提出联合格罗莫夫-瓦瑟斯坦方法，实现多对象同时匹配
The Joint Gromov Wasserstein Objective for Multiple Object Matching
- 扩展经典格罗莫夫-瓦瑟斯坦框架，支持多对多对象匹配
- 在合成与真实数据上实现更高精度和更快计算速度
- 适用于几何形状与生物分子复合物等复杂匹配任务
格罗莫夫-瓦瑟斯坦（GW）距离是度量空间中对象匹配的有力工具，但传统形式仅限于单对象间的成对匹配，难以应用于需要多对一或多对多匹配的场景。本文提出联合格罗莫夫-瓦瑟斯坦（JGW）目标，将原始框架扩展至多个对象集合的同步匹配。该方法提供非负的差异度量，可识别部分同构的毫米空间分布，并具备点采样收敛性。通过适配最优传输中的传统算法（包括熵正则化），可在点云表示下求解。基准测试表明，相比其他GW变体，在部分匹配任务中具有更优的准确率与计算效率。在合成与真实数据集上的实验验证了其在多形状匹配（包括几何体与生物分子复合物）中的有效性，展现出在计算机图形学与结构生物学原子模型构建等领域的广阔应用前景。
原文摘要 · Abstract (English)
The Gromov-Wasserstein (GW) distance serves as a powerful tool for matching objects in metric spaces. However, its traditional formulation is constrained to pairwise matching between single objects, limiting its utility in scenarios and applications requiring multiple-to-one or multiple-to-multiple object matching. In this paper, we introduce the Joint Gromov-Wasserstein (JGW) objective and extend the original framework of GW to enable simultaneous matching between collections of objects. Our formulation provides a non-negative dissimilarity measure that identifies partially isomorphic distributions of mm-spaces, with point sampling convergence. We also show that the objective can be formulated and solved for point cloud representations by adapting traditional algorithms in Optimal Transport, including entropic regularization. Our benchmarking with other variants of GW for partial matching indicates superior performance in accuracy and computational efficiency of our method, while experiments on both synthetic and real-world datasets show its effectiveness for multiple shape matching, including geometric shapes and biomolecular complexes, suggesting promising applications for solving complex matching problems across diverse domains, including computer graphics and atomic model building for structural biology.
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