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.
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