Abstract
All morphological transformations discussed so far involved combinations of one input image with specific structuring elements. The approach taken with geodesic transformations is to consider two input images. A morphological transformation is applied to the first image and it is then forced to remain either greater or lower to the second image. Authorised morphological transformations are restricted to elementary erosions and dilations. The choice of specific structuring elements is therefore eluded. In practice, geodesic transformations are iterated until stability making the choice of a size unnecessary. It is actually the combination of appropriate pairs of input images which produces new morphological primitives. These primitives are at the basis of formal definitions of many important image structures for both binary and grey scale images.
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Bibliographical notes and references
Beucher, S. (1990), Segmentation d’images et morphologie mathématique, PhD thesis, Ecole des Mines de Paris.
Breen, E. & Jones, R. (1996), ‘Attribute openings, thinnings, and granulometries’, Computer Vision and Image Understanding 64 (3), 377–389.
Canny, J. (1986), ‘A computational approach to edge detection’, IEEE Transactions on Pattern Analysis and Machine Intelligence 8 (6), 679–698.
Goetcherian, V. (1980), ‘From binary to grey tone image processing using fuzzy logic concepts’, Pattern Recognition 12, 7–15.
Grimaud, M. (1991), Géodésie numérique en morphologie mathématique. Application à la détection automatique de microcalcifications en mammographies numériques, PhD thesis, Ecole des Mines de Paris.
Grimaud, M. (1992), New measure of contrast: dynamics, in P. Gader, E. Dougherty & J. Serra, eds, ‘Image algebra and morphological image processing III’, Vol. SPIE-1769, pp. 292–305.
Hanusse, P. & Guillataud, P. (1991), Sémantique des images par analyse dendronique, in ‘Reconnaissance des Formes et Intelligence Artificielle’, AFCET, pp. 577–588.
Jochems, T. (1994), Morphologie mathématique appliquée au contrôle industriel de pièces coulées, PhD thesis, Ecole des Mines de Paris.
Meyer, F. & Beucher, S. (1990), ‘Morphological segmentation’, Journal of Visual Communication and Image Representation 1 (1), 21–46.
Soille, P. (1991), ‘Spatial distributions from contour lines: an efficient methodology based on distance transformations’, Journal of Visual Communication and Image Representation 2 (2), 138–150.
Soille, P. & Ansoult, M. (1990), ‘Automated basin delineation from digital elevation models using mathematical morphology’, Signal Processing 20, 171–182.
Soille, P. & Gratin, C. (1994), ‘An efficient algorithm for drainage networks extraction on DEMs’, Journal of Visual Communication and Image Representation 5 (2), 181–189.
Vincent, L. (1993), ‘Morphological grayscale reconstruction in image analysis: applications and efficient algorithms’, IEEE Transactions on Image Processing 2 (2), 176–201.
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© 1999 Springer-Verlag Berlin Heidelberg
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Soille, P. (1999). Geodesic Transformations. In: Morphological Image Analysis. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03939-7_6
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DOI: https://doi.org/10.1007/978-3-662-03939-7_6
Publisher Name: Springer, Berlin, Heidelberg
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