Support and approximation properties of Hermite splines

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Application of optimal spline subspaces for the removal of spurious outliers in isogeometric discretizations

Espen Sande

We show that isogeometric Galerkin discretizations of eigenvalue problems related to the Laplace operator subject to any standard type of homogeneous boundary conditions have no outliers in certain optimal spline subspaces. Roughly speaking, these optimal ...

2022

Synthesis and Analysis of 3D shapes with Geometric Deep Learning in Computer-Aided Engineering

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In this thesis, we advocate that Computer-Aided Engineering could benefit from a Geometric Deep Learning revolution, similarly to the way that Deep Learning revolutionized Computer Vision. To do so, we consider a variety of Computer-Aided Engineering pr ...

EPFL2022

Radical Intangibles: Materializing the Ephemeral

Sarah Irene Brutton Kenderdine, Lillian Hibberd, Jeffrey Shaw

New materialism considers that the world and its histories are produced by a range of material forces that extend from the physical and the biological to the psychological, social and cultural. In recognizing that heritage is not held in objects alone, new ...

2021

Light Path Gradients for Forward and Inverse Rendering

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Physically based rendering is a process for photorealistic digital image synthesis and one of the core problems in computer graphics. It involves simulating the light transport, i.e. the emission, propagation, and scattering of light through a virtual scen ...

EPFL2021

Mathematical and numerical models for the cardiac electromechanical function

Alfio Quarteroni, Francesco Regazzoni

This paper deals with the mathematical model that describes the function of the human heart. More specifically, it addresses the equations that express the electromechanical process, that is the mechanical deformation (contraction and relaxation) of the he ...

EUROPEAN MATHEMATICAL SOC-EMS2021

Visual Attention and Perceptual Quality in Omnidirectional Imaging

Evgeniy Upenik

Omnidirectional imaging has reached a level of widespread availability driven by recent advances in integrated circuit technology, image sensors, and computer graphics which allow now capturing, rendering and displaying of such type of immersive content in ...

EPFL2020

Continuous-Domain Signal Reconstruction Using L-p-Norm Regularization

Michaël Unser, Pakshal Narendra Bohra

We focus on the generalized-interpolation problem. There, one reconstructs continuous-domain signals that honor discrete data constraints. This problem is infinite-dimensional and ill-posed. We make it well-posed by imposing that the solution balances data ...

2020

Generating Sparse Stochastic Processes Using Matched Splines

Michaël Unser, Leello Tadesse Dadi, Shayan Aziznejad

We provide an algorithm to generate trajectories of sparse stochastic processes that are solutions of linear ordinary differential equations driven by Levy white noises. A recent paper showed that these processes are limits in law of generalized compound-P ...

2020

From Modular Origami Robots to Polygon-based Modular Systems: a New Paradigm in Reconfigurable Robotics

Christoph Heinrich Belke

A useful robot is one that fulfils its intended function. In a factory setting, where robots have been used successfully for decades, this function is often singular and clearly defined. Similarly, the surroundings of the robot are mostly known, sterile, a ...

EPFL2020

Fast Least-Squares Padé approximation of problems with normal operators and meromorphic structure

Fabio Nobile, Francesca Bonizzoni, Davide Pradovera

In this work, we consider the approximation of Hilbert space-valued meromorphic functions that arise as solution maps of parametric PDEs whose operator is the shift of an operator with normal and compact resolvent, e.g., the Helmholtz equation. In this res ...

2020

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