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- 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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- Asplund, Teo, et al.
(författare)
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Mathematical Morphology on Irregularly Sampled Signals
- 2017
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Ingår i: Computer Vision – ACCV 2016 Workshops. - Cham : Springer. - 9783319544267 - 9783319544274 ; , s. 506-520
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Konferensbidrag (refereegranskat)abstract
- This paper introduces a new operator that can be used to ap-proximate continuous-domain mathematical morphology on irregularly sampled surfaces. We define a new way of approximating the continuous domain dilation by duplicating and shifting samples according to a flat continuous structuring element. We show that the proposed algorithm can better approximate continuous dilation, and that dilations may be sampled irregularly to achieve a smaller sampling without greatly com-promising the accuracy of the result.
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- Asplund, Teo
(författare)
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Precise Image-Based Measurements through Irregular Sampling
- 2019
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Mathematical morphology is a theory that is applicable broadly in signal processing, but in this thesis we focus mainly on image data. Fundamental concepts of morphology include the structuring element and the four operators: dilation, erosion, closing, and opening. One way of thinking about the role of the structuring element is as a probe, which traverses the signal (e.g. the image) systematically and inspects how well it "fits" in a certain sense that depends on the operator.Although morphology is defined in the discrete as well as in the continuous domain, often only the discrete case is considered in practice. However, commonly digital images are a representation of continuous reality and thus it is of interest to maintain a correspondence between mathematical morphology operating in the discrete and in the continuous domain. Therefore, much of this thesis investigates how to better approximate continuous morphology in the discrete domain. We present a number of issues relating to this goal when applying morphology in the regular, discrete case, and show that allowing for irregularly sampled signals can improve this approximation, since moving to irregularly sampled signals frees us from constraints (namely those imposed by the sampling lattice) that harm the correspondence in the regular case. The thesis develops a framework for applying morphology in the irregular case, using a wide range of structuring elements, including non-flat structuring elements (or structuring functions) and adaptive morphology. This proposed framework is then shown to better approximate continuous morphology than its regular, discrete counterpart.Additionally, the thesis contains work dealing with regularly sampled images using regular, discrete morphology and weighting to improve results. However, these cases can be interpreted as specific instances of irregularly sampled signals, thus naturally connecting them to the overarching theme of irregular sampling, precise measurements, and mathematical morphology.
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- Curic, Vladimir, et al.
(författare)
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Adaptive hit or miss transform
- 2015
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Ingår i: Mathematical Morphology and Its Applications to Signal and Image Processing. - Cham : Springer. - 9783319187198 ; , s. 741-752
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Konferensbidrag (refereegranskat)abstract
- The Hit or Miss Transform is a fundamental morphological operator, and can be used for template matching. In this paper, we present a framework for adaptive Hit or Miss Transform, where structuring elements are adaptive with respect to the input image itself. We illustrate the difference between the new adaptive Hit or Miss Transform and the classical Hit or Miss Transform. As an example of its usefulness, we show how the new adaptive Hit or Miss Transform can detect particles in single molecule imaging.
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- Curic, Vladimir, et al.
(författare)
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Salience adaptive structuring elements
- 2012
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Ingår i: IEEE Journal on Selected Topics in Signal Processing. - 1932-4553 .- 1941-0484. ; 6:7, s. 809-819
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Tidskriftsartikel (refereegranskat)abstract
- Spatially adaptive structuring elements adjust their shape to the local structures in the image, and are often defined by a ball in a geodesic distance or gray-weighted distance metric space. This paper introduces salience adaptive structuring elements as spatially variant structuring elements that modify not only their shape, but also their size according to the salience of the edges in the image. Morphological operators with salience adaptive structuring elements shift edges with high salience to a less extent than those with low salience. Salience adaptive structuring elements are less flexible than morphological amoebas and their shape is less affected by noise in the image. Consequently, morphological operators using salience adaptive structuring elements have better properties.
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