An Efficient Global-to-Local Rotation Optimization Approach via Spherical Harmonics
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Date
2025
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and John Wiley & Sons Ltd.
Abstract
This 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.
Description
CCS Concepts: Computing methodologies → Shape analysis; Volumetric models
@article{10.1111:cgf.70185,
journal = {Computer Graphics Forum},
title = {{An Efficient Global-to-Local Rotation Optimization Approach via Spherical Harmonics}},
author = {He, Zihang and Yang, Yuezhi and Deng, Congyue and Lu, Jiaxin and Guibas, Leonidas and Huang, Qixing},
year = {2025},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.70185}
}