用对称感知的双谱方法提升数据集比对的语义保真度
Bispectral OT: Dataset Comparison using Symmetry-Aware Optimal Transport
- 用双谱替代原始特征，捕捉对称性下的信号结构
- 在含视觉对称的数据上，分类保真度显著优于传统OT
- 适合处理带对称噪声的图像/点云数据比对任务
最优传输（OT）是机器学习、图形学和视觉领域中用于对齐两个分布或数据集的常用技术，依赖原始特征间的成对几何距离。但在具有丰富对称性的场景中，仅基于原始特征距离的OT可能忽略数据的内在一致性结构。本文提出双谱最优传输（Bispectral OT），一种离散OT的对称性感知扩展方法，通过双谱——一种群傅里叶不变量——表示元素，保留全部信号结构的同时去除仅由群作用引起的变异。实验表明，在经视觉对称变换的基准数据集上，使用双谱OT计算的传输方案比基于原始特征的OT实现更高的类别保真度，生成的对应关系更准确地反映数据集的潜在语义标签结构，同时消除不影响类别或内容的干扰变化。
原文摘要 · Abstract (English)
Optimal transport (OT) is a widely used technique in machine learning, graphics, and vision that aligns two distributions or datasets using their relative geometry. In symmetry-rich settings, however, OT alignments based solely on pairwise geometric distances between raw features can ignore the intrinsic coherence structure of the data. We introduce Bispectral Optimal Transport, a symmetry-aware extension of discrete OT that compares elements using their representation using the bispectrum, a group Fourier invariant that preserves all signal structure while removing only the variation due to group actions. Empirically, we demonstrate that the transport plans computed with Bispectral OT achieve greater class preservation accuracy than naive feature OT on benchmark datasets transformed with visual symmetries, improving the quality of meaningful correspondences that capture the underlying semantic label structure in the dataset while removing nuisance variation not affecting class or content.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。