uu.seUppsala University Publications

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Precise Image-Based Measurements through Irregular SamplingPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2019 (English)Doctoral thesis, comprehensive summary (Other academic)Alternative title
##### Description

##### Abstract [en]

##### 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 [en]

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: urn:nbn:se:uu:diva-395205ISBN: 978-91-513-0783-1 (print)OAI: oai:DiVA.org:uu-395205DiVA, id: diva2:1361810
##### Public defence

2019-12-06, Room 2446, ITC, Lägerhyddsvägen 2, Uppsala, 13:00 (English)
##### Opponent

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##### Supervisors

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#####

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##### Funder

Swedish Research Council, 2014-5983Available from: 2019-11-13 Created: 2019-10-17 Last updated: 2019-11-13
##### List of papers

Noggranna bildbaserade mätningar via irreguljär sampling (Swedish)

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.

1. Mathematical morphology on irregularly sampled data in one dimension$(function(){PrimeFaces.cw("OverlayPanel","overlay1168876",{id:"formSmash:j_idt687:0:j_idt697",widgetVar:"overlay1168876",target:"formSmash:j_idt687:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Mathematical Morphology on Irregularly Sampled Signals$(function(){PrimeFaces.cw("OverlayPanel","overlay1053063",{id:"formSmash:j_idt687:1:j_idt697",widgetVar:"overlay1053063",target:"formSmash:j_idt687:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Mathematical Morphology on Irregularly Sampled Data Applied to Segmentation of 3D Point Clouds of Urban Scenes$(function(){PrimeFaces.cw("OverlayPanel","overlay1333651",{id:"formSmash:j_idt687:2:j_idt697",widgetVar:"overlay1333651",target:"formSmash:j_idt687:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. Adaptive Mathematical Morphology on Irregularly Sampled Signals in Two Dimensions$(function(){PrimeFaces.cw("OverlayPanel","overlay1361042",{id:"formSmash:j_idt687:3:j_idt697",widgetVar:"overlay1361042",target:"formSmash:j_idt687:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

5. Estimating the Gradient for Images with Missing Samples Using Elliptical Structuring Elements$(function(){PrimeFaces.cw("OverlayPanel","overlay1361037",{id:"formSmash:j_idt687:4:j_idt697",widgetVar:"overlay1361037",target:"formSmash:j_idt687:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

6. A Faster, Unbiased Path Opening by Upper Skeletonization and Weighted Adjacency Graphs$(function(){PrimeFaces.cw("OverlayPanel","overlay1051614",{id:"formSmash:j_idt687:5:j_idt697",widgetVar:"overlay1051614",target:"formSmash:j_idt687:5:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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