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Mathematical Morphology on Irregularly Sampled Signals
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.ORCID iD: 0000-0002-0612-558x
Flagship Biosciences Inc., Westminster, USA.
Luleå University of Technology, Luleå, Sweden.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.
2017 (English)In: Computer Vision – ACCV 2016 Workshops. ACCV 2016, Springer, 2017, Vol. 10117, p. 506-520Conference paper, Published paper (Refereed)
Abstract [en]

This paper introduces a new operator that can be used to approximate 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 compromising the accuracy of the result.

Place, publisher, year, edition, pages
Springer, 2017. Vol. 10117, p. 506-520
Series
Lecture Notes in Computer Science, ISSN 0302-9743, E-ISSN 1611-3349 ; 10117
National Category
Computer Sciences Computational Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-309921DOI: 10.1007/978-3-319-54427-4_37ISI: 000426193700037ISBN: 978-3-319-54427-4 (electronic)ISBN: 978-3-319-54426-7 (print)OAI: oai:DiVA.org:uu-309921DiVA, id: diva2:1053063
Conference
13th Asian Conference on Computer Vision (ACCV), Taipei, Taiwan, November 20-24, 2016
Funder
Swedish Research Council, 2014-5983Available from: 2016-12-08 Created: 2016-12-08 Last updated: 2019-10-17Bibliographically approved
In thesis
1. Precise Image-Based Measurements through Irregular Sampling
Open this publication in new window or tab >>Precise Image-Based Measurements through Irregular Sampling
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Alternative title[sv]
Noggranna bildbaserade mätningar via irreguljär sampling
Abstract [en]

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.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2019. p. 63
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1869
Keywords
image analysis, image processing, mathematical morphology, irregular sampling, adaptive morphology, missing samples, continuous morphology, path opening.
National Category
Signal Processing Other Computer and Information Science
Research subject
Computerized Image Processing
Identifiers
urn:nbn:se:uu:diva-395205 (URN)978-91-513-0783-1 (ISBN)
Public defence
2019-12-06, Room 2446, ITC, Lägerhyddsvägen 2, Uppsala, 13:00 (English)
Opponent
Supervisors
Funder
Swedish Research Council, 2014-5983
Available from: 2019-11-13 Created: 2019-10-17 Last updated: 2019-11-13

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Asplund, Teo

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