Titre :

A projection method on measures sets

Auteur(s) :

Chauffert, Nicolas [Auteur]
Modelling brain structure, function and variability based on high-field MRI data [PARIETAL]
Service NEUROSPIN [NEUROSPIN]
Ciuciu, Philippe [Auteur]
Modelling brain structure, function and variability based on high-field MRI data [PARIETAL]
Service NEUROSPIN [NEUROSPIN]
Kahn, Jonas [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Weiss, Pierre [Auteur]
Institut des Technologies Avancées en sciences du Vivant [ITAV]

Mot(s)-clé(s) en anglais :

Constructive quantization
measure theory
nonconvex optimization
stippling
continuous line drawing.

Discipline(s) HAL :

Mathématiques [math]/Optimisation et contrôle [math.OC]
Informatique [cs]/Mathématique discrète [cs.DM]
Informatique [cs]/Synthèse d'image et réalité virtuelle [cs.GR]
Sciences de l'Homme et Société/Art et histoire de l'art

Résumé en anglais : [en]

We consider the problem of projecting a probability measure π on a set MN of Radon measures. The projection is defined as a solution of the following variational problem: inf µ∈M N h (µ − π) 2 2 , where h ∈ L 2 (Ω) is a ...
Lire la suite >We consider the problem of projecting a probability measure π on a set MN of Radon measures. The projection is defined as a solution of the following variational problem: inf µ∈M N h (µ − π) 2 2 , where h ∈ L 2 (Ω) is a kernel, Ω ⊂ R d and denotes the convolution operator. To motivate and illustrate our study, we show that this problem arises naturally in various practical image rendering problems such as stippling (representing an image with N dots) or continuous line drawing (representing an image with a continuous line). We provide a necessary and sufficient condition on the sequence (MN) N ∈N that ensures weak convergence of the projections (µ * N) N ∈N to π. We then provide a numerical algorithm to solve a discretized version of the problem and show several illustrations related to computer-assisted synthesis of artistic paintings/drawings.Lire moins >

Langue :

Anglais

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL