Related papers: Unbalanced optimal transport for stochastic partic…
We describe a method to track particles undergoing large displacements. Starting with a list of particle positions sampled at different time points, we assign particle identities by minimizing the sum across all particles of the trace of…
Despite significant advances in particle imaging technologies over the past two decades, few advances have been made in particle tracking, i.e. linking individual particle positions across time series data. The state-of-the-art tracking…
The standard approach to densely reconstruct the motion in a volume of fluid is to inject high-contrast tracer particles and record their motion with multiple high-speed cameras. Almost all existing work processes the acquired multi-view…
Deterministically solving charged particle transport problems at a sufficient spatial and angular resolution is often prohibitively expensive, especially due to their highly forward peaked scattering. We propose a model order reduction…
We present a novel method for estimating the circulations and positions of point vortices using trajectory data of passive particles in the presence of Gaussian noise. The method comprises two algorithms: the first one calculates the vortex…
This article details a novel numerical scheme to approximate gradient flows for optimal transport (i.e. Wasserstein) metrics. These flows have proved useful to tackle theoretically and numerically non-linear diffusion equations that model…
We present a new multiscale algorithm for solving regularized Optimal Transport problems on the GPU, with a linear memory footprint. Relying on Sinkhorn divergences which are convex, smooth and positive definite loss functions, this method…
Methods to extract information from the tracking of mobile objects/particles have broad interest in biological and physical sciences. Techniques based on simple criteria of proximity in time-consecutive snapshots are useful to identify the…
Given a set of points $P = (P^+ \sqcup P^-) \subset \mathbb{R}^d$ for some constant $d$ and a supply function $\mu:P\to \mathbb{R}$ such that $\mu(p) > 0~\forall p \in P^+$, $\mu(p) < 0~\forall p \in P^-$, and $\sum_{p\in P}{\mu(p)} = 0$,…
Geochemical systems are known to exhibit highly variable spatiotemporal behavior. This may be observed both in non-smooth concentration curves in space for a single sampling time and also in variability between samples taken from the same…
The modeling of phenomenological structure is a crucial aspect in inverse imaging problems. One emerging modeling tool in computational imaging is the optimal transport framework. Its ability to model geometric displacements across an…
Optimizing the energy efficiency of driving processes provides valuable insights into the underlying physics and is of crucial importance for numerous applications, from biological processes to the design of machines and robots. Knowledge…
In machine learning and computer vision, optimal transport has had significant success in learning generative models and defining metric distances between structured and stochastic data objects, that can be cast as probability measures. The…
The geometric transportation problem takes as input a set of points $P$ in $d$-dimensional Euclidean space and a supply function $\mu : P \to \mathbb{R}$. The goal is to find a transportation map, a non-negative assignment $\tau : P \times…
Optimal transport has found widespread applications in signal processing and machine learning. Among its many equivalent formulations, optimal transport seeks to reconstruct a random variable/vector with a prescribed distribution at the…
Automated particle locating algorithms have revolutionized microscopy image analysis, enabling researchers to rapidly locate many particles to within a few pixels in a microscope image. The vast majority of these algorithms operate through…
3D particle tracking velocimetry (PTV) is a key technique for analyzing turbulent flow, one of the most challenging computational problems of our century. At the core of 3D PTV is the dual-frame fluid motion estimation algorithm, which…
Replacing the quadratic proximal penalty familiar from Hilbert spaces by an unbalanced optimal transport distance, we develop forward-backward type optimisation methods in spaces of Radon measures. We avoid the actual computation of the…
Confocal microscopy in combination with real-space particle tracking has proven to be a powerful tool in scientific fields such as soft matter physics, materials science and cell biology. However, 3D tracking of anisotropic particles in…
In this paper we investigate the numerical approximation of an analogue of the Wasserstein distance for optimal transport on graphs that is defined via a discrete modification of the Benamou--Brenier formula. This approach involves the…