Search Results for author: Bernhard Schmitzer

Found 11 papers, 5 papers with code

Data-driven entropic spatially inhomogeneous evolutionary games

no code implementations9 Mar 2021 Mauro Bonafini, Massimo Fornasier, Bernhard Schmitzer

We prove convergence of minimizing solutions obtained from a finite number of observations to a mean field limit and the minimal value provides a quantitative error bound on the data-driven evolutions.

Optimization and Control

The Linearized Hellinger--Kantorovich Distance

1 code implementation17 Feb 2021 Tianji Cai, Junyi Cheng, Bernhard Schmitzer, Matthew Thorpe

Working with the local linearization and the corresponding embeddings allows for the advantages of the Euclidean setting, such as faster computations and a plethora of data analysis tools, whilst still enjoying approximately the descriptive power of the Hellinger--Kantorovich metric.

Optimization and Control

Dynamic Cell Imaging in PET with Optimal Transport Regularization

no code implementations20 Feb 2019 Bernhard Schmitzer, Klaus P. Schäfers, Benedikt Wirth

In contrast to conventional PET reconstruction our method combines the information from all detected events not only to reconstruct the dynamic evolution of the radionuclide distribution, but also to improve the reconstruction at each single time point by enforcing temporal consistency.

Image Reconstruction

A Framework for Wasserstein-1-Type Metrics

no code implementations8 Jan 2017 Bernhard Schmitzer, Benedikt Wirth

We propose a unifying framework for generalising the Wasserstein-1 metric to a discrepancy measure between nonnegative measures of different mass.

Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems

3 code implementations20 Oct 2016 Bernhard Schmitzer

Scaling algorithms for entropic transport-type problems have become a very popular numerical method, encompassing Wasserstein barycenters, multi-marginal problems, gradient flows and unbalanced transport.

Optimization and Control Computational Engineering, Finance, and Science Numerical Analysis

Scaling Algorithms for Unbalanced Transport Problems

3 code implementations20 Jul 2016 Lenaic Chizat, Gabriel Peyré, Bernhard Schmitzer, François-Xavier Vialard

This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport.

Optimization and Control 65K10

Image Labeling by Assignment

no code implementations16 Mar 2016 Freddie Åström, Stefania Petra, Bernhard Schmitzer, Christoph Schnörr

We introduce a novel geometric approach to the image labeling problem.

Unbalanced Optimal Transport: Geometry and Kantorovich Formulation

1 code implementation21 Aug 2015 Lenaic Chizat, Gabriel Peyré, Bernhard Schmitzer, François-Xavier Vialard

These distances are defined by two equivalent alternative formulations: (i) a "fluid dynamic" formulation defining the distance as a geodesic distance over the space of measures (ii) a static "Kantorovich" formulation where the distance is the minimum of an optimization program over pairs of couplings describing the transfer (transport, creation and destruction) of mass between two measures.

Optimization and Control

An Interpolating Distance between Optimal Transport and Fisher-Rao

1 code implementation22 Jun 2015 Lenaic Chizat, Bernhard Schmitzer, Gabriel Peyré, François-Xavier Vialard

This metric interpolates between the quadratic Wasserstein and the Fisher-Rao metrics and generalizes optimal transport to measures with different masses.

Analysis of PDEs

Globally Optimal Joint Image Segmentation and Shape Matching Based on Wasserstein Modes

no code implementations15 Jul 2014 Bernhard Schmitzer, Christoph Schnörr

While the overall functional is non-convex, non-convexity is confined to a low-dimensional variable.

Semantic Segmentation

Contour Manifolds and Optimal Transport

no code implementations9 Sep 2013 Bernhard Schmitzer, Christoph Schnörr

Describing shapes by suitable measures in object segmentation, as proposed in [24], allows to combine the advantages of the representations as parametrized contours and indicator functions.

Semantic Segmentation

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