Abstract
Gabor feature space is elaborated for representation, processing and segmentation of textured images. As a first step of preprocessing of images represented in this space, we introduce an algorithm for Gabor feature space denoising. It is a geometric-based algorithm that applies diffusion-like equation derived from a minimal weighted area functional, introduced previously and applied in the context of stereo reconstruction models [6,12]. In a previous publication we have already demonstrated how to generalize the intensity-based geodesic active contours model to the Gabor spatial-feature space. This space is represented, via the Bel-trami framework, as a 2D Riemannian manifold embedded in a 6D space. In this study we apply the minimal weighted area method to smooth the Gabor space features prior to the application of the geodesic active contour mechanism. We show that this “Weighted Beltrami” approach preserves edges better than the original Beltrami diffusion. Experimental results of this feature space denoising process and of the geodesic active contour mechanism applied to the denoised feature space are presented.
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References
P. Brodatz, Textures: A photographic album for Artists and Designers, New York, NY, Dover, 1996.
V. Caselles and R. Kimmel and G. Sapiro, “Geodesic Active Contours”, International Journal of Computer Vision, 22(1), 1997, 61–97.
R. Conners and C. Harlow “A Theoretical Comparison of Texture Algorithms “IEEE Transactions on PAMI, 2, 1980, 204–222.
G.R. Cross and A.K. Jain, “Markov Random Field Texture Models“ IEEE Transactions on PAMI, 5, 1983, 25–39.
J.G. Daugman, “Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters “, J. Opt. Soc. Amer. 2(7), 1985, 1160–1169.
O. Faugeras and R. Keriven, “Variational Principles, surface evolution PDE’s, level set methods, and the stereo problem ” ,IEEE Trans. on Image Processing, 7(3), (1998) 336–344.
D. Gabor “Theory of communication “J. IEEE, 93, 1946, 429–459.
S. Geman and D. Geman “Stochastic relaxation, Gibbs distribution and the Bayesian restoration of images“, IEEE Transactions on PAMI, 6, 1984, 721–741.
B. Julesz “Texton Gradients: The Texton Theory Revisited“, Biol Cybern, 54, (1986) 245–251.
M. Kaas, A. Witkin and D. Terzopoulos, “Snakes: Active Contour Models“, International Journal of Computer Vision, 1, 1988, 321–331.
S. Kichenassamy, A. Kumar, P. Olver, A. Tannenbaum and A. Yezzi, “Gradient Flows and Geometric Active Contour Models”, Proceedings ICCV’95, Boston, Massachusetts, 1995, 810–815.
R. Kimmel, “3D Shape Reconstruction from Autostereograms and Stereo”, Special issue on PDEs in Image Processing, Computer Vision, and Computer Graphics, Journal of Visual Communication and Image Representation. In press.
R. Kimmel, N. Sochen and R. Malladi, “On the geometry of texture”, Proceedings of the 4th International conference on Mathematical Methods for Curves and Surfaces, St. Malo, 1999.
R. Kimmel and N. Sochen. “Orientation Diffusion or How to Comb a Porcupine?“, Special issue on PDEs in Image Processing, Computer Vision, and Computer Graphics, Journal of Visual Communication and Image Representation. In press.
T.S. Lee, “Image Representation using 2D Gabor-Wavelets“, IEEE Transactions on PAMI, 18(10), 1996, 959–971.
S. Marcelja, “Mathematical description of the response of simple cortical cells”, J. Opt. Soc. Amer., 70, 1980, 1297–1300.
J. Morlet, G. Arens, E. Fourgeau and D. Giard, “Wave propagation and sampling theory-part 2: sampling theory and complex waves”, Geophysics, 47(2), 1982, 222–236.
M. Porat and Y.Y. Zeevi, “The generalized Gabor scheme of image representation in biological and machine vision“, IEEE Transactions on PAMI, 10(4), 1988, 452–468.
M. Porat and Y.Y. Zeevi, “Localized texture processing in vision: Analysis and synthesis in the gaborian space“, IEEE Transactions on Biomedical Engineering, 36(1), 1989, 115–129.
S.J. Osher and J.A. Sethian, “Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations“, J of Computational Physics, 79, 1988, 12–49.
C. Sagiv, N. Sochen, and Y.Y. Zeevi, “Gabor Space Geodesic Active Contours”, G. Sommer, Y.Y. Zeevi (Eds.), Algebraic Frames for the Perception-Action Cycle, Lecture Notes in Computer Science, Vol. 1888, Springer, Berlin, 2000.
N. Sochen, R. Kimmel and R. Malladi, “A general framework for low level vision”, IEEE Trans. on Image Processing, 7, (1998) 310–318.
S.C. Zhu, Y.N. Wu and D.B. Mumford, “Equivalence of Julesz ensembles and FRAME models“, International Journal of Computer Vision, 38(3), 2000, 247–265.
M. Zibulski and Y.Y. Zeevi, “Analysis of multiwindow Gabor-type schemes by frame methods“, Applied and Computational Harmonic Analysis, 4, 1997, 188–221.
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Sagiv, C., Sochen, N.A., Zeevi, Y.Y. (2001). Gabor Feature Space Diffusion via the Minimal Weighted Area Method. In: Figueiredo, M., Zerubia, J., Jain, A.K. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2001. Lecture Notes in Computer Science, vol 2134. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44745-8_41
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DOI: https://doi.org/10.1007/3-540-44745-8_41
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