Abstract
A morphological scale-space representation is presented based on a morphological strong filter, the levelings. The scale-properties are analysed and illustrated. From one scale to the next, details vanish, but the contours of the remaining objects are preserved sharp and perfectly localised. This paper is followed by a companion paper on pde formula- tions of levelings.
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R.A. Hummel and B.C. Gidas. Zero crossings and the heat equation. Technical report, New York Univ., Courant Institute of Math. Sciences, Computer Science Division, 1984.
J.J Koenderink. The structure of images. Biol. Cybern., 50:363–370, 1984.
T. Lindeberg. On scale selection for differential operators. In B. Braathen K. Heia, K.A. Hogdra, editor, Proc. 8th Scandinavian Conf. Image Analysis, Trømso, Norway, 1993. Norwegian Society for Image Processing and Pattern Recognition.
M. Baudin J. Babaud, A.P. Witkin and R.O. Duda. Uniqueness of the gaussian kernel for scale-space filtering. IEEE Trans. Pattern Analysis and Machine Intelligence, 8(1):26–33, 1986.
P. Perona and J. Malik. Scale space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Machine Intell., pages 629–639, July 1989.
J. Weickert. Theoretical Foundations of Anisotropic Diffusion in Image Processing, volume 11 of Computing Supplement, pages 221–246. Springer, 1996.
P.T. Jackway and M. Deriche. Scale-space properties of multiscale morphological dilation-erosion. IEEE Trans. Pattern Analysis and Machine Intelligence, 18(1):38–51, 1996.
G. Matheron. Random Sets and Integral Geometry. New York: Wiley, 1975.
P. Maragos. Pattern spectrum and multiscale shape representation. IEEE Trans. Pattern Analysis and Machine Intelligence, 11:701–716, 1989.
J. Serra. Mathematical Morphology: Vol. II, chapter Alternating Sequential Filters. London: Academic Press, 1988.
L. Vincent. Morphological grayscale reconstruction in image analysis: Applications and efficient algorithms. IEEE Trans. in Image Procesing, 1993.
G. Matheron. Les nivellements. Technical report, Centre de Morphologie Mathématique, 1997.
F. Meyer. From connected operators to levelings. In H. Heijmans and J. Roerdink, editors, Mathematical Morphology and its Applications to Image and Signal Processing, pages 191–199. Kluwer, 1998.
F. Meyer. The levelings. In H. Heijmans and J. Roerdink, editors, Mathematical Morphology and Its Applications to Image Processing, pages 199–207. Kluwer, 1998.
J. Serra. Quelques propriétés des nivellements. Technical Report 30/98/MM, CMM, 1998.
P. Salembier and J. Serra. Flat zone filtering, connected operators and filters by reconstruction. IEEE Trans. Image Processing, 4:1153–1160, Aug. 1995.
J. Serra. Set connectons and discrete filtering. In M. Couprie G. Bertrand and L. Perroton, editors, Discrete Geometry for Computer Imagery, Lecture Notes in Computer Science 1568, pages 191–207. Springer, 1999.
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Meyer, F., Maragos, P. (1999). Morphological Scale-Space Representation with Levelings. 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_17
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DOI: https://doi.org/10.1007/3-540-48236-9_17
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