Abstract
This paper presents a decomposition scheme for a large class of greyscale structuring elements from mathematical morphology. In contrast with many existing decomposition schemes, our method is valid in the continuous domain. Conditions are given under which this continuous method can be properly discretized. The class of functions that can be decomposed with our method contains the class of quadratic functions, that are of major importance in, for instance, distance transforms and morphological scale space. In the continuous domain, the size of the structuring elements resulting from the decomposition, can be chosen arbitrarily small. For functions from the mentioned class, that can be separated along the standard image axes, a discrete decomposition in 3 × 3 elements can be guaranteed.
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© 2002 Kluwer Academic/Plenum Publishers
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Van Den Boomgaard, R., Engbers, E.A., Smeulders, A.W.M. (2002). Decomposition of Separable Concave Structuring Functions. 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_4
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DOI: https://doi.org/10.1007/0-306-47025-X_4
Publisher Name: Springer, Boston, MA
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