Sparse convolution-based digital derivatives, fast estimation for noisy signals and approximation results - Université Clermont Auvergne Accéder directement au contenu
Article Dans Une Revue Theoretical Computer Science Année : 2016

Sparse convolution-based digital derivatives, fast estimation for noisy signals and approximation results

Résumé

We provide a general notion of a Digital Derivative in 1−dimensional grids, which has real or integer-only versions. From any such masks, a family of masks called skipping masks are defined. We prove general results of multigrid convergence for skipping masks. We propose a few examples of digital derivative masks, including the now well-known binomial mask. The corresponding skipping masks automatically have multigrid convergence properties. We study the cases of parametric curves tangents and curvature. We propose a novel interpretation of digital convolutions as computing points on a smooth curve, the regularity of which depends on the mask. We establish, in the case of binomial and B−spline masks, a close relationship between the derivatives of the smooth curve, and the digital derivatives provided by the mask.
Fichier principal
Vignette du fichier
article-vFinale.pdf (854.57 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01296759 , version 1 (01-04-2016)

Identifiants

Citer

Henri-Alex Esbelin, Rémy Malgouyres. Sparse convolution-based digital derivatives, fast estimation for noisy signals and approximation results. Theoretical Computer Science, 2016, 624, pp.2-24. ⟨10.1016/j.tcs.2015.12.018⟩. ⟨hal-01296759⟩
336 Consultations
259 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More