GreenCloud: Volumetric Gradient Filtering via Regularized Green's Functions

dc.contributor.authorTojo, Kenjien_US
dc.contributor.authorUmetani, Nobuyukien_US
dc.contributor.editorAttene, Marcoen_US
dc.contributor.editorSellán, Silviaen_US
dc.date.accessioned2025-06-20T07:40:57Z
dc.date.available2025-06-20T07:40:57Z
dc.date.issued2025
dc.description.abstractGradient-based optimization is a fundamental tool in geometry processing, but it is often hampered by geometric distortion arising from noisy or sparse gradients. Existing methods mitigate these issues by filtering (i.e., diffusing) gradients over a surface mesh, but they require explicit mesh connectivity and solving large linear systems, making them unsuitable for point-based representation. In this work, we introduce a gradient filtering method tailored for point-based geometry. Our method bypasses explicit connectivity by leveraging regularized Green's functions to directly compute the filtered gradient field from discrete spatial points. Additionally, our approach incorporates elastic deformation based on Green's function of linear elasticity (known as Kelvinlets), reproducing various elastic behaviors such as smoothness and volume preservation while improving robustness in affine transformations. We further accelerate computation using a hierarchical Barnes-Hut style approximation, enabling scalable optimization of one million points. Our method significantly improves convergence across a wide range of applications, including reconstruction, editing, stylization, and simplified optimization experiments with Gaussian splatting.en_US
dc.description.number5
dc.description.sectionheadersFields on Meshes
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume44
dc.identifier.doi10.1111/cgf.70207
dc.identifier.issn1467-8659
dc.identifier.pages13 pages
dc.identifier.urihttps://doi.org/10.1111/cgf.70207
dc.identifier.urihttps://diglib.eg.org/handle/10.1111/cgf70207
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 → Shape modeling; Rendering
dc.subjectComputing methodologies → Shape modeling
dc.subjectRendering
dc.titleGreenCloud: Volumetric Gradient Filtering via Regularized Green's Functionsen_US
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