The Joint Gromov Wasserstein Objective for Multiple Object Matching

• URL: http://arxiv.org/abs/2511.16868v1
• Date: Fri, 21 Nov 2025 00:31:21 GMT
• Title: The Joint Gromov Wasserstein Objective for Multiple Object Matching
• Authors: Aryan Tajmir Riahi, Khanh Dao Duc,
• Abstract summary: We introduce the Joint Gromov-Wasserstein (JGW) objective and extend the original framework of GW to enable simultaneous matching between collections of objects.<n>Our formulation provides a non-negative dissimilarity measure that identifies partially isomorphic of mm-spaces, with point sampling convergence.<n>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.
• Score: 0.6875312133832079
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 object 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 structural biology.

Related papers

• Geometry-aware RL for Manipulation of Varying Shapes and Deformable Objects [14.481805160449282]
  Manipulating objects with varying geometries and deformable objects is a major challenge in robotics.<n>We frame this problem through the lens of a heterogeneous graph that comprises smaller sub-graphs.<n>We present a novel and challenging reinforcement learning benchmark, including rigid insertion of diverse objects.
  arXiv  Detail & Related papers  (2025-02-10T20:10:25Z)
• Interpetable Target-Feature Aggregation for Multi-Task Learning based on Bias-Variance Analysis [53.38518232934096]
  Multi-task learning (MTL) is a powerful machine learning paradigm designed to leverage shared knowledge across tasks to improve generalization and performance. We propose an MTL approach at the intersection between task clustering and feature transformation based on a two-phase iterative aggregation of targets and features. In both phases, a key aspect is to preserve the interpretability of the reduced targets and features through the aggregation with the mean, which is motivated by applications to Earth science.
  arXiv  Detail & Related papers  (2024-06-12T08:30:16Z)
• RGM: A Robust Generalizable Matching Model [49.60975442871967]
  We propose a deep model for sparse and dense matching, termed RGM (Robust Generalist Matching) To narrow the gap between synthetic training samples and real-world scenarios, we build a new, large-scale dataset with sparse correspondence ground truth. We are able to mix up various dense and sparse matching datasets, significantly improving the training diversity.
  arXiv  Detail & Related papers  (2023-10-18T07:30:08Z)
• SIGMA: Scale-Invariant Global Sparse Shape Matching [50.385414715675076]
  We propose a novel mixed-integer programming (MIP) formulation for generating precise sparse correspondences for non-rigid shapes. We show state-of-the-art results for sparse non-rigid matching on several challenging 3D datasets.
  arXiv  Detail & Related papers  (2023-08-16T14:25:30Z)
• BOtied: Multi-objective Bayesian optimization with tied multivariate ranks [33.414682601242006]
  In this paper, we show a natural connection between non-dominated solutions and the extreme quantile of the joint cumulative distribution function. Motivated by this link, we propose the Pareto-compliant CDF indicator and the associated acquisition function, BOtied. Our experiments on a variety of synthetic and real-world problems demonstrate that BOtied outperforms state-of-the-art MOBO acquisition functions.
  arXiv  Detail & Related papers  (2023-06-01T04:50:06Z)
• Global and Preference-based Optimization with Mixed Variables using Piecewise Affine Surrogates [0.6083861980670925]
  This paper proposes a novel surrogate-based global optimization algorithm to solve linearly constrained mixed-variable problems.<n>The proposed approach is based on constructing a piecewise affine surrogate of the objective function over feasible samples.<n>The two algorithms are evaluated on several unconstrained and constrained mixed-variable benchmark problems.
  arXiv  Detail & Related papers  (2023-02-09T15:04:35Z)
• Multi-objective optimization via equivariant deep hypervolume approximation [3.069335774032178]
  We show how to approximate the hypervolume function with a deep neural network. We evaluate our method against exact, and approximate hypervolume methods in terms of accuracy, computation time, and generalization.
  arXiv  Detail & Related papers  (2022-10-05T12:07:13Z)
• Finding Geometric Models by Clustering in the Consensus Space [61.65661010039768]
  We propose a new algorithm for finding an unknown number of geometric models, e.g., homographies. We present a number of applications where the use of multiple geometric models improves accuracy. These include pose estimation from multiple generalized homographies; trajectory estimation of fast-moving objects.
  arXiv  Detail & Related papers  (2021-03-25T14:35:07Z)
• Fine-Grained Dynamic Head for Object Detection [68.70628757217939]
  We propose a fine-grained dynamic head to conditionally select a pixel-level combination of FPN features from different scales for each instance. Experiments demonstrate the effectiveness and efficiency of the proposed method on several state-of-the-art detection benchmarks.
  arXiv  Detail & Related papers  (2020-12-07T08:16:32Z)
• Isometric Multi-Shape Matching [50.86135294068138]
  Finding correspondences between shapes is a fundamental problem in computer vision and graphics. While isometries are often studied in shape correspondence problems, they have not been considered explicitly in the multi-matching setting. We present a suitable optimisation algorithm for solving our formulation and provide a convergence and complexity analysis.
  arXiv  Detail & Related papers  (2020-12-04T15:58:34Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.