Publications related to Hermite interpolation

Performance and accuracy of cross‐section tracking methods for hydromorphological habitat assessment in wadable rivers with sparse canopy conditions

Giovanni De Cesare, Paolo Perona, Robin Schroff

This article investigates the performance and accuracy of continuous Real-Time Kinematic (RTK) Global Navigation Satellite System (GNSS) position tracking for hydromorphological surveys, based on a comprehensive river restoration monitoring campaign. The a ...

2024

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

Axel Elie Joseph Séguin

The goal of this thesis is the development and the analysis of numerical methods for problems where the unknown is a curve on a smooth manifold. In particular, the thesis is structured around the three following problems: homotopy continuation, curve inter ...

EPFL2023

Stable Nonconvex-Nonconcave Training via Linear Interpolation

Volkan Cevher, Thomas Michaelsen Pethick, Wanyun Xie

This paper presents a theoretical analysis of linear interpolation as a principled method for stabilizing (large-scale) neural network training. We argue that instabilities in the optimization process are often caused by the nonmonotonicity of the loss lan ...

2023

Perturbed Fourier uniqueness and interpolation results in higher dimensions

Martin Peter Stoller, Joao Pedro Gonçalves Ramos

We obtain new Fourier interpolation and uniqueness results in all dimensions, extending methods and results by the first author and M. Sousa [11] and the second author [12]. We show that the only Schwartz function which, together with its Fourier transform ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

Choreography Controlled (ChoCo) brain MRI artifact generation for labeled motion-corrupted datasets

Michel Kocher, François Lazeyras, Bastien Chopard, Sébastien Courvoisier, Julien Songeon

MRI is a non-invasive medical imaging modality that is sensitive to patient motion, which constitutes a major limitation in most clinical applications. Solutions may arise from the reduction of acquisition times or from motion-correction techniques, either ...

ELSEVIER SCI LTD2022

Fourier Interpolation From Spheres

Martin Peter Stoller

In every dimension d >= 2, we give an explicit formula that expresses the values of any Schwartz function on R-d only in terms of its restrictions, and the restrictions of its Fourier transform, to all origin-centered spheres whose radius is the square roo ...

2021

On Linear Interpolation in the Latent Space of Deep Generative Models

Quentin Christian Becker, Mike Yan Michelis

The underlying geometrical structure of the latent space in deep generative models is in most cases not Euclidean, which may lead to biases when comparing interpolation capabilities of two models. Smoothness and plausibility of linear interpolations in lat ...

2021

Fully-Asynchronous Fully-Implicit Variable-Order Variable-Timestep Simulation of Neural Networks

Felix Schürmann, Michael Lee Hines, Bruno Ricardo Da Cunha Magalhães

State-of-the-art simulations of detailed neurons follow the Bulk Synchronous Parallel execution model. Execution is divided in equidistant communication intervals, with parallel neurons interpolation and collective communication guiding synchronization. Su ...

2020

Examining the Effects of Privacy-Aware Blended Learning Scenarios in Executive Training for Policymakers and Government Officials

Denis Gillet, Isabelle Barbara Marie-Hélène Cardia, Juan Carlos Farah, Maria Gaci

Enabling blended learning scenarios that foster participation and interaction is an important consideration in the design of executive training programs. To investigate this design process, our study focuses on two aspects that are present in such scenario ...

Springer2020

Low-Rank Tensor Approximation for Chebyshev Interpolation in Parametric Option Pricing

Daniel Kressner, Francesco Statti, Kathrin Beatrice Glau

Treating high dimensionality is one of the main challenges in the development of computational methods for solving problems arising in finance, where tasks such as pricing, calibration, and risk assessment need to be performed accurately and in real-time. ...

2020

Integrating the Finite Element Method with a Data-Driven Approach for Dam Displacement Prediction

Zhenzhu Meng, Yating Hu, Chenfei Shao

Both numerical simulations and data-driven methods have been applied in dam's displacement modeling. For monitored displacement data-driven methods, the physical mechanism and structural correlations were rarely discussed. In order to take the spatial and ...

2020

Regularity results for rough solutions of the incompressible Euler equations via interpolation methods

Maria Colombo, Luigi Forcella, Luigi De Rosa

Given any solutionuof the Euler equations which is assumed to have some regularity in space-in terms of Besov norms, natural in this context-we show by interpolation methods that it enjoys a corresponding regularity in time and that the associated pressure ...

IOP2019

Approximation of Non-decaying Signals from Shift-Invariant Subspaces

Michaël Unser, Quy Ha Nguyen

In our recent work, the sampling and reconstruction of non-decaying signals, modeled as members of weighted-L-p spaces, were shown to be stable with an appropriate choice of the generating kernel for the shift-invariant reconstruction space. In this paper, ...

2019

Domain-Informed Spline Interpolation

Dimitri Nestor Alice Van De Ville, Zafer Dogan, Hamid Behjat

Standard interpolation techniques are implicitly based on the assumption that the signal lies on a single homogeneous domain. In contrast, many naturally occurring signals lie on an inhomogeneous domain, such as brain activity associated to different brain ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2019

Neural BTF Compression and Interpolation

Wenzel Alban Jakob

The Bidirectional Texture Function (BTF) is a data-driven solution to render materials with complex appearance. A typical capture contains tens of thousands of images of a material sample under varying viewing and lighting conditions. While capable of fait ...

WILEY2019

Predicting the reflectivity and colour of metals from first principles

Gianluca Prandini

Gold and copper are the only two elemental metals that show a characteristic colour, due to the presence of a drop in the reflectivity curve inside the visible range. Reflectivities of all other metals are in general high and flat for all visible frequenci ...

EPFL2019

Entropy stable essentially non-oscillatory methods based on RBF reconstructions

Jan Sickmann Hesthaven, Fabian Mönkeberg

To solve hyperbolic conservation laws on general grids we propose to use high-order essentially nonoscillatory methods based on radial basis functions. We introduce an entropy stable arbitrary high-order finite dierence method (RBF-TeCNOp) and an entropy s ...

2019

Spatial interpolation of precipitation from multiple rain gauge networks and weather radar data for operational applications in Alpine catchments

Giovanni De Cesare, Javier García Hernández, Bettina Schaefli, Alain Tommy Foehn

Increasing meteorological data availability and quality implies an adaptation of the interpolation methods for data combination. In this paper, we propose a new method to efficiently combine weather radar data with data from two heated rain gauge networks ...

2018

Graph-Based Interpolation for Zooming in 3D Scenes

Pascal Frossard, Pinar Akyazi

In multiview systems, color plus depth format builds 3D representations of scenes within which the users can freely navigate by changing their viewpoints. In this paper we present a framework for view synthesis when the user requests an arbitrary viewpoint ...

2017

Landmark Active Contours for Bioimage Analysis : A Tale of Points and Curves

Virginie Sophie Uhlmann

The problem of identifying the outline of objects in images can be approached from two starting points, either by considering localized features (landmarks, keypoints or regions), or by searching for global contours. Features are regions or points of int ...

EPFL2017