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Titolo:
Edge direction preserving image zooming: A mathematical and numerical analysis
Autore:
Malgouyres, F; Guichard, F;
Indirizzi:
ENS Cachan, CMLA, F-94235 Cachan, France ENS Cachan Cachan France F-94235 NS Cachan, CMLA, F-94235 Cachan, France Poseidon Technol, F-92100 Boulogne, France Poseidon Technol Boulogne France F-92100 chnol, F-92100 Boulogne, France
Titolo Testata:
SIAM JOURNAL ON NUMERICAL ANALYSIS
fascicolo: 1, volume: 39, anno: 2001,
pagine: 1 - 37
SICI:
0036-1429(20010323)39:1<1:EDPIZA>2.0.ZU;2-2
Fonte:
ISI
Lingua:
ENG
Soggetto:
BOUNDED VARIATION; RECONSTRUCTION; REGULARIZATION; INTERPOLATION; RESTORATION; ALGORITHMS;
Keywords:
image reconstruction; image restoration; image interpolation; Fourier analysis; variational methods; total variation; numerical approximation;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Citazioni:
30
Recensione:
Indirizzi per estratti:
Indirizzo: Malgouyres, F ENS Cachan, CMLA, 61 Ave President Wilson, F-94235 Cachan, France ENS Cachan 61 Ave President Wilson Cachan France F-94235 ce
Citazione:
F. Malgouyres e F. Guichard, "Edge direction preserving image zooming: A mathematical and numerical analysis", SIAM J NUM, 39(1), 2001, pp. 1-37

Abstract

We focus in this paper on some reconstruction/restoration methods whose aim is to improve the resolution of digital images. The main point here is tostudy the ability of such methods to preserve one-dimensional (1D) structures. Indeed, such structures are important since they are often carried by the image edges. First we focus on linear methods, give a general frameworkto design them, and show that the preservation of 1D structures pleads in favor of the cancellation of the periodization of the image spectrum. More precisely, we show that preserving 1D structures implies the linear methodsto be written as a convolution of the sinc interpolation. As a consequence, we cannot cope linearly with Gibbs effects, sharpness of the results, andthe preservation of the 1D structure. Second, we study variational nonlinear methods and, in particular, the one based on total variation. We show that this latter permits us to avoid these shortcomings. We also prove the existence and consistency of an approximate solution to this variational problem. At last, this theoretical study is highlighted by experiments, both onsynthetic and natural images, which show the effects of the described methods on images as well as on their spectrum.

ASDD Area Sistemi Dipartimentali e Documentali, Università di Bologna, Catalogo delle riviste ed altri periodici
Documento generato il 26/01/20 alle ore 22:16:22