Double-sided probing by map of Asplund's distances using Logarithmic Image Processing in the framework of Mathematical Morphology
| Autor: | Noyel, Guillaume, Jourlin, Michel |
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| Rok vydání: | 2017 |
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| Zdroj: | 13th International Symposium on Mathematical Morphology, ISMM 2017, May 2017, Fontainebleau, France. Springer International Publishing, pp.408-420, 2017, Mathematical Morphology and Its Applications to Signal and Image Processing: 13th International Symposium, ISMM 2017, Fontainebleau, France, May 15--17, 2017, Proceedings. http://cmm.ensmp.fr/ismm2017/ |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/978-3-319-57240-6_33 |
| Popis: | We establish the link between Mathematical Morphology and the map of Asplund's distances between a probe and a grey scale function, using the Logarithmic Image Processing scalar multiplication. We demonstrate that the map is the logarithm of the ratio between a dilation and an erosion of the function by a structuring function: the probe. The dilations and erosions are mappings from the lattice of the images into the lattice of the positive functions. Using a flat structuring element, the expression of the map of Asplund's distances can be simplified with a dilation and an erosion of the image; these mappings stays in the lattice of the images. We illustrate our approach by an example of pattern matching with a non-flat structuring function. Comment: The final publication is available at link.springer.com |
| Databáze: | arXiv |
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