Abstract
We decompose images into “shapes”, based on connected components of level sets, which can be put in a tree structure. This tree contains the purely geometric information present in the image, sepa- rated from the contrast information. This structure allows to suppress easily some shapes without affecting the others, which yields a peculiar kind of scale-space, where the information present at each scale is already present in the original image.
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References
Meyer, Y.: Wavelets: Algorithms and Applications, SIAM, Philadelphia (1993)
Mallat, S.: A Wavelet Tour of Signal Processing, Academic Press (1998)
Alvarez, L., Guichard, F., Lions, P.L., Morel, J.M.: Axioms and Fundamental Equations of Image Processing, Arch. Rational Mech. and Anal., 16, 9 (1993) 200–257
Ed. Romeny, B.M. ter Haar: Geometry-Driven Diffusion in Computer Vision, Kluwer Academic Publishers (1994)
Marr, D.: Vision, Freeman and Co. (1982)
Hummel, R.A.: Representations Based on Zero-Crossing in Scale-Space, Proc. of CVPR. IEEE (1986) 204–209
Canny, J.: A Computational Approach to Edge Detection, IEEE Trans. on PAMI, 8, 6 (1986) 679–698
Nitzberg, M., Mumford, D.: The 2.1 Sketch, Proc. of ICCV, Osaka, Japan (1990)
Morel, J.M., Solimini, S.: Variational Methods in Image Processing, Birkhäuser (1994)
Koenderink, J.J.: The Structure of Images, Biological Cybernetics, 50 (1984) 363–370
Witkin, A.P.: Scale-Space Filtering, Proc. of IJCAI, Karlsruhe (1983) 1019–1022
Matheron, G.: Random Sets and Integral Geometry, John Wiley, N.Y. (1975)
Serra, J.: Image Analysis and Mathematical Morphology, Academic Press (1982)
Caselles, V., Coll, B., Morel, J.M.: Topographic Maps, preprint CMLA (1997)
Monasse, P., Guichard, F.: Fast Computation of a Contrast-Invariant Image Representation, Preprint CMLA 9815, available from http://www.cmla.ens-cachan.fr/index.html (1998)
Guichard, F., Morel, J.M.: Partial Differential Equations and Image Iterative Filtering, Tutorial ICIP, Washington D.C. (1995)
Guichard, F., Morel, J.M.: Partial Differential Equations and Image Iterative Filtering, State of the Art in Numerical Analysis (1996)
Vincent, L.: Grayscale Area Openings and Closings, Their Efficient Implementation and Applications, Proc. of 1st Workshop on Math. Morphology and its Appl. to Signal Proc., J. Serra and Ph. Salembrier, Eds. (1993) 22–27
Masnou, S., Morel, J.M.: Image Restoration Involving Connectedness, Proc. of the 6th Int. Workshop on Digital I.P. and Comp. Graphics, SPIE 3346, Vienna, Austria (1998)
Monasse, P.: Contrast Invariant Image Registration, Proc. of ICASSP, Vol. 6, (1999) 3221–3224
Monasse, P.: An Inclusion Tree Describing the Topological Structure of an Image, in preparation
Cheng, F., Venetsanopoulos, A.N.: An Adaptive Morphological Filter for Image Processing, IEEE Trans. on PAMI, Vol. 1, 4 (1992) 533–539
Andrew Bangham, J., Ling, P.D., Harvey, R.: Scale-Space from Nonlinear Filters, IEEE Trans. on PAMI, Vol. 18, 5 (1996) 520–528
Andrew Bangham, J., Ling, P.D., Harvey, R., Aldridge, R.V.: Morphological Scale-Space Preserving Transforms in Many Dimensions, Journal of Electronic Imaging, Vol. 5, 3 (1996) 283–299
Caselles, V., Coll, B., Morel, J.M.: Is Scale-Space Possible?, Proc. of the 1st Workshop on Scale-Space Theories in Computer Vision, Utrecht, the Netherlands (1997)
Guichard, F., Morel, J.M.: Image Iterative Filtering, Lecture Notes of Institut Henri Poincaré (1998)
Kong, T.Y., Rosenfeld, A.: Digital Topology: Introduction and Survey, CVGIP, Vol. 48, 3 (1989) 357–393
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Monasse, P., Guichard, F. (1999). Scale-Space from a Level Lines Tree. In: Nielsen, M., Johansen, P., Olsen, O.F., Weickert, J. (eds) Scale-Space Theories in Computer Vision. Scale-Space 1999. Lecture Notes in Computer Science, vol 1682. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48236-9_16
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DOI: https://doi.org/10.1007/3-540-48236-9_16
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