Abstract
This paper proposes a general algebraic definition for image scale-spaces. The basic idea is to first downscale the image by a factor t using an invertible scaling, then apply an image operator at a unit scale, and finally resize the image to its original scale. It is then required that the resulting one-parameter family of image operators satisfies some semigroup property. In this paper only the morphological erosions are considered. In this case, classical tools from convex analysis play an important role.
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© 2002 Kluwer Academic/Plenum Publishers
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Van Den Boomgaard, R., Heijmans, H.J.A.M. (2002). Morphological Scale-Space Operators: An Algebraic Framework. In: Goutsias, J., Vincent, L., Bloomberg, D.S. (eds) Mathematical Morphology and its Applications to Image and Signal Processing. Computational Imaging and Vision, vol 18. Springer, Boston, MA. https://doi.org/10.1007/0-306-47025-X_31
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DOI: https://doi.org/10.1007/0-306-47025-X_31
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-7923-7862-4
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