Measuring Shape Ellipticity

Aktaş, Mehmet; Žunić, Joviša

doi:10.1007/978-3-642-23672-3_21

Cited by 9 publications

(5 citation statements)

References 17 publications

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“…3(c). This is in line with numerous studies dealing with the quantification of shapes that emphasize the need for the use of several different shape descriptors (circularity, elipticity, orientability) [15,25,31]. This is conditioned by the fact that no descriptor is sufficiently reliable to perform shape characterization solely on the basis of it.…”

Section: Resultssupporting

confidence: 77%

“…For this analysis, a mathematical tool is needed to describe the shapes quantitatively. For this purpose, a number of shape descriptors are developed to answer the question of how much a shape is similar to the corresponding observed shape, such as a circle (circularity), a square (squareness), an ellipse (ellipticity), a triangle (triangularity), a rectangle (rectangularity) [8,[15][16][17][18][19][20][21][22][23][24][25][26][27]. In order to be useful, each of the shape descriptors should ensure that the appropriate measure is invariant with respect to translation, rotation and scaling.…”

Section: Introductionmentioning

confidence: 99%

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Nanoparticle shapes: Quantification by elongation, convexity and circularity measures

Kopanja

Lončar

Žunić

et al. 2019

Journal of Electrical Engineering

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The goal of the nanoparticle synthesis is, first of all, the production of nanoparticles that will be more similar in size and shape. This is very important for the possibility of studying and applying nanomaterials because of their characteristics that are very sensitive to size and shape such as, for example, magnetic properties. In this paper, we propose the shape analysis of the nanoparticles using three shape descriptors – elongation, convexity and circularity. Experimental results were obtained by using TEM images of hematite nanoparticles that were, first of all, subjected to segmentation in order to obtain isolated nanoparticles, and then the values of elongation, convexity and circularity were measured. Convexity Cx(S) is regarded as the ratio between shape’s area and area of the its convex hull. The convexity measure defines the degree to which a shape differs from a convex shape while the circularity measure defines the degree to which a shape differs from an ideal circle. The range of convexity and circularity values is (0, 1], while the range of elongation values is [1, ∞). The circle has lowest elongation (ε = 1), while it has biggest convexity and circularity values (Cx = 1; C = 1). The measures ε(S), Cx(S), C(S) proposed and used in the experiment have the few desirable properties and give intuitively expected results. None of the measures is good enough to describe all the shapes, and therefore it is suggested to use a variety of measures so that the shapes can be described better and then classify and control during the synthesis process.

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Section: Resultssupporting

confidence: 77%

Section: Introductionmentioning

confidence: 99%

Nanoparticle shapes: Quantification by elongation, convexity and circularity measures

Kopanja

Lončar

Žunić

et al. 2019

Journal of Electrical Engineering

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“…While center-of-mass motion is the standard quantity of which to keep track, , a good descriptor for shape is less obvious. Principal axes, moments, ellipticity, , and degree of asymmetry are some of the metrics that have been used to describe shapes. While each captures some important aspects of the shape, such single-number quantifications cannot describe internal degrees of freedom, such as twists and turns within the shape.…”

Section: Introductionmentioning

confidence: 99%

Extending Particle Tracking Capability with Delaunay Triangulation

Chen

Anthony²,

Granick³

2014

Langmuir

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Particle tracking, the analysis of individual moving elements in time series of microscopic images, enables burgeoning new applications, but there is need to better resolve conformation and dynamics. Here we describe the advantages of Delaunay triangulation to extend the capabilities of particle tracking in three areas: (1) discriminating irregularly shaped objects, which allows one to track items other than point features; (2) combining time and space to better connect missing frames in trajectories; and (3) identifying shape backbone. To demonstrate the method, specific examples are given, involving analyzing the time-dependent molecular conformations of actin filaments and λ-DNA. The main limitation of this method, shared by all other clustering techniques, is the difficulty to separate objects when they are very close. This can be mitigated by inspecting locally to remove edges that are longer than their neighbors and also edges that link two objects, using methods described here, so that the combination of Delaunay triangulation with edge removal can be robustly applied to processing large data sets. As common software packages, both commercial and open source, can construct Delaunay triangulation on command, the methods described in this paper are both computationally efficient and easy to implement.

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“…Nakon segmentacije potreban je matematički alat kojim bi se kvantitativno opisali oblici. Razvijaju se brojni deskriptori oblika koji daju odgovor na pitanje koliko je neki oblik sličan odgovarajućem posmatranom obliku kao što je krug (circularity), kvadrat (squareness), elipsa (ellipticity), trougao (triangularity), pravougaonik (rectangularity) [3,[10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Kako bi bio upotrebljiv svaki od deskriptora oblika treba da obezbedi da odgovarajuća mera bude invarijantna u odnosu na translaciju, rotaciju i skaliranje.…”

Section: Uvodunclassified

“…Rezultat algoritma segmentacije je devet izolovanih nanočestica hematita koje su prikazane na slici 4 i numerisane brojevima (1)(2)(3)(4)(5)(6)(7)(8)(9). S druge strane, treba naglasiti da bi za bolju karakterizaciju oblika korisno bilo uključiti i druge deskriptore (cirkularnost, eliptičnost, orijentabilnost) [10,21,[30][31]. Kao primer možemo navesti veoma sličnu vrednost izduženosti nanočestica N 7 i N 2 dok seoblici ovih nanočestica ipak prilično razlikuju te mera izduženosti ne može biti jedini deskriptor koji se pouzdano može koristiti za karakterizaciju oblika.…”

Section: Slika 3 Filtrirana Mikroskopska Slika Nanočestica Hematite unclassified

Quantifying the shape of nanoparticles: Segmentation and elongation measure

Kopanja¹,

Ivković²,

Lončar³

et al. 2017

Zas Mat

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Kvantifikovanje oblika nanočestica: segmentacija i mera izduženosti IZVOD UVODZbog velikih mogućnosti za primenu proučava-nje nanomaterijala zauzima veoma važno mesto u nauci o materijalima. Nanomaterijali su sistemi u kojima su veličine čestica manje od 100 nm. Smanjenjem veličine magnetnih čestica dolazi do promene magnetnih svojstava, tako da magnetni nanomaterijali pokazuju drugačija fizička svojstva: velika koercitivnost, superparamagnetizam, velika magnetna otpornost, niska ili visoka magnetizacija, smanjenje Kirijeve/Nelove temperature. Jedna od veoma važnih anizotropija nanočestica koja određuje magnetna svojstva nanočestičnog materijala je anizotropija oblika, koja je u direktnoj vezi sa oblikom nanočestica. Kod istih materijala vrednosti magnetnih parametara se mogu razlikovati i po desetak puta u zavisnosti od oblika nanočestica [1,2]. Uticaj oblika nanočestica na makroskopska magnetna svojstva nanomaterijala sve više se proučava u literaturi [3,4]. Kao jedno od važnih svojstava oblika izduženost oblika ima bitnu ulogu u razumevanju magnetnih svojstava nanočestičnih materijala (npr. poznato je da se koercitativnost *Autor za korespondenciju: Lazar Kopanja E-mail: kopanjal@yahoo.com Rad primljen: 29. 06. 2017. Rad prihvaćen: 30. 07. 2017 Rad je dostupan na sajtu: www.idk.org.rs/casopis povećava s povećanjem izduženosti). Stoga je pored merenja fizičkih svojstava veoma važno imati način za merenje oblika, odnosno dodeljivanje obliku kvantitativnih vrednosti na osnovu kojih se oni mogu porediti i klasifikovati.Polazna tačka za merenje oblika su mikroskopske slike nanočestičnih materijala koje se zatim analiziraju u cilju utvrđivanja kvantitativnih karakteristika nanočestica i njihovih međusobnih relacija. U postupcima analize slike segmentacija je jedan od prvih i najvažnijih koraka [5][6][7][8]. Kao deo naučne oblasti digitalne slike, koja zauzima sve veću primenu u različitim poljima istraživanja, segmentacija se ne može posmatrati bez uzimanja u obzir velikog boja parametara slike. Naime, za različite potrebe različito se definišu i segmenti, naravno, sve zavisno od situacije u kojoj se slika analizira. Nekada je bitno da se izdvoje samo svetliji delovi slike, pa je onda osnov za segmentaciju luminenca piksela. U drugom slučaju je bitno da se alaliziraju segmenti sa određenim koncentracijama boja, pa su tada RGB komponente osnov za segmentaciju [9]. Ovih primera ima mnogo, a svi oni se svrstavaju u prvi uslov za segmentaciju -zajednička karakteristika pojedinačnih segmenata. Drugi uslov za segmentaciju se definiše u neprekidnosti piksela koji kao prvi detektovani čini jedan segment. Odnosno, segment slike definiše grupa piksela sa

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Measuring Shape Ellipticity

Cited by 9 publications

References 17 publications

Nanoparticle shapes: Quantification by elongation, convexity and circularity measures

Nanoparticle shapes: Quantification by elongation, convexity and circularity measures

Extending Particle Tracking Capability with Delaunay Triangulation

Quantifying the shape of nanoparticles: Segmentation and elongation measure

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