| 1. |
- Asplund, Teo, et al.
(författare)
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Adaptive Mathematical Morphology on Irregularly Sampled Signals in Two Dimensions
- 2020
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Ingår i: Mathematical Morphology : Theory and Applications. - : Walter de Gruyter. - 2353-3390. ; 4:1, s. 108-126
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Tidskriftsartikel (refereegranskat)abstract
- This paper proposes a way of better approximating continuous, two-dimensional morphologyin the discrete domain, by allowing for irregularly sampled input and output signals. We generalizeprevious work to allow for a greater variety of structuring elements, both flat and non-flat. Experimentallywe show improved results over regular, discrete morphology with respect to the approximation ofcontinuous morphology. It is also worth noting that the number of output samples can often be reducedwithout sacrificing the quality of the approximation, since the morphological operators usually generateoutput signals with many plateaus, which, intuitively do not need a large number of samples to be correctlyrepresented. Finally, the paper presents some results showing adaptive morphology on irregularlysampled signals.
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| 2. |
- Asplund, Teo, et al.
(författare)
-
Mathematical Morphology on Irregularly Sampled Data in One Dimension
- 2017
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Ingår i: Mathematical Morphology : Theory and Applications. - : Walter de Gruyter. - 2353-3390. ; 2:1, s. 1-24
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Tidskriftsartikel (refereegranskat)abstract
- Mathematical morphology (MM) on grayscale images is commonly performed in the discretedomain on regularly sampled data. However, if the intention is to characterize or quantify continuousdomainobjects, then the discrete-domain morphology is affected by discretization errors that may bealleviated by considering the underlying continuous signal, given a correctly sampled bandlimited image.Additionally, there are a number of applications where MM would be useful and the data is irregularlysampled. A common way to deal with this is to resample the data onto a regular grid. Often this createsproblems where data is interpolated in areas with too few samples. In this paper, an alternative way ofthinking about the morphological operators is presented. This leads to a new type of discrete operatorsthat work on irregularly sampled data. These operators are shown to be morphological operators thatare consistent with the regular, morphological operators under the same conditions, and yield accurateresults under certain conditions where traditional morphology performs poorly
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