Fitting local, low-dimensional parameterizations of optical turbulence modeled from optimal transport velocity vectors

Emerson, Tegan; Nichols, Jonathan M.

doi:10.1016/j.patrec.2019.10.023

Cited by 7 publications

(4 citation statements)

References 17 publications

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“…The motivation of LGW is based on linear optimal transport (LOT), which was introduced by Wang et al [8]. Since its introduction, LOT has been successfully applied for several tasks in nuclear structure-based pathology [9], parametric signal estimation [10], signal and image classification [11][12][13][14], modeling of turbulences [15], cancer detection [16][17][18], Alzheimer disease detection [19], vehicle-type recognition [20] as well as for de-multiplexing vortex modes in optical communications [21]. Both LOT and LGW make use of the geometrical structure of the (Gromov-)Wasserstein space and compute distances in the tangent space with respect to some a priori fixed reference.…”

Section: Introductionmentioning

confidence: 99%

Multi‐marginal Approximation of the Linear Gromov–Wasserstein Distance

Beier

Beinert

2023

Proc Appl Math and Mech

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Recently, two concepts from optimal transport theory have successfully been brought to the Gromov–Wasserstein (GW) setting. This introduces a linear version of the GW distance and multi‐marginal GW transport. The former can reduce the computational complexity when computing all GW distances of a large set of inputs. The latter allows for a simultaneous matching of more than two marginals, which can for example be used to compute GW barycenters. The aim of this paper is to show an approximation result which characterizes the linear version as a limit of a multi‐marginal GW formulation.

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Section: Introductionmentioning

confidence: 99%

Multi‐marginal Approximation of the Linear Gromov–Wasserstein Distance

Beier

Beinert

2023

Proc Appl Math and Mech

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show abstract

“…The motivation of LGW is based on linear optimal transport (LOT), which was introduced by Wang et al [8]. Since its introduction, LOT has been successfully applied for several tasks in nuclear structure-based pathology [9], parametric signal estimation [10], signal and image classification [11,12,13,14], modeling of turbulences [15], cancer detection [16,17,18], Alzheimer disease detection [19], vehicle-type recognition [20] as well as for demultiplexing vortex modes in optical communications [21]. Both LOT and LGW make use of the geometrical structure of the (Gromov-)Wasserstein space and compute distances in the tangent space with respect to some a priori fixed reference.…”

Section: Introductionmentioning

confidence: 99%

Multi-marginal Approximation of the Linear Gromov-Wasserstein Distance

Beier¹,

Beinert²

2022

Preprint

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Recently, two concepts from optimal transport theory have successfully been brought to the Gromov-Wasserstein (GW) setting. This introduces a linear version of the GW distance and multi-marginal GW transport. The former can reduce the computational complexity when computing all GW distances of a large set of inputs. The latter allows for a simultaneous matching of more than two marginals, which can for example be used to compute GW barycenters. The aim of this paper is to show an approximation result which characterizes the linear version as a limit of a multi-marginal GW formulation.

show abstract

“…Meanwhile LOT has been successfully applied for several tasks in nuclear structure-based pathology [35], parametric signal estimation [27], signal and image classification [17,22], modeling of turbulences [11], cancer detection [5,21,32], Alzheimer disease detection [10], vehicle-type recognition [14] as well as for de-multiplexing vortex modes in optical communications [23]. On the real line, LOT can further be written using the cumulative density function of the random variables associated to the involved measures.…”

Section: Introductionmentioning

confidence: 99%

On a linear Gromov-Wasserstein distance

Beier,

Beinert,

Steidl

2021

Preprint

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Gromov-Wasserstein distances are generalization of Wasserstein distances, which are invariant under certain distance preserving transformations. Although a simplified version of optimal transport in Wasserstein spaces, called linear optimal transport (LOT), was successfully used in certain applications, there does not exist a notation of linear Gromov-Wasserstein distances so far. In this paper, we propose a definition of linear Gromov-Wasserstein distances. We motivate our approach by a generalized LOT model, which is based on barycentric projections. Numerical examples illustrate that the linear Gromov-Wasserstein distances, similarly as LOT, can replace the expensive computation of pairwise Gromov-Wasserstein distances in certain applications.

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Fitting local, low-dimensional parameterizations of optical turbulence modeled from optimal transport velocity vectors

Cited by 7 publications

References 17 publications

Multi‐marginal Approximation of the Linear Gromov–Wasserstein Distance

Multi‐marginal Approximation of the Linear Gromov–Wasserstein Distance

Multi-marginal Approximation of the Linear Gromov-Wasserstein Distance

On a linear Gromov-Wasserstein distance

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