Gromov–Wasserstein Distances and the Metric Approach to Object Matching

By Facundo M'emoli. Foundations of Computational Mathematics, 2011

783 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/03a4f1c1975237a5e1e501dd26811b4ce55a35a9

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Citations in the corpus

Product Manifold Filter: Non-rigid Shape Correspondence via Kernel Density Estimation in the Product Space (2017, methodology): “Several methods formulated soft correspondence as a masstransportation problem [28, 39].”
Diffusion Schrödinger Bridge with Applications to Score-Based Generative Modeling (2021, methodology): “For example, DSB could be used to solve multi-marginal Schrödinger bridges problems (Di Marino and Gerolin, 2020), compute Wasserstein barycenters, find the minimizers of entropy-regularized Gromov–Wasserstein problems (Mémoli, 2011) or perform domain adaptation in continuous state-spaces.”
Learning shape correspondence with anisotropic convolutional neural networks (2016, methodology): “Traditional hand-crafted correspondence approaches are divided into two main categories: point-wise correspondence methods [17], which establish the matching between (a subset of) the points on two or more shapes by minimizing metric distortion, and soft correspondence methods [23], which establish ”
The Gromov–Hausdorff distance between spheres (2021, background): “The Gromov-Hausdorff distance is also a natural choice for expressing the stability of invariants in applied algebraic topology [5, 6, 7] and has also been invoked in applications related to shape matching [3, 23, 24] as a notion of dissimilarity between shapes.”
Dense Non-rigid Shape Correspondence Using Random Forests (2014, methodology): “A natural choice for such regularity term is the Lp-relaxed GromovHausdorff metric distortion [11, 16]”
A spectral notion of Gromov–Wasserstein distance and related methods (2011, background): “These issues were addressed in [11,13,14], where the author defines the Gromov–Wasserstein distance (GW from now on) based on ideas from mass transportation.”
Optimal Transport Kernels for Sequential and Parallel Neural Architecture Search (2020, methodology): “In addition, we compare our approach with the BO using the Gromov-Wasserstein distance (Mémoli, 2011) (BO-GW) and path encoding (BO-Path Encoding) as used in (White et al., 2021).”
Optimal Transport for structured data with application on graphs (2018, methodology): “This new distance is called the FGW distance as it acts as a generalization of the Wasserstein (Villani, 2008) and Gromov-Wasserstein (Memoli, 2011) distances as stated in the following theorem: Theorem 3.1.”
The Space of Spaces: Curvature Bounds and Gradient Flows on the Space of Metric Measure Spaces (2012, background): “roduced and analyzed various distances (partly for ﬁnite, partly for compact mm-spaces) with emphasis on computational aspects and in view of applications to shape matching and object recognition. In [Mém11], he presented an exhaustive survey on the distances ∆∆p and Dp (which he denoted by 2Dp and ”
Gromov-Wasserstein Learning for Graph Matching and Node Embedding (2019, methodology): “The GW discrepancy is suitable for solving matching problems like shape and object matching (Mémoli, 2009; 2011).”
Bayesian Inference of Bijective Non-Rigid Shape Correspondence (2016, methodology): “Several methods formulated soft correspondence as a masstransportation problem [26, 38].”
Computational Optimal Transport (2018, methodology): “23) and as explained in [Mémoli, 2011], it is possible to rewrite equivalently the GH distance using couplings as follows:”
The time-evolving epileptic brain network: concepts, definitions, accomplishments, perspectives (2024, background): “…ﬁ cult task (Bronstein et al., 2006; Andrade et al., 2008; Muskulus et al., 2009; Dimitriadis et al., 2010; Gao et al., 2010; van Wijk et al., 2010; Mémoli, 2011; De Domenico and Biamonte, 2016; Schieber et al., 2017; Fraiman and Fraiman, 2018; Carpi et al., 2019; Martínez and Chavez, 2019;…”