Journal of mathematical imaging and vision, 2013, Vol.45 (1), p.69-75
2013
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Details
- Autor(en) / Beteiligte
- Titel
- On the Compatibility of Granulometry with Wavelet Analysis
- Ist Teil von
- Journal of mathematical imaging and vision, 2013, Vol.45 (1), p.69-75
- Ort / Verlag
- Boston: Springer US
- Erscheinungsjahr
- 2013
- Quelle
- Alma/SFX Local Collection
- Beschreibungen/Notizen
- In this paper, regular closed Jordan measurable sets are proposed as models of digital images, and it is shown, that these are precisely the sets that are well approximated by their family of granulometric openings in measure theoretic sense. Moreover, compatibility of mathematical morphology and wavelet analysis is established in the following sense: two sets, that are indistinguishable by wavelets (i.e. their symmetric difference is a Lebesgue zero set) have undistinguishable granulometric openings, and a finite resolution wavelet approximation to a Jordan measurable set is sufficient to determine its granulometric openings up to a specified margin of error.
- Sprache
- Englisch
- Identifikatoren
- ISSN: 0924-9907eISSN: 1573-7683DOI: 10.1007/s10851-012-0345-zTitel-ID: cdi_crossref_primary_10_1007_s10851_012_0345_z
- Format
- –
- Schlagworte
- Applications of Mathematics, Applied sciences, Artificial intelligence, Computer Science, Computer science, control theory, systems, Exact sciences and technology, Image Processing and Computer Vision, Mathematical Methods in Physics, Pattern recognition. Digital image processing. Computational geometry, Signal,Image and Speech Processing