Anisotropic Gauss Reconstruction and Global Orientation with Octree-based Acceleration

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dc.contributor.authorMa, Yuejien_US
dc.contributor.authorShen, Jialuen_US
dc.contributor.authorMeng, Yanzunen_US
dc.contributor.authorXiao, Dongen_US
dc.contributor.authorShi, Zuoqiangen_US
dc.contributor.authorWang, Binen_US
dc.contributor.editorAttene, Marcoen_US
dc.contributor.editorSellán, Silviaen_US
dc.date.accessioned2025-06-20T07:40:30Z
dc.date.available2025-06-20T07:40:30Z
dc.date.issued2025
dc.description.abstractUnoriented surface reconstruction is an important task in computer graphics. Recently, methods based on the Gauss formula or winding number have achieved state-of-the-art performance in both orientation and surface reconstruction. The Gauss formula or winding number, derived from the fundamental solution of the Laplace equation, initially found applications in calculating potentials in electromagnetism. Inspired by the practical necessity of calculating potentials in diverse electromagnetic media, we consider the anisotropic Laplace equation to derive the anisotropic Gauss formula and apply it to surface reconstruction, called ''anisotropic Gauss reconstruction''. By leveraging the flexibility of anisotropic coefficients, additional constraints can be introduced to the indicator function. This results in a stable linear system, eliminating the need for any artificial regularization. In addition, the oriented normals can be refined by computing the gradient of the indicator function, ultimately producing high-quality normals and surfaces. Regarding the space/time complexity, we propose an octree-based acceleration algorithm to achieve a space complexity of O(N) and a time complexity of O(NlogN). Our method can reconstruct ultra-large-scale models (exceeding 5 million points) within 4 minutes on an NVIDIA RTX 4090 GPU. Extensive experiments demonstrate that our method achieves state-of-the-art performance in both orientation and reconstruction, particularly for models with thin structures, small holes, or high genus. Both CuPy-based and CUDA-accelerated implementations are made publicly available at https://github.com/mayueji/AGR.en_US
dc.description.number5
dc.description.sectionheadersReconstruction
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume44
dc.identifier.doi10.1111/cgf.70199
dc.identifier.issn1467-8659
dc.identifier.pages16 pages
dc.identifier.urihttps://doi.org/10.1111/cgf.70199
dc.identifier.urihttps://diglib.eg.org/handle/10.1111/cgf70199
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.rightsAttribution 4.0 International License
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectCCS Concepts: Computing methodologies → Mesh models; Computer graphics; Shape modeling
dc.subjectComputing methodologies → Mesh models
dc.subjectComputer graphics
dc.subjectShape modeling
dc.titleAnisotropic Gauss Reconstruction and Global Orientation with Octree-based Accelerationen_US
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