发表机构
Murdoch University; The University of Western Australia; The Johns Hopkins University（莫道克大学; 西澳大学; 约翰霍普金斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对非刚性3D/4D形状分析中SRNF不可逆且反演计算昂贵的问题，提出连续、高精度、高效的神经表示NeuralSRNF，在测地线计算等任务上大幅超越现有方法。
AI 中文摘要
我们提出了NeuralSRNF，一个用于经历非刚性形变的亏格为零的3D和4D物体的统计形状分析与生成的新框架。传统方法依赖于复杂且计算成本高昂的非线性弹性度量来测量弯曲和拉伸。弹性形状分析的最新进展通过将输入3D形状映射到平方根法向场（SRNF）空间来实现计算效率，在该空间中L2度量近似于部分弹性度量，极大地促进了测地线和汇总统计的计算过程。然而，SRNF不可逆，且用于将SRNF映射回原始表面空间的数值算法计算成本仍然非常高昂，并且常常导致近似结果。本文使用一种新颖的神经表示（称为NeuralSRNF）来解决这一基本的SRNF反演问题。与常用的数值SRNF不同，NeuralSRNF（1）是连续的，因此与分辨率无关，能够实现完整的函数形状分析，（2）更准确，且（3）计算效率更高，因为它可以在不到3秒内计算沿测地线路径的逆SRNF映射，而数值SRNF则需要超过10分钟。我们使用各种数据集，展示了所提出的NeuralSRNF在多个弹性3D和4D形状分析任务中的实用性和效率，例如测地线计算、形变迁移、汇总统计计算和3D形状生成。我们表明，在大多数评估的数据集和指标上，它在准确性和计算效率方面都大幅优于竞争方法。源代码和额外结果可在https://awaisnizamani16.github.io/awais/NeuralSRNF/获取。
英文摘要
We introduce NeuralSRNF, a novel framework for the statistical shape analysis and generation of genus-zero 3D and 4D objects that undergo nonrigid deformations. Traditional methods rely on complex and computationally expensive nonlinear elastic metrics that measure bending and stretching. Recent advances in elastic shape analysis achieve computational efficiency by mapping input 3D shapes to the space of Square Root Normal Fields (SRNFs) where the L2 metric approximates the partial elastic metric, significantly facilitating the process of computing geodesics and summary statistics. SRNFs, however, are not invertible, and the numerical algorithms used to map SRNFs back to the original space of surfaces remain computationally very expensive and often lead to approximate results. This paper addresses this fundamental SRNF inversion problem using a novel neural representation, termed NeuralSRNF. Unlike the commonly used numerical SRNF, NeuralSRNF is (1) continuous, and thus resolution-agnostic, enabling full functional shape analysis, (2) more accurate, and (3) computationally more efficient as it can compute inverse SRNF maps along a geodesic path in less than 3 s compared to over 10 min for the numerical SRNF. We demonstrate, using various datasets, the utility and efficiency of the proposed NeuralSRNF in multiple elastic 3D and 4D shape analysis tasks such as geodesic computation, deformation transfer, statistical summaries computation, and 3D shape generation. We show that it outperforms competing methods on most evaluated datasets and metrics by a wide margin in both accuracy and computational efficiency. The source code and additional results are available at https://awaisnizamani16.github.io/awais/NeuralSRNF/.
Comments13 pages, 17 figures, journal submission
