An Efficient Global-to-Local Rotation Optimization Approach via Spherical Harmonics

dc.contributor.authorHe, Zihangen_US
dc.contributor.authorYang, Yuezhien_US
dc.contributor.authorDeng, Congyueen_US
dc.contributor.authorLu, Jiaxinen_US
dc.contributor.authorGuibas, Leonidasen_US
dc.contributor.authorHuang, Qixingen_US
dc.contributor.editorAttene, Marcoen_US
dc.contributor.editorSellán, Silviaen_US
dc.date.accessioned2025-06-20T07:39:08Z
dc.date.available2025-06-20T07:39:08Z
dc.date.issued2025
dc.description.abstractThis paper studies the classical problem of 3D shape alignment, namely computing the relative rotation between two shapes (centered at the origin and normalized by scale) by aligning spherical harmonic coefficients of their spherical function representations. Unlike most prior work, which focuses on the regime in which the inputs have approximately the same shape, we focus on the more general and challenging setting in which the shapes may differ. Central to our approach is a stability analysis of spherical harmonic coefficients, which sheds light on how to align them for robust rotation estimation. We observe that due to symmetries, certain spherical harmonic coefficients may vanish. As a result, using a robust norm for alignment that automatically discards such coefficients offers more accurate rotation estimates than the widely used L2 norm. To enable efficient continuous optimization, we show how to analytically compute the Jacobian of spherical harmonic coefficients with respect to rotations. We also introduce an efficient approach for rotation initialization that requires only a sparse set of rotation samples. Experimental results show that our approach achieves better accuracy and efficiency compared to baseline approaches.en_US
dc.description.number5
dc.description.sectionheadersShape Analysis
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume44
dc.identifier.doi10.1111/cgf.70185
dc.identifier.issn1467-8659
dc.identifier.pages13 pages
dc.identifier.urihttps://doi.org/10.1111/cgf.70185
dc.identifier.urihttps://diglib.eg.org/handle/10.1111/cgf70185
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 analysis; Volumetric models
dc.subjectComputing methodologies → Shape analysis
dc.subjectVolumetric models
dc.titleAn Efficient Global-to-Local Rotation Optimization Approach via Spherical Harmonicsen_US
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