FSH3D: 3D Representation via Fibonacci Spherical Harmonics

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dc.contributor.authorLi, Zikuanen_US
dc.contributor.authorHuang, Anyien_US
dc.contributor.authorJia, Wenruen_US
dc.contributor.authorWu, Qiaoyunen_US
dc.contributor.authorWei, Mingqiangen_US
dc.contributor.authorWang, Junen_US
dc.contributor.editorChen, Renjieen_US
dc.contributor.editorRitschel, Tobiasen_US
dc.contributor.editorWhiting, Emilyen_US
dc.date.accessioned2024-10-13T18:08:37Z
dc.date.available2024-10-13T18:08:37Z
dc.date.issued2024
dc.description.abstractSpherical harmonics are a favorable technique for 3D representation, employing a frequency-based approach through the spherical harmonic transform (SHT). Typically, SHT is performed using equiangular sampling grids. However, these grids are non-uniform on spherical surfaces and exhibit local anisotropy, a common limitation in existing spherical harmonic decomposition methods. This paper proposes a 3D representation method using Fibonacci Spherical Harmonics (FSH3D). We introduce a spherical Fibonacci grid (SFG), which is more uniform than equiangular grids for SHT in the frequency domain. Our method employs analytical weights for SHT on SFG, effectively assigning sampling errors to spherical harmonic degrees higher than the recovered band-limited function. This provides a novel solution for spherical harmonic transformation on non-equiangular grids. The key advantages of our FSH3D method include: 1) With the same number of sampling points, SFG captures more features without bias compared to equiangular grids; 2) The root mean square error of 32-degree spherical harmonic coefficients is reduced by approximately 34.6% for SFG compared to equiangular grids; and 3) FSH3D offers more stable frequency domain representations, especially for rotating functions. FSH3D enhances the stability of frequency domain representations under rotational transformations. Its application in 3D shape reconstruction and 3D shape classification results in more accurate and robust representations. Our code is publicly available at https://github.com/Miraclelzk/Fibonacci-Spherical-Harmonics.en_US
dc.description.number7
dc.description.sectionheadersGeometric Processing II
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume43
dc.identifier.doi10.1111/cgf.15231
dc.identifier.issn1467-8659
dc.identifier.pages11 pages
dc.identifier.urihttps://doi.org/10.1111/cgf.15231
dc.identifier.urihttps://diglib.eg.org/handle/10.1111/cgf15231
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectCCS Concepts: Computing methodologies → Point-based models; Mathematics of computing → Computation of transforms
dc.subjectComputing methodologies → Point
dc.subjectbased models
dc.subjectMathematics of computing → Computation of transforms
dc.titleFSH3D: 3D Representation via Fibonacci Spherical Harmonicsen_US
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