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Mathematical Morphology on Irregularly Sampled Data in One Dimension
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction.ORCID iD: 0000-0002-0612-558X
(Flagship Biosciences Inc, Colorado, USA.)
(LuleƄ tekniska universitet)
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction.
(English)In: Mathematical Morphology - Theory and Applications, ISSN 2353-3390Article in journal (Refereed) Accepted
Abstract [en]

Mathematical morphology (MM) on grayscale images is commonly performed in the discrete domainon regularly sampled data. However, if the intention is to characterize or quantify continuous-domainobjects, then the discrete-domain morphology is affected by discretization errors that may be alleviated byconsidering the underlying continuous signal. Given a band-limited image, for example, a real image projectedthrough a lens system, which has been correctly sampled, the continuous signal may be reconstructed.Using information from the continuous signal when applying morphology to the discrete samples can thenaid in approximating the continuous morphology. Additionally, there are a number of applications where MMwould be useful and the data is irregularly sampled. A common way to deal with this is to resample the dataonto a regular grid. Often this creates problems where data is interpolated in areas with too few samples. Inthis paper, an alternative way of thinking about the morphological operators is presented. This leads to a newtype of discrete operators that work on irregularly sampled data. These operators are shown to be morphologicaloperators that are consistent with the regular, morphological operators under the same conditions,and yield accurate results under certain conditions where traditional morphology performs poorly.

Place, publisher, year, edition, pages
De Gruyter Open.
Keywords [en]
Irregular sampling, One-dimensional, Continuous morphology.
National Category
Signal Processing
Research subject
Computerized Image Processing
Identifiers
URN: urn:nbn:se:uu:diva-337288DOI: 10.1515/mathm-2017-0001OAI: oai:DiVA.org:uu-337288DiVA, id: diva2:1168876
Funder
Swedish Research Council, 2014-5983Available from: 2017-12-21 Created: 2017-12-21 Last updated: 2018-01-22

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