each mesh indicate the number of triangular facets, the simplification rate and the similarity error, respectively ((a) Input; (b) QEM; (c) PolyFit; (d) Simplygon reduction; (e) Simplygon remeshing; (f) Ours)

表1 整个数据集上结果的统计

Table 1 Statistics of results on the whole data set

方法	W(%)	M(%)	$\text{N}_{\text{F}}^{\text{avg}}$	r^avg	e^avg
输入	0	11.54	17557	-	-
QEM	3.85	26.92	85	0.015 5	2805
PolyFit	0	76.92	328	0.051 1	2024
Simplygon reduction	0	0	701	0.039 8	764
Simplygon remeshing	100	100	85	0.015 7	654
Ours	100	100	85	0.015 7	485

图6 本文结果与Simplygon remeshing在不同分辨率下的结果对比

Fig. 6 Our results are compared with those of Simplygon remeshing at different resolutions

参考文献 39

[1]	GARLAND M, HECKBERT P S. Surface simplification using quadric error metrics[C]// The 24th Annual Conference on Computer Graphics and Interactive Techniques. New York: ACM, 1997: 209-216.
[2]	Simplygon.com. Simplygon: the standard in 3D games content optimization[EB/OL]. [2022-05-20]. https://www.statscrop.com/www/simplygon.com.
[3]	PORTANERI C, ROUXEL-LABBÉ M, HEMMER M, et al. Alpha wrapping with an offset[J]. ACM Transactions on Graphics, 2022, 41(4): 127.
[4]	SCHROEDER W J. A topology modifying progressive decimation algorithm[C]// Proceedings of Visualization ’97. New York:IEEE Press, 2002: 205-212.
[5]	LOW K L, TAN T S. Model simplification using vertex-clustering[C]// 1997 Symposium on Interactive 3D Graphics. New York: ACM, 1997: 75-82.
[6]	LUEBKE D, ERIKSON C. View-dependent simplification of arbitrary polygonal environments[C]// The 24th Annual Conference on Computer Graphics and Interactive Techniques. New York: ACM, 1997: 199-208.
[7]	LINDSTROM P, TURK G. Image-driven simplification[J]. ACM Transactions on Graphics, 2000, 19(3): 204-241. DOI URL
[8]	COHEN J, VARSHNEY A, MANOCHA D, et al. Simplification envelopes[C]// The 23rd Annual Conference on Computer Graphics and Interactive Techniques. New York: ACM, 1996: 119-128.
[9]	COHEN-STEINER D, ALLIEZ P, DESBRUN M. Variational shape approximation[J]. ACM Transactions on Graphics, 2004, 23(3): 905-914. DOI URL
[10]	MEHRA R, ZHOU Q N, LONG J, et al. Abstraction of man-made shapes[J]. ACM Transactions on Graphics, 2009, 28(5): 1-10.
[11]	NAN L L, WONKA P. PolyFit: polygonal surface reconstruction from point clouds[C]// 2017 IEEE International Conference on Computer Vision. New York: IEEE Press, 2017: 2372-2380.
[12]	BAUCHET J P, LAFARGE F. Kinetic shape reconstruction[J]. ACM Transactions on Graphics, 2020, 39(5): 156.
[13]	FANG H, LAFARGE F. Connect-and-slice: an hybrid approach for reconstructing 3D objects[C]// 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition. New York: IEEE Press, 2020: 13487-13495.
[14]	MILDENHALL B, SRINIVASAN P P, TANCIK M, et al. NeRF: representing scenes as neural radiance fields for view synthesis[M]//Computer Vision - ECCV 2020. Cham: Springer International Publishing, 2020: 405-421.
[15]	WANG P, LIU L J, LIU Y, et al. NeuS: learning neural implicit surfaces by volume rendering for multi-view reconstruction[EB/OL]. [2022-05-20]. https://arxiv.org/abs/2106.10689.
[16]	CHEN Z Q, ZHANG H. Learning implicit fields for generative shape modeling[C]// The IEEE/CVF Conference on Computer Vision and Pattern Recognition. New York: IEEE Press, 2019: 5939-5948.
[17]	MESCHEDER L, OECHSLE M, NIEMEYER M, et al. Occupancy networks: learning 3D reconstruction in function space[C]// 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition. New York: IEEE Press, 2019: 4455-4465.
[18]	PARK J J, FLORENCE P, STRAUB J, et al. DeepSDF: learning continuous signed distance functions for shape representation[C]// 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition. New York: IEEE Press, 2019: 165-174.
[19]	LAINE S, HELLSTEN J, KARRAS T, et al. Modular primitives for high-performance differentiable rendering[J]. ACM Transactions on Graphics, 2020, 39(6): 1-14.
[20]	HASSELGREN J, MUNKBERG J, LEHTINEN J, et al. Appearance-driven automatic 3D model simplification[EB/OL]. [2022-05-10]. https://arxiv.org/abs/2104.03989.
[21]	LUAN F J, ZHAO S, BALA K, et al. Unified shape and SVBRDF recovery using differentiable Monte Carlo rendering[J]. Computer Graphics Forum, 2021, 40(4): 101-113. DOI URL
[22]	NICOLET B, JACOBSON A, JAKOB W. Large steps in inverse rendering of geometry[J]. ACM Transactions on Graphics, 2021, 40(6): 248.
[23]	ATTENE M, CAMPEN M, KOBBELT L. Polygon mesh repairing: an application perspective[J]. ACM Computing Surveys, 2013, 45(2): 15.
[24]	JU T. Robust repair of polygonal models[J]. ACM Transactions on Graphics, 2004, 23(3): 888-895. DOI URL
[25]	NOORUDDIN F S, TURK G. Simplification and repair of polygonal models using volumetric techniques[J]. IEEE Transactions on Visualization and Computer Graphics, 2003, 9(2): 191-205. DOI URL
[26]	HORNUNG A, KOBBELT L. Robust reconstruction of watertight 3D models from non-uniformly sampled point clouds without normal information[C]// The 4th Eurographics Symposium on Geometry Processing. New York: ACM, 2006: 41-50.
[27]	KAZHDAN M, HOPPE H. Screened poisson surface reconstruction[J]. ACM Transactions on Graphics, 2013, 32(3): 29.
[28]	MURALI T M, FUNKHOUSER T A. Consistent solid and boundary representations from arbitrary polygonal data[C]// 1997 Symposium on Interactive 3D Graphics. New York: ACM, 1997: 155-162.
[29]	HU Y X, ZHOU Q N, GAO X F, et al. Tetrahedral meshing in the wild[J]. ACM Transactions on Graphics, 2018, 37(4): 60.
[30]	ATTENE M. A lightweight approach to repairing digitized polygon meshes[J]. The Visual Computer, 2010, 26(11): 1393-1406. DOI URL
[31]	ATTENE M. Direct repair of self-intersecting meshes[J]. Graphical Models, 2014, 76(6): 658-668. DOI URL
[32]	AKENINE-MÖLLER T. Fast 3D triangle-box overlap testing[J]. Journal of Graphics, GPU & Game Tools, 2001, 6(1): 29-33.
[33]	ZHOU Q N, GRINSPUN E, ZORIN D, et al. Mesh arrangements for solid geometry[J]. ACM Transactions on Graphics, 2016, 35(4): 39.
[34]	BOTSCH M. Polygon mesh processing[M]. Massachusetts: A K Peters, Ltd, 2010: 12.
[35]	MeshLab. MeshLab[EB/OL]. [2022-05-20]. https://www.meshlab.net/.
[36]	CHEN D Y, TIAN X P, SHEN Y T, et al. On visual similarity based 3D model retrieval[J]. Computer Graphics Forum, 2003, 22(3): 223-232. DOI URL
[37]	CORSINI M, CIGNONI P, SCOPIGNO R. Efficient and flexible sampling with blue noise properties of triangular meshes[J]. IEEE Transactions on Visualization and Computer Graphics, 2012, 18(6): 914-924. DOI URL
[38]	JIAO C Y, BI C K, YANG L, et al. ESRGAN-based visualization for large-scale volume data[J]. Journal of Visualization, 2022: 1-17.
[39]	LI M L. Feature-preserving 3D mesh simplification for urban buildings[J]. ISPRS Journal of Photogrammetry and Remote Sensing, 2021, 173: 135-150. DOI URL

三维建筑模型的低模网格生成

3D low-poly mesh generation for building models

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