Restauração e Análise de Imagens via Equações Diferenciais Parciais
DOI:
https://doi.org/10.5540/tema.2002.03.02.0001Abstract
O uso de equações diferenciais parciais em processamento de imagens tem sido amplamente usado nos últimos anos. A idéia básica é a de modificar uma dada imagem inicial u(x; t) via uma equação diferencial parcial e obter os resultados esperados como a solução desta equação. Apresentamos aqui uma descrição dos principais modelos não lineares para suavização, eliminação de ruídos e detecção de bordas em imagens. Abordamos modelos que têm por base os métodos variacionais bem como os de fluxo geométrico. São também abordados os principais aspectos da implementação computacional dos modelos.References
[1] L. Alvarez, P.L. Lions e J.M. Morel, Image selective smoothing and edge detection by nonlinear diffusion, SIAM J. Numer. Anal., 29 (1992), 845-866.
L. Ambrosio e V.M. Tortorelli, On the approximation of free discontinuity problems, Boll. Un. Mat. Ital., 7, No. 6-B (1992), 105-123.
C.A.Z. Barcelos, M. Boaventura e E.C. Silva Jr, A well-balanced flow equation for noise removal and edge detection, submetido para publicação.
C.A.Z. Barcelos e Y. Chen, Heat flows and related minimization problem in image restoration, Computers and Mathematics with Applications, 39 (2000), 81-97.
J.F. Canny, A computational approach to edge detection, IEEE Trans. Pattern Analysis and Machine Intelligence, 8 (1986), 679-698.
V.Caselle, F.Catté, T.Cool e Dibos, A geometric model for active contourns in image processing. Numerische Mathematik, 66 (1993), 1-31.
A. Chambolle e P.L. Lions, Image recovery via total variation minimization and related problems, Numerische Mathematik, 76 (1997), 167-188.
Y. Chen, B.C. Vemuri e L. Wang, Image denoising and segmentation via nonlinear diffusion, Comput. Math. Appl., 39 (2000), 131-149.
L.C. Evans e J. Spruck, Motion of level sets by mean curvature, I. J. Differ. Geom., 33 (1991).
F. Guichard e J.M. Morel, Image iterative smoothing and PDE’s - School on Mathematica Problems in Image Processing, ICTP, Trieste, It., (2000), 305.
J. Malik e P. Perona, Scale-space and edge detection using anisotropic diffusion, IEEE TPAMI, 12, No. 7 (1990), 629-639.
D. Marr e E. Hildreth, Theory of edge detection, Proc. Royal Soc. Lond., B 207 (1980), 187-217.
J.M. Morel e S. Solimini, “Variational Methods in Image Segmentation”, Birkha¨auser, Boston, 1995.
S. Osher e J. Sethian, Fronts propagating with curvature depend. Algorithms based on the Hamilton-Jacobi formulation, J. Comput. Phys., 79 (1988), 12-49.
L. Rudin, S. Osher e E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D, 60 (1992), 259-268.
J.A. Sethian, “Level Set Methods”, Cambridge University Press, 1996.
J. Shah, A common framework for curve evolution, segmentation and anisotropic diffusion, “IEEE Conf. on Computer Vision and Pattern Recognition”, 1996.
A.J. Tabatabai and O.R. Mitchel, Edge location to subpixel values in digital imagery, IEEE Trans. on Pattern Analysis and Machine Intelligence, 6, No. 2 (1984), 188-201.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish in this journal agree to the following terms:
Authors retain copyright and grant the journal the right of first publication, with the work simultaneously licensed under the Creative Commons Attribution License that allows the sharing of the work with acknowledgment of authorship and initial publication in this journal.
Authors are authorized to assume additional contracts separately, for non-exclusive distribution of the version of the work published in this journal (eg, publish in an institutional repository or as a book chapter), with acknowledgment of authorship and initial publication in this journal.
Authors are allowed and encouraged to publish and distribute their work online (eg, in institutional repositories or on their personal page) at any point before or during the editorial process, as this can generate productive changes as well as increase impact and the citation of the published work (See The effect of open access).
This is an open access journal which means that all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles, or use them for any other lawful purpose, without asking prior permission from the publisher or the
author. This is in accordance with the BOAI definition of open access
Intellectual Property
All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License under attribution BY.