Measu emen Science and Technology
Meas. Sci. Technol. 32 (2021) 122001 (17pp) h ps://doi.o g/10.1088/1361-6501/ac1b40
Topical Re iew
Re iew o po osi y unce ain y
es ima ion me hods in compu ed
omog aphy da ase
Vic o y A J Jaques1, An on Du Plessis2, Ma ek Zemek1, Jakub Šalplach a1,
Zuzana S ubiano ´
a1, Tom´
aš Zikmund1,∗and Joze Kaise 1
1CEITEC—Cen al Eu opean Ins i u e o Technology, B no Uni e si y o Technology, Pu kyˇ
no a 123,
B no 612 00, Czech Republic
2Resea ch G oup 3D Inno a ion, S ellenbosch Uni e si y, S ellenbosch 7602, Sou h A ica
E-mail: [email p o ec ed].cz
Recei ed 15 June 2021, e ised 28 July 2021
Accep ed o publica ion 6 Augus 2021
Published 23 Augus 2021
Abs ac
X- ay compu ed omog aphy is a common ool o non-des uc i e es ing and analysis. One
majo applica ion o his imaging echnique is 3D po osi y iden i ica ion and quan i ica ion,
which in ol es image segmen a ion o he analysed da ase . This segmen a ion s ep, which is
mos commonly pe o med using a global h esholding algo i hm, has a majo impac on he
esul s o he analysis. The e o e, a ho ough desc ip ion o he wo k low and a gene al
unce ain y es ima ion should be p o ided alongside he esul s o po osi y analysis o ensu e a
ce ain le el o con idence and ep oducibili y. A e iew o cu en li e a u e in he ield shows
ha a su icien wo k low desc ip ion and an unce ain y es ima ion o he esul a e o en
missing. This wo k p o ides ecommenda ions on how o epo he p ocessing s eps o
po osi y e alua ion in compu ed omog aphy da a using global h esholding, and e iews he
me hods o he es ima ion o he gene al unce ain y in po osi y measu emen s.
Keywo ds: compu ed omog aphy, po osi y e alua ion, unce ain y es ima ion,
esul s compa ison, segmen a ion , global h esholding
(Some igu es may appea in colou only in he online jou nal)
1. In oduc ion
Po ous ma e ials and samples a e common in a wide ange o
scien i ic ields. Fo ins ance, pe meabili y and ese oi cha -
ac e is ics o po ous ocks a e use ul pa ame e s in he oil and
∗Au ho o whom any co espondence should be add essed.
O iginal Con en om his wo k may be used unde he
e ms o he C ea i e Commons A ibu ion 4.0 licence. Any
u he dis ibu ion o his wo k mus main ain a ibu ion o he au ho (s) and
he i le o he wo k, jou nal ci a ion and DOI.
gas indus y and ela ed luid esea ch [1], whe eas in pale-
on ology, he shape and olume o po es a e used o iden i y
ossils [2]. Po osi y analysis is also widely used in enginee -
ing [3], manu ac u ing [4,5], o ma e ial de elopmen [6] as
an indica o o a ma e ial’s s eng h [7]. Po es in me als o en
indica e c ack ini ia ion loca ions in cyclic loading applica-
ions, and hey e en in luence s a ic s eng h and duc ili y o
ma e ials, making non-des uc i e po osi y es ing aluable o
quali y con ol pu poses [8,9].
Gene ally, po osi y e e s o a measu emen o he p es-
ence o oids wi hin a sample. Allaby [10] de ines po es as
oids ha can be emp y o illed wi h apped gas and/o luids,
and su ounded by any ype o ma e ial. Using his de ini ion,
1361-6501/21/122001+17$33.00 1 © 2021 The Au ho (s). Published by IOP Publishing L d P in ed in he UK
Meas. Sci. Technol. 32 (2021) 122001 Topical Re iew
po osi y is he olume o all po es p esen in a sample [10]. I
is commonly exp essed as a pe cen age o emp y space wi hin
he o al olume o an objec [11]:
Po osi y [%] = Volume o po es
Volume o solid (incl.po es)×100.(1)
The shape and olume o po es is connec ed o he ma e -
ial’s o ma ion, empe a u e, en i onmen and ype [12]. Po es
can be cylind ical, sli s, conical, sphe ical, ink bo le-like,
and in e s i ial [13], bu hey can also ea u e mo e complex
shapes. Po es can o m ne wo ks ha may o may no be
accessible om he ou side o he objec (open po osi y), o
hey can be isola ed (closed po osi y) [14]. Po e cha ac e is -
ics in luence bulk densi y, mechanical s eng h, and he mal
conduc i i y o objec s [8].
Va ious me hods can be used o analyze he po osi y o a
sample. The choice o a me hod depends on he ype o po os-
i y p esen in he pa icula sample, as well as on o he pa a-
me e s. X- ay compu ed omog aphy (CT) is among he mos
widesp ead and b oadly applicable me hods. CT is an imaging
modali y which is based on he abso p ion o x- ays in ma e -
ials [15], and makes non-des uc i e h ee-dimensional ana-
lysis o samples and hei in e nal s uc u es possible [16]. The
ou pu o a ypical CT measu emen is a se o c oss-sec ional
slices s acked in a 3D olume ( igu e 1S eps 1 and 2). This
o ms a g id o oxels, which a e olume ic elemen s wi h
a speci ic g ay alue de e mined by he densi y and a omic
numbe o ma e ials con ained wi hin, and he x- ay ene gy
used [17]. The edge leng h o a oxel in luences he bes pos-
sible esolu ion o a measu emen . The scanning, omog aphic
econs uc ion, and subsequen analysis o a CT da ase a e all
po en ial sou ces o unce ain y and a ia ion be ween meas-
u emen s ( igu e 1).
The a ious e o sou ces in igu e 1in luence he quali y o
he esul ing images, which in u n has a majo impac on po e
segmen a ion and he subsequen po osi y measu emen [18].
In his case, quali y e e s o he combina ion o noise le el,
con as be ween ma e ial and po es, and sha pness o edges
be ween he wo egions [19]. As an example o he complex
in luences o he image quali y on po osi y assessmen , image
denoising may dec ease he amoun o noise alsely de ec ed
as po es, bu i may also cause some smalle po es o be blu ed
and he e o e missed, skewing he esul s [20,21]. Due o his,
i is impo an o epo on he a ious sample, measu emen ,
and p ocessing pa ame e s used in a po osi y s udy, and o
ake unce ain y in o accoun [18]. Da a used in s udies can be
sha ed h ough da a eposi o ies such as he GigaScience Da a-
base, see Goodman [22], as in he case o Du Plessis e al [23].
The wo k lows and p o ocols can also be sha ed on se ices
like P o ocols.io [24].
Cha ac e iza ion o po osi y in a CT da ase is di ec ly
ela ed o he segmen a ion p ocedu e, he pa i ioning o a
olume in o wo o mo e sepa a e sec ions (e.g. ma e ial and
oids). Segmen a ion is based on he in insic cha ac e is ics
o oxels o egions o he olume, such as g ay alues, edges,
o ex u e [28].
Figu e 1. The c ea ion o a 3D da ase om a gi en objec using
x- ay CT has h ee s eps: (1) he scan o measu emen , (2)
econs uc ion, and (3) segmen a ion. Then, analysis (4) o he
olume can be done. E o s ha occu du ing s ep 1 can lead o
omog aphic a i ac s (disc epancies be ween an objec and i s
image). In s eps 2–4, o he ypes o e o s can lead o unce ain y in
he inal analysed esul s. The ed lines show he ocus o his wo k.
Figu e inspi ed by Villa aga-Gómez e al [25], Sme e al [26] and
Hille and Reindl [27].
One o he mos widely used segmen a ion me hods is
h esholding [29], whe e oxels a e sepa a ed in o dis inc
ca ego ies based on a h eshold se o one o mo e o he
cha ac e is ics men ioned abo e. Th esholding can be global
o locally adap i e [30,31]. The la e is mainly used o
complex objec s, whe e he op imal h eshold alue may
change h oughou he da ase [32]. On he o he hand, global
h esholding de ines a single h eshold alue o he en i e
da ase , in luencing all u he analysis and in e p e a ions
[29]. Fo i s simplici y, ease o use, and ease o access, global
h esholding is he go- o segmen a ion me hod in many CT
da a analyses.
Po osi y analysis may yield di e en esul s based on
he chosen me hod o segmen a ion and esea che inpu
[33]. The conclusions d awn om a s udy can be ambigu-
ous i he me hodology used o segmen a ion is no clea ly
desc ibed. This has caused some esea che s o call o
s anda disa ion [18,34–37]. I is commonplace o desc ibe
measu emen pa ame e s used o da a acquisi ion in po os-
i y s udies, such as he ube ol age and cu en , and he
oxel size. Howe e , o ensu e ep oducibili y, he applied
segmen a ion app oach should be desc ibed and he unce -
ain y o he esul s should be es ima ed oo. O he wise, he
2
Meas. Sci. Technol. 32 (2021) 122001 Topical Re iew
Figu e 2. The ela ionship be ween accu acy and p ecision shown
using mul iple measu emen s (small ed do s) and a e e ence alue
(big g een do ). P ecision es ima ion can be de e mined wi h se e al
measu emen s. A s andalone CT measu emen (small blue do ) has
no e e ence alue ( he g een do is unknown) and di e en a
di e en app oach mus be adop ed o p ecision and unce ain y
es ima ion. This igu e was inspi ed by Pospíšil and Lud ík [48],
and Taylo [49].
eliabili y o hese s udies uns he isk o being dispu ed
[26,29,38,39].
Measu emen s a e ypically exp essed wi h an e o a io,
a con idence in e al, o a s anda d de ia ion p esen ed as
a± alue. This alue is based on he cumula i e e ec o
de ice, measu emen and p ocessing e o s [27,40].
Knigge [41] s a es ha a measu emen does no need o be
accu a e (close o he e e ence alue), bu i s p ecision should
be known ( igu e 2). The accu acy e e s o he closeness
be ween a measu ed alue and a e e ence alue [42,43]. A
p ecise measu emen is no necessa ily close o he e e ence
alue, bu i has li le a iabili y when epea ed. Thus, p eci-
sion quan i ies he ep oducibili y and le el o unce ain y o a
measu emen . In e na ional me ological s anda ds o es im-
a ing he measu emen unce ain y exis [44–46], bu hey can-
no be di ec ly applied o he pu poses discussed he e, as hey
do no p o ide speci ic guidelines o he unce ain y o 3D CT
da a segmen a ion [47].
Two causes o e o s [42] can a ec he p ecision and accu -
acy o a esul , namely: sys ema ic e o (a ec s all meas-
u emen s in a simila manne , obse able h ough epea ed
measu emen s [50,51]), and andom e o (mainly caused
by ope a o e o s, and a ec s indi idual measu emen s and
hus he measu emen p ecision [52]). Acquisi ion, ha dwa e,
and econs uc ion disc epancies all signi ican ly in luence he
inal po osi y e alua ion.
A complex analysis o unce ain ies in CT measu emen s
is he domain o me ology and o some indus ial ields,
whe e calib a ed de ices o calib a ion me hodologies a e used
[51,53,54]. Wi hou a g ound u h, which is a measu emen
ha is conside ed o ha e he exac ue alue, accu acy o a
measu emen canno be assessed [55]. In e ms o p ecision,
he in luence o unce ain ies s emming om he measu emen
p ocess is a complex issue, and i is al eady he subjec o ho -
ough esea ch [40]. In con as , unce ain ies associa ed wi h
segmen a ion a e seldom e e enced o explained ho oughly
wi hin cu en li e a u e.
This wo k o e s an o e iew o CT da a segmen a ion
me hods ha use global h esholding and a e commonly used
o po osi y analysis. C ucial aspec s o he segmen a ion p o-
cess, which should be disclosed in s udies, a e iden i ied in
he sec ion ‘Th esholding and ep oducibili y’. The need o a
ho ough desc ip ion o app oaches used in s udies is suppo -
ed by a sys ema ic e iew o ecen ele an li e a u e. Me h-
ods o he unce ain y es ima ion o po osi y analysis in CT
da a a e discussed in he sec ion ‘Unce ain ies o CT da a seg-
men a ion’. Due o inancial and ime cons ain s, esea che s
may o en only ha e access o a single CT da ase o ana-
lysis [9], so pa icula a en ion is paid o hose me hods ha
can be used in hese si ua ions. Unce ain y es ima ion is s ill
needed in such cases, bu he app oaches o pe o m i may be
less ob ious. We hope o p o ide a p ac ical o e iew o he
possibili ies a ailable o esea che s o ensu e he ep oducib-
ili y o hei esul s.
2. Th esholding and ep oducibili y
Global h esholding me hods can be di ided in o manual,
semi-au oma ic, and au oma ic [56], depending on he ex en
o ope a o in ol emen in he selec ion o he h eshold
alue. Au oma ic algo i hms calcula e a h eshold objec -
i ely based on he cha ac e is ics o he inpu da ase , such
as oxel g ayscale alues and ea u es o he image his o-
g am ( igu e 3). Common au oma ic algo i hms include min-
imum e o h esholding [57], O su’s me hod [58], alley-
emphasis [59], op imal h esholding [60], his og am conca -
i y analysis [61], i e a i e h esholding (isoda a me hod) [62],
en opy-based h esholding [63], Bayesian h esholding [64],
and o he s. The esul s o hese may be used di ec ly o u he
ine- uned manually. Manual h eshold selec ion is subjec i e
and obse e -dependen , and i is usually based on isualiz-
ing he segmen a ion esul on a slice o he CT da ase and
uning i un il i is sa is ac o y [35]. The po en ial human bias
inhe en in manual h esholding may lead o la ge di e ences
be ween da a segmen ed by di e en ope a o s. Despi e his,
manual h esholding is s ill e y common due o i s simplici y.
One o he simples global h esholding me hods is ISO50,
which se s a h eshold a he mean o wo ex eme peak
alues in he g ayscale his og am o a da ase [65]. Resul s
o his me hod end o be sa is ac o y when he analysed
his og am is bi- o mul i-modal ( igu e 3) [66]. Howe e ,
Ho ne e al [67] showed ha ISO50 migh be in luenced
by local a ia ions in he image, in which case he h eshold
should be modi ied acco dingly. I is also challenging o
use i wi h low po osi y alues because he his og am o
3
Meas. Sci. Technol. 32 (2021) 122001 Topical Re iew
Figu e 3. Tomog aphic images wi h a uni- (a), (d), bi- (b), (e), and mul imodal (c), ( ) g ayscale his og am. The his og ams show h esholds
se using O su’s me hod (da k dashed ed line) and ISO50 (ligh g een line). The mul imodal his og am in ( ) shows mul i-le el
h esholding, which di ides he da ase in o h ee pa s. Bounda ies o segmen ed a eas a e shown in (a)–(c) using an ou line wi h colo s
co esponding o he wo h esholds. The slices show da ase s measu ed in ou labo a o y: (a) and (b) a e slices o a chalk sample, while
(c) is an image o a seed.
such da a may lack a clea peak co esponding o po e
alues.
O su’s h esholding [58] is ano he simple me hod, and
along wi h Ki le ’s h esholding [57], i is one o he mos
used algo i hms o po osi y segmen a ion ( able 2). Simila o
ISO50, he esul s o O su’s me hod a e a ec ed by he mod-
ali y o he his og am [29]. Algo i hms such as O su’s me hod
can also be used o mul ile el h esholding, which may be
used o classi y da ase s in o po es, g ains and high-densi y
inclusions ( igu es 3(e) and ( )) [68,69]. In cases whe e a
da ase ’s his og am is app oxima ely unimodal, he algo i hms
men ioned abo e a e likely o pe o m poo ly, and a h eshold
can be se using p obabili y-based algo i hms [59].
The e is no consensus in he scien i ic communi y abou
which h esholding me hod is ideal o po osi y analysis in
CT da a. In ac , he wide selec ion o published specialized
algo i hms in a ious ields sugges s ha he e ec i eness
o an algo i hm changes wi h he da ase ype and applica-
ion [29,37,70,71]. The e is, howe e , an ag eemen ha he
ep oducibili y o manual segmen a ion is lowe han ha o
an au oma ed o ainable p ocedu e, as ema ked by Kalaso ´
a
e al [72].
A ound obin es , which is po osi y in a speci ic scan
e alua ed by mul iple ope a o s, was epo ed by Du Plessis
e al [18]. This s udy ound a good ag eemen in he quali a i e
po e dis ibu ion assessmen o en ope a o s, bu quan i a i e
esul s a ied signi ican ly, pa ly due o he low po osi y con-
en in he es sample used. Wo ks o Zikmund e al [11,73]
and Ba eye e al [37] also ea u e a compa ison o a ious
manual segmen a ion s a egies in addi ion o algo i hm-based
ones. Signi ican disc epancies we e ound bo h wi hin and
be ween hese g oups. The e o e, au oma ed me hods do no
ensu e an accu a e o eliable esul ei he , as he choice o
algo i hm signi ican ly impac s he h eshold alue and he
ob ained esul s ( igu e 3) [26,29,37,38,74,75].
Rega dless o he segmen a ion me hod used, po osi y ana-
lysis needs o be ep oducible o a eliable in e -s udy com-
pa ison o esul s. This means ha pa ame e s o he segmen -
a ion p ocess should be desc ibed and explained ho oughly,
as ema ked in mul iple wo ks [18,34–36,73].
2.1. Analysis o published po osi y me hodologies
To assess he ends ega ding ep oducibili y in he cu en
li e a u e, we chose 53 a icles om geosciences and ma e -
ial sciences (indus y, enginee ing, me ology, ag icul u e,
and cul u al he i age) ha deal wi h po osi y analysis in CT
da a, and analysed hei segmen a ion me hodologies ( able 2).
The a icles we e selec ed h ough Google Schola using he
keywo ds CT, Po osi y, Segmen a ion, Global Th esholding,
Quan i a i e analysis, and Unce ain y e alua ion. Ou selec-
ion was na owed down o a icles ha we e ci ed a leas
once.
Twen y o he 53 a icles (57%) ea u ed ei he no desc ip-
ion o he segmen a ion p ocedu e, o hei desc ip ion was
no su icien o hei esul s o be eliably ep oducible.
Ten o hese a icles (19%) had a desc ip ion bu was no
accompanied by any isualiza ion o he his og am and
4
Meas. Sci. Technol. 32 (2021) 122001 Topical Re iew
h eshold alue. Ou o he emaining 23 a icles (43%),
en (19%) ea u ed a su icien desc ip ion and p o ided an
example CT slice showing segmen a ion esul s, along wi h
ei he a g ayscale his og am o he slice, o an es ima ion o
he unce ain y o he esul s. These esul s can be conside ed
ep oducible, bu no op imally so. Only 13 (25%) o he su -
eyed a icles disclosed all pa ame e s needed o ensu e meas-
u emen ep oducibili y, including a desc ip ion, an example
slice along wi h i s his og am, an unce ain y es ima ion o he
h eshold alue, and a men ion o he so wa e used.
O e he obse ed pe iod (1992–2020), he o e all ho -
oughness o h esholding me hodology desc ip ions seems o
no ha e changed. The e a e no clea dis inc ions be ween
me hodology desc ip ions in he a ious ields o s udy, excep
ha wo ks dealing wi h soil po osi y (21% o he s udied a -
icles) a e mo e p one o in e -s udy compa ison, and he e o e
hey gene ally include a mo e ho ough de ini ion o he pa a-
me e s used o h esholding.
The examined s udies a e mos ly based on a single seg-
men a ion me hod (43% o he examined a icles), ollowed
by compa ison (28%) and combina ion (19%) o segmen -
a ion me hods. O su’s me hod is he mos commonly used
(36%), bo h on i s own and in compa ison o, o in combin-
a ion wi h, o he echniques. I is closely ollowed by manual
global h esholding segmen a ion (34%). This is ai ly consis -
en ac oss he ields, which shows ha he choice o h eshold-
ing me hod is p obably mainly dependen on he ope a o
expe ience and sample ype.
A men ion o he so wa e used, which is p esen in 68% o
he selec ed a icles, can aid in he ep oducibili y o esul s.
The mos commonly men ioned so wa e in able 2includes
VG S udio (15%; Volume G aphics GmbH, Heidelbe g/D),
ImageJ/Fiji (15%; Na ional Ins i u es o Heal h, Be hesda,
Ma yland/US and LOCI, Uni e si y o Wisconsin-Madison,
Madison, Wisconsin/US), and A izo (13%; The moFishe
Scien i ic, Wal ham, Massachuse s/US). We ha e obse ed
ha indus ial and enginee ing ields end o u ilize VG S u-
dio and A izo, whe eas he selec ion o so wa e used in
geosciences and geology is b oade . This may be because he
complex samples in geosciences a e di icul o p ocess in gen-
e al pu pose image p ocessing so wa e, o cing esea che s o
use mo e specialized solu ions.
2.2. Rep oducibili y
Analysis o able 2and p e ious wo k done by Taina e al [76],
Lie e s and Pilkey [77], and Iassono e al [74] has led o
he iden i ica ion o six majo pa ame e s o he h esholding
p ocess, which should be included in a s udy o ensu e esul
ep oducibili y. These pa ame e s include: his og am shape,
an image o a slice om he da ase showing po e de e mina-
ion, he chosen h eshold alue, desc ip ion o he h eshold-
ing p ocedu e, and he name and e sion o he so wa e used.
The pa ame e s a e also lis ed in able 1[74,76,77].
The mos common h esholding algo i hms ope a e on
he g ayscale his og ams o images, and manually selec-
ed h esholding is o en pa ly de e mined by he his og am
shape, oo. The e o e, including an example his og am in a
Table 1. Th esholding pa ame e s ha ensu e me hodology
ep oducibili y, lis ed in he o de o hei impo ance. Fo he sake
o cla i y, abb e ia ions used in able 2a e included he e, as well.
Th esholding pa ame e s
1 [h] His og am
2 [s] Slice showing po e de e mina ion
3 [ ] Th eshold g ey-le el alue
4 [d] Manual: Reason o he h eshold choice ( isual o
ma e ial-dependen , o wi h e e ence)
Semi-au oma ed: Algo i hm choice wi h e e ence
and modi ica ions
Au oma ed: Implemen ed so wa e algo i hm i le and
alues chosen
5 [u] Unce ain y es ima ion (±)
6 So wa e + e sion
s udy can aid i s ep oducibili y. Likewise, including a slice
illus a ing he inal segmen a ion and he h eshold alue
p o ides a aluable isual and nume ic e e ence.
Documen ing he so wa e used, along wi h i s e sion, may
also be ele an o ep oducibili y. In some ypes o so wa e,
he in e nal wo kings o he algo i hms may no be accessible
o he end use ( hese algo i hms a e called black boxes). Due
o his, analyses ca ied ou in di e en so wa e may be ha d
o compa e, and he name and e sion o he so wa e used o
a gi en s udy becomes ele an .
An impo an bu o en omi ed piece o in o ma ion
( able 2) in e ms o ep oducibili y is he es ima ion o he
po osi y esul unce ain y. Po osi y measu emen in CT is di -
ec ly ela ed o he segmen a ion p ocess, which a ec s he
size, shape, dis ibu ion, and o al olume o po es [71]. Di e -
en segmen a ion me hods may lead o an o e - o unde es im-
a ion and inc eased unce ain y o po osi y ( igu e 3) [33]. An
unce ain y ange will he e o e help o he esea che s assess
whe he hei ep oduced esul s di e signi ican ly om he
ou comes o he o iginal s udy. Howe e , unce ain y o po os-
i y in CT da a may no always be s aigh o wa d o es ima e.
The nex sec ion goes o e a selec ion o possible app oaches
o pe o m his es ima ion in a a ie y o scena ios.
3. Unce ain ies o CT da a segmen a ion
Se e al s udies we e conduc ed conce ning he unce ain y
es ima ion o bo h manual and au oma ic h eshold selec ion in
CT da ase s [51,53]. These wo ks desc ibe a ious p ocedu es
o es ima ing he unce ain y o po osi y analysis ( able 3),
which can be sepa a ed in o empi ical, analy ical, and sensi -
i i y app oaches. All hese p ocedu es mi iga e di e en kinds
o e o s in he inal unce ain y es ima ion.
Empi ical p ocedu es a e based on he compa ison o a CT
da ase wi h a e e ence. This e e ence may ake he o m
o a calib a ed wo kpiece o a measu emen conduc ed using
ano he calib a ed me hod. Such p ocedu es a e demanding,
cos ly, and imp ac ical o e y complex o non-homogeneous
samples. Since hese me hods equi e a e e ence measu e-
men , hey will inc ease he e o sou ces o s ep 1 in igu e 1
(mos ly sys ema ic e o s) bu will educe ope a o e o s.
5

Meas. Sci. Technol. 32 (2021) 122001 Topical Re iew
Table 2. A lis o a icles ha use CT o po osi y analysis in di e en ields, highligh ing he amoun o in o ma ion p o ided conce ning he h eshold selec ion.
Au ho Yea Th eshold selec ion based on So wa e
Th eshold
pa ame e s
Field o
esea ch Ma e ial
Lin e al [78] 2016 Cp—O su [58], Liao e al [69], Wa e -
shed
A izo d, s, h, u Geosciences Limes one
Fishman e al [79] 2010 O su [58] Fiji d, s, h, u Indus y Fibe s
F ei e-Go maly e al [80] 2014 Cb—O su [58], Ji e al [81] Fiji d, s, h, u Geology Limes one, dolomi e
Abe a e al [29] 2017 Cp—Ki le and Illingwo h [82],
O su [58], Kapu e al [63], Johannsen
and Bille [83], Pun [84]
Ma lab +Image-P o +S an-
dalone segmen a ion so wa e
d, s, h, u Enginee ing Glass beads, con-
c e e, sand
Sleu el e al [36] 2008 Manual Mo pho+ ool Vlassenb oeck
e al [85]
d, s, h, u Geosciences Soil
Ba eye e al [37] 2010 Cp—O su [58], I e a i e, en opy, IK,
manual, Sezgin and Sanku [31]
OTIMEC d, s, h, u Geosciences Soil
Rozenbaum e al [86] 2012 O su [58] VG S udio d, s, h, u Geosciences Soil
Bo ges de Oli ei a e al [87] 2016 Cp—ISO-50, ad anced local-mode,
egion g owing, g eyscale, ROI
VG S udio MAX 2.2.6 d, s, h, u Me ology Polyme
Zikmund e al [73] 2019 Cp—O su [58], K-means RIdle
e al [62], manual
VG S udio MAX 3.0 d, s, h, u Indus y Addi i e manu ac u -
ing
He manek e al [66] 2019 Cb—ISO-50, ROI I e a i e op imiza-
ion
VG S udio MAX 3.0 (De ec
analysis module)
d, s, h, u Me ology Aluminium
Sme e al [26] 2018 Cp—O su [58], IK, g adien mask,
po osi y-based Becke s e al [88]
MATLAB R2015a, AWIK
(cus om)
d, s, h, u, Geosciences Soil
Wang e al [89] 2011 Cp—Sahoo e al [90], O su [58],
Ridle e al [62], IK, en opy, i e a i e
R, 3DMA-Rock d, s, h, u, Geosciences Rock
Gan ze and Ande son [91] 2002 Cb—‘Th eshold ea u e’, ‘Measu e’
ool
ImageJ 1.20 d, s, h, Ag icul u e Soil
Luo e al [92]2010 Maximum en opy Jassogne e al [93] ImageJ 1.39 d, s, u Geosciences Soil
Thompson e al [34] 1992 Manual No men ion d, s, u Geosciences Soil
Sande e al [94] 2008 Manual Slice Dice d, s, u Ag icul u e Soil
Ishu o e al [1] 2015 Manual 3D is, pa a iew d, s, h Geosciences Rock
Ji e al [81] 2012 O su [58] ImageJ d, s, h Geology Limes one
Coke e al [95] 1996 Edge-based Cocke e al [96] No men ion d, s, h Geology Sands one
Taud e al [11] 2005 Cp—G ey-le el, manual, k-means
Riedle e al [62]
No men ion d, s, h Enginee ing Rock
Schlü e e al [97] 2010 Cb—Yanowi z and B ucks ein [98],
Vogel and K e zschma [99]
No men ion d, s, h Geosciences Soil
And ä e al [75] 2013 Cp—VSG, Kongju, S an o d No men ion d, s, h Geosciences Sands one, ca bona e,
sphe e pack
Zhang e al [100] 2017 O su [58] ImageJ d, s, Geosciences Shale
(Con inued.)
6
Meas. Sci. Technol. 32 (2021) 122001 Topical Re iew
Table 2. (Con inued.)
Au ho Yea Th eshold selec ion based on So wa e
Th eshold
pa ame e s
Field o
esea ch Ma e ial
Heinzl [101] 2007 Cp—O su [58], Manual, Wa e shed,
Calypso
Ca l Zeiss Calypso d, u Indus y Me al
Mo oni and Pe `
o [33] 2016 Cp—ISO-50, manual No men ion d, u Me ology Calib a ed balls
He manek and Ca migna o [102] 2017 ISO-50, local adap a i e VG S udio MAX 2.2.6
(De ec analysis module
‘Only h eshold’), Volume
Playe , iVolume,
d, u Me ology Mul i-ma e ial
Sala ian and Toyse kani [103] 2018 Cb—G eyscale, mo phological ope a-
ion, manual
D agon ly P o 3.1 d, s Indus y Aluminium
Manahilo [104] 2013 Cp +Cb—O su [58], Region-based,
i e a i e minimiza ion, manual, wa e -
shed
Image-P o Plus d, s Geosciences Soil, sand, glass
beads
Iassono and Tulle [105] 2010 O su [58] No men ion d, s Geosciences Ben oni e, glass
beads
Alya ei e al [68] 2015 O su [58] No men ion d, s Geology Sands one, limes one
Rezaei e al [38] 2019 Cp—Ki le and Illingwo h [57],
O su [58], Ridle e al [62], h ee
locally adap a i e (Niblack 1986,
Sau ola 2000, Be nsen 1986)
No men ion d, s Enginee ing Limes ones, dolomi e
Kuma e al [106] 2012 Cb—Au oma ic his og am-based
h eshold (10% sensi i i y manual),
‘De ec de ec ion’ module
VG S udio MAX 2.0 (De ec
de ec ion module)
d, s Enginee ing Foam
Pa an e al [107]. 2018 O su [58] VG S udio MAX 2.2 (De ec
analysis module ‘Only
h eshold’)
d, s Indus y Lase sin e ed PA12
Rogasik e al [108]. 2003 Manual No men ion d Geosciences Soil
And ä e al [75]2013 Cp—O su [58], VGL (manual +
wa e shed), Kongju (single h eshold),
s an o d
No men ion d Geosciences Sands one, Ca bona e
Mad a e al [109] 2014 Cp—Manual, h esholding, lea ning
algo i hm ( ainable WEKA)
Fiji p, s, u Enginee ing Plas ic +glass ibe s
Fusi and Ma inez-Ma inez [110] 2013 Manual A izo p, s, Enginee ing Dolos one, limes one,
ma ble
Spie ings e al [111] 2011 Manual VG S udio MAX 2.0 p, u Indus y Me al
Sko pa e al [112] 2017 ‘In e ac i e h esholding’ based on
g eyscale
A izo p, s Geosciences Chalk, cemen , sand-
s one
Blun e al [113] 2013 O su [58] No men ion p, s Geology Limes one, ca bon-
a e, sands one
Vande esse e al [114] 2011 Manual A izo p Indus y Cas Al-alloy
Mahan a e al [115] 2020 Cb—G eyscale And ä e al [75],
Wa e shed
A izo 9.0 p Geosciences Sands ones
(Con inued.)
7
Meas. Sci. Technol. 32 (2021) 122001 Topical Re iew
Table 2. (Con inued.)
Au ho Yea Th eshold selec ion based on So wa e
Th eshold
pa ame e s
Field o
esea ch Ma e ial
We e s e al [116] 2012 Cb—O su [58] , Manual ImageJ, CTAn, A izo p Enginee ing Mul i-ma e ial
A ns e al [117] 2019 Cb—Manual, Ac i e con ou om
Sheppa d e al [118]
No men ion p Geosciences Limes one
Pea ce e al [119] 2016 G eyscale Golab e al [120] QEMSCAN p Geosciences Rock
Bugani e al [121] 2007 ROI CTAn package n, s, u Cul u al he i age Limes one
Mülle e al [122] 2012 Cb—Au oma ic ‘op imal’, local
adap a i e
No men ion n, s Me ology Aluminium, polyme
Jiang e al [123] 2013 No men ion Po e Analysis Tools (PAT,
cus om)
n, s Geosciences Rock
V åls ad and Sko pa [124] 2020 No men ion A izo n Enginee ing Cemen
Mai e e al [125] 2007 Cp—G eyscale, egion g owing No men ion n Indus y Ce amic
Nicole o e al [126] 2010 No men ion No men ion n Enginee ing Al-alloy
Pak e al [127] 2016 Jiang e al [123] No men ion n Geosciences Ca bona e
Fin o ´
ae al [128] 2010 No men ion O iginal so wa e n Enginee ing Al–Si alloys
Cp: compa ison; Cb: combina ion; Th eshold choice me hod d: desc ibed, p: pa ially desc ibed, n: non desc ibed; h: his og am; s: slice; : h eshold alue; u: unce ain y; ROI: egion o in e es ; IK: indica o k iging
[129].
8
Meas. Sci. Technol. 32 (2021) 122001 Topical Re iew
Table 3. An o e iew o unce ain y es ima ion p ocedu es o po osi y segmen a ion. The numbe o h esholds, objec s, ope a o s, and CT
da ase s equi ed o each me hod a e lis ed, bu he lis ed alues should se e only as a gene al guideline. The a angemen o he able
ollows ha o he ex below, wi h mul i-da ase me hods lis ed i s , and single-da ase me hods second. This able can be used o selec an
app op ia e me hod o a pa icula si ua ion by ma ching i wi h he pa ame e s in columns ‘Sample’ o ‘g ound u h’.
Unce ain y
es ima ion
p ocedu e Sample Objec Da ase Ope a o
Th esholding
p ocess Type
G ound
u h Re e ence
EMP. Me hods
co ela ion
Open po osi y,
des uc ible
1≥2 1 2 Compa ison Yes [11,130]
Calib a ed
objec (CAD)
Known shapes,
dis ibu ion
2 2 1 2 Compa ison Yes [51,53,
66,102,
131]
Re e ence
objec
Known
e e ence’s
po osi y
2111Compa ison Yes [131]
ANAL. In e -s udies All ≥2≥2≥2≥1 Compa ison No [132]
Mul iple scans All 1 ≥2 1 ≥2 A e aging No [133]
Mul iple
loca ion
Homogeneous 1 1 1 1 A e aging No [134]
G ound u h
c ea ion
All 1 1 1 ≥3 Compa ison
A e aging
Yes [135,
136]
SENS. Mul iple
manual
All 1 1 ≥2≥2 A e aging No [37]
Manual ±n%All 1 1 1 1 ±n%A e aging No [73]
E osion/Dila ion All 1 1 1 1 ±npixels A e aging No [137]
Analy ical app oaches use a ious s a is ical concep s o
enume a e unce ain y. They usually u ilize mul iple po osi y
measu emen s in some way, so hey can be ime-consuming
and po en ially expensi e. This makes hem unsui able o
la ge amoun s o da a. Despi e his, analy ical app oaches a e
applicable o a la ge a ie y o samples. When his app oach is
used, da a p ocessing e o s a e inc eased, and s a is ical and
ope a o e o s a e educed.
Sensi i i y app oaches a e based on he ope a o ’s beha io ,
knowledge o he da ase , and expec a ions. He e, an unce -
ain y o he ope a o ’s measu emen is es ima ed using some
heu is ics. Me hods in his ca ego y can be un eliable i ce -
ain ules a e no ollowed, bu hey a e usually quick, cheap,
and easy o apply on any da ase and in a wide ange o so -
wa e ( able 3). Since sensi i i y app oaches a e based on he
expe ience o he ope a o and isualiza ion o he da a, hey
a e expec ed o educe sys ema ic and analy ical e o s, bu
inc ease andom e o s [73].
I should be emphasized ha he unce ain y es ima ed
using any o hese me hods is ela i e, no absolu e. Va ious
me hods in he h ee ca ego ies desc ibed abo e a e sui able
o di e en scena ios, depending on he numbe o samples,
ope a o s, ime, and o he esou ces a ailable.
The ollowing ex discusses he me hods in able 3, and
o e s ecommenda ions conce ning hei p ope applica ion.
As he numbe o a ailable da ase s is likely o be a majo
ac o when choosing an app op ia e me hod o unce ain y
es ima ion, he ex is p ima ily di ided in o app oaches o
mul iple da ase s and o a single da ase . Despi e hei impo -
ance, app oaches ha equi e mul iple da ase s a e desc ibed
b ie ly, as hey ha e al eady been exhaus i ely desc ibed in
he li e a u e. Single-da ase me hods a e o en easie o apply
and i a wide ange o da ase s, bu hey a e a ely explained in
su icien de ail. Fo his eason, we desc ibe hose app oaches
mo e ho oughly.
3.1. Se e al da ase s
3.1.1. Empi ical app oach. Co ela ion o esul s o a i-
ous measu emen me hods o he same sample ( igu e 4(c);
able 3) is a common app oach. Fo example, Taud e al [11]
and Robin e al [130] es ima ed he unce ain y o hei po os-
i y measu emen by compa ing he esul s o CT and helium
injec ion measu emen s. Taud e al [11] ound an unce ain y
o abou ±2%. This app oach is s aigh o wa d and eliable,
bu he me hods ha a e compa ed mus be selec ed ca e ully,
and he measu emen mus be clea ly planned ou be o ehand.
Addi ional demands a e placed on he esea che s who choose
his app oach, as hey need bo h access o, and he know-
how o , mul iple measu emen me hods. Di e en me hods
a e sui ed o e alua ing di e en ypes o po osi y, making
he compa ison complex. The oxel size o a CT scan s ongly
in luences measu emen esul s, pa icula ly in samples wi h
a wide ange o po e sizes (e.g. conc e e). Fo mo e p ecise
esul s, mul iple CT scans migh be equi ed [138]. Simil-
a ly, o he quan i ica ion me hods a e limi ed o speci ic anges
o po e sizes, making a di ec compa ison be ween me h-
ods challenging. Addi ionally, i a chosen me hod is des uc -
i e, he non-des uc i e na u e o CT may no longe be an
ad an age.
9
Meas. Sci. Technol. 32 (2021) 122001 Topical Re iew
[82] Ki le J and Illingwo h J 1986 Minimum e o h esholding
Pa e n Recogni . 19 41–7
[83] Johannsen G and Bille, J 1982 A h eshold selec ion me hod
using in o ma ion measu es In . Con . on Pa e n
Recogni ion, P oc. 6 h (Munich) pp 140–3
[84] Pun T 1980 A new me hod o g ey-le el pic u e
h esholding using he en opy o he his og am Signal
P ocess. 2223–37
[85] Vlassenb oeck J, Die ick M, Masschaele B, Cnudde V,
Hoo ebeke L V and Jacobs P 2007 So wa e ools o
quan i ica ion o x- ay mic o omog aphy a he UGCT
Nucl. Ins . Me hods Phys. Res. A580 442–5 (P oceedings
o he 10 h In . Symp. on Radia ion Physics)
[86] Rozenbaum O, B uand A and Le T ong E 2012 Soil po osi y
esul ing om he assemblage o sil g ains wi h a clay
phase: new pe spec i es ela ed o u iliza ion o x- ay
synch o on compu ed mic o omog aphy Comp es Rendus
Geosc. 344 516–25
[87] Bo ges de Oli ei a F, S ol i A, Ba sche M, Chi e L and
Neuschae e -Rube U 2016 Expe imen al in es iga ion o
su ace de e mina ion p ocess on mul i-ma e ial
componen s o dimensional compu ed omog aphy Case
s ud. Nondes uc . Tes . E al. 693–103
[88] Becke s E, Plougon en E, Roisin C, Hapca S, Léona d A and
Deg é A 2014 X- ay mic o omog aphy: a po osi y-based
h esholding me hod o imp o e soil po e ne wo k
cha ac e iza ion Geode ma 219–220 145–54
[89] Wang W, K a chenko A, Smucke A and Ri e s M 2011
Compa ison o image segmen a ion me hods in simula ed
2D and 3D mic o omog aphic images o soil agg ega es
Geode ma 162 231–41
[90] Sahoo P, Wilkins C and Yeage J 1997 Th eshold selec ion
using Renyi’s en opy Pa e n Recogni . 30 71–84
[91] Gan ze C J and Ande son S H 2002 Compu ed omog aphic
measu emen o mac opo osi y in chisel-disk and
no- illage seedbeds Soil Tillage Res. 64 101–11
[92] Luo L, Lin H and Li S 2010 Quan i ica ion o 3-D soil
mac opo e ne wo ks in di e en soil ypes and land uses
using compu ed omog aphy J. Hyd ol. 393 53–64 (Soil
A chi ec u e and P e e en ial Flow ac oss Scales)
[93] Jassogne L, McNeill A and Chi lebo ough D 2007
3D- isualiza ion and analysis o mac o-and meso-po osi y
o he uppe ho izons o a sodic, ex u e-con as soil Eu .
J. Soil Sci. 58 589–98
[94] Sande T, Ge ke H H and Rogasik H 2008 Assessmen o
Chinese paddy-soil s uc u e using x- ay compu ed
omog aphy Geode ma 145 303–14
[95] Coke D A, To qua o S and Dunsmui J H 1996 Mo phology
and physical p ope ies o Fon ainebleau sands one ia a
omog aphic analysis J. Geophys. Res.: Solid Ea h
101 17497–506
[96] Coke D, Lindquis W 1994 Edge-based algo i hm o il e
omog aphic da a se s, p ep in SUNYIT-MS-1-1994
[97] Schlü e S, Welle U and Vogel H-J 2010 Segmen a ion o
x- ay mic o omog aphy images o soil using g adien
masks Compu . Geosci. 36 1246–51
[98] Yanowi z S D and B ucks ein A M 1989 A new me hod o
image segmen a ion Compu . Vis. G aph. Image P ocess.
46 82–95
[99] Vogel H J and K e zschma A 1996 Topological
cha ac e iza ion o po e space in soil—sample p epa a ion
and digi al image-p ocessing Geode ma 73 23–38
[100] Zhang P, Lu S, Li J, Zhang P, Xie L, Xue H and Zhang J 2017
Mul i-componen segmen a ion o x- ay compu ed
omog aphy (CT) image using mul i-O su h esholding
algo i hm and scanning elec on mic oscopy Ene gy
Explo . Exploi . 35 281–94
[101] Heinzl C, Kas ne J, Geo gi B and Le enbaue H 2007
Compa ison o su ace de ec ion me hods o e alua e cone
beam compu ed omog aphy da a o h ee dimensional
me ology In . Symp. on Digi al Indus ial Radiology and
Compu ed Tomog aphy - DIR 2007 (Villeu banne, F ance,
25–27 June 2007) (Lion, F ance) pp 21–9
[102] He manek P and Ca migna o S 2017 Po osi y measu emen s
by x- ay compu ed omog aphy: accu acy e alua ion using
a calib a ed objec P ecis. Eng. 49 377–87
[103] Sala ian M and Toyse kani E 2018 The use o nano-compu ed
omog aphy (nano-CT) in non-des uc i e es ing o
me allic pa s made by lase powde -bed usion addi i e
manu ac u ing In . J. Ad . Manu . Technol. 98 3147–53
[104] Manahiloh K N 2013 Mic os uc u al analysis o unsa u a ed
g anula soils using x- ay compu ed omog aphy PhD
Thesis Depa men o Ci il and En i onmen al
Enginee ing, Washing on S a e Uni e si y
[105] Iassono P and Tulle M 2010 Applica ion o segmen a ion
o co ec ion o in ensi y bias in x- ay compu ed
omog aphy images Vadose Zone J. 9187–91
[106] Kuma J, Abul ub A H G, A idge A and Williams M A
2012 E ec o x- ay compu ed omog aphy scanning
pa ame e s on he es ima ed po osi y o oam specimens
Mechanical and Ae ospace Enginee ing, ICMAE2011
ol 110 ed Fan W Applied Mechanics and Ma e ials
(Zu ich: T ans Tech Publica ions L d) pp 808–15
[107] Pa an M, C aeghs T, K u h J-P and Dewul W 2018
In es iga ing he in luence o x- ay CT pa ame e s on
po osi y measu emen o lase sin e ed PA12 pa s
using a design-o -expe imen app oach Polym. Tes .
66 203–12
[108] Rogasik H, Onasch I, B uno e J, Jegou D and Wend o h O
2003 Assessmen o soil s uc u e using x- ay compu ed
omog aphy Geol. Soc. Spec. Publ. 215 151–65
[109] Mad a A, Hajj N E and Benzeggagh M 2014 X- ay
mic o omog aphy applica ions o quan i a i e and
quali a i e analysis o po osi y in wo en glass ibe
ein o ced he moplas ic Compos. Sci. Technol.
95 50–8
[110] Fusi N and Ma inez-Ma inez J 2013 Me cu y po osime y
as a ool o imp o ing quali y o mic o-CT images in low
po osi y ca bona e ocks Eng. Geol. 166 272–82
[111] Spie ings A B, Schneide M and Eggenbe ge R 2011
Compa ison o densi y measu emen echniques o
addi i e manu ac u ed me allic pa s Rapid P o o yp. J.
17 380–6
[112] Sko pa R, Todo o ic J and To sæ e M 2017 Po osi y
changes in mud-a ec ed ock and cemen upon eac ion
wi h CO2Ene gy P ocedia 114 5266–74
[113] Blun M J, Bijeljic B, Dong H, Gha bi O, Iglaue S,
Mos aghimi P, Paluszny A and Pen land C 2013
Po e-scale imaging and modelling Ad . Wa e Resou .
51 197–216
[114] Vande esse N, Bu ie e J-Y, Mai e E and Chabod A 2011
E ec o po osi y on he a igue li e o a cas Al alloy
Op ical Measu emen s, Modeling and Me ology ed
P oulx T (Con . P oc. o he Socie y o Expe imen al
Mechanics, ol 5) (New Yo k: Sp inge ) pp 55–61
[115] Mahan a B, Vishal V, Ranji h P and Singh T 2020 An insigh
in o po e-ne wo k models o high- empe a u e hea - ea ed
sands ones using compu ed omog aphy J. Na . Gas Sci.
Eng. 77 103227
[116] We e s M, Ke ckho s G, Pyka G, He emans E, Van Ende A,
Hend ickx R and Wilde jans E 2012 X- ay compu ed
omog aphy o nondes uc i e es ing P oc. ICT 2012,
In . Con . on Indus ial Compu ed Tomog aphy (Wels,
Aus ia) pp 13–29
[117] A ns C H, Jiang H, Dai H, Shikho I, Sayedak am N and
A ns J-Y 2019 A digi al ock physics app oach o e ec i e
and o al po osi y o complex ca bona es: po e- yping and
applica ions o elec ical conduc i i y The 2018 In . Symp.
16

Meas. Sci. Technol. 32 (2021) 122001 Topical Re iew
o he Socie y o Co e Analys s (SCA 2018) E3S Web o
Con . (T ondheim, Now ay,27–31 Augus 2018) ol 89, ed
Nico B (EDP Sciences) p 05002
[118] Sheppa d A P, Sok R M and A e dunk H 2004 Techniques
o image enhancemen and segmen a ion o omog aphic
images o po ous ma e ials Phys. A339 145–51
[119] Pea ce J K, Golab A, Dawson G K, Knue ing L, Goodwin C
and Golding S D 2016 Mine alogical con ols on po osi y
and wa e chemis y du ing O2-SO2-CO2 eac ion o CO2
s o age ese oi and cap- ock co e Appl. Geochem.
75 152–68
[120] Golab A N, Knacks ed M A, A e dunk H, Senden T,
Bu che A R and Jaime P 2010 3D po osi y and
mine alogy cha ac e iza ion in igh gas sands ones
Leading Edge 29 1476–83
[121] Bugani S, Camai i M, Mo selli L, Van de Cas eele E and
Janssens K 2007 In es iga ion on po osi y changes o
Lecce s one due o conse a ion ea men s by means o
x- ay nano- and imp o ed mic o-compu ed omog aphy:
p elimina y esul s X-Ray Spec om. 36 316–20
[122] Mülle P, Hille J, Can a o e A and De Chi e L 2012 A
s udy on e alua ion s a egies in dimensional x- ay
compu ed omog aphy by es ima ion o measu emen
unce ain ies In . J. Me ol. Quali y Eng. 3107–15
[123] Jiang Z, Van Dijke M, So bie K S and Couples G D 2013
Rep esen a ion o mul iscale he e ogenei y ia mul iscale
po e ne wo ks Wa e Resou . Res. 49 5437–49
[124] V åls ad T and Sko pa R 2020 Digi al cemen in eg i y: a
me hodology o 3D isualiza ion o c acks and
mic oannuli in well cemen Sus ainabili y 12 41128
[125] Mai e E, Colombo P, Ad ien J, Babou L and Biase o L 2007
Cha ac e iza ion o he mo phology o cellula ce amics
by 3D image p ocessing o x- ay omog aphy J. Eu .
Ce am. Soc. 27 1973–81
[126] Nicole o G, Anzelo i G and Koneˇ
cn´
a R 2010 X- ay
compu ed omog aphy s. me allog aphy o po e sizing
and a igue o cas Al-alloys P ocedia
Enginee ing—Fa igue 2010 ol 2, ed Luk´
aš L
(Ams e dam: Else ie ) p 7
[127] Pak T, Bu le I B, Geige S, an Dijke M I, Jiang Z and
Su mas R 2016 Mul iscale po e-ne wo k ep esen a ion o
he e ogeneous ca bona e ocks Wa e Resou . Res.
52 5433–41
[128] Fin o ´
a S, Anzelo i G, Koneˇ
cn´
a R and Nicole o G 2010
Cas ing po e cha ac e iza ion by x- ay compu ed
omog aphy and me allog aphy A ch. Mech. Eng. 57
263–73
[129] Oh W and Lindquis B 1999 Image h esholding by indica o
k iging IEEE T ans. Pa e n Anal. Mach. In ell.
21 590–602
[130] Robin V, Sa dini P, Mazu ie A, Regnaul O and Descos es M
2016 E ec i e po osi y measu emen s o poo ly
consolida ed ma e ials using non-des uc i e me hods
Eng. Geol. 205 24–9
[131] Du Plessis A, le Roux S G, Booysen G and Els J 2016 Quali y
con ol o a lase addi i e manu ac u ed medical implan
by x- ay omog aphy 3D P in . Addi . Manu . 3175–82
[132] Ke ckho s G, Sch oo en J, Van Cleynenb eugel T,
Lomo S V and We e s M 2008 Valida ion o x- ay
mic o ocus compu ed omog aphy as an imaging ool o
po ous s uc u es Re . Sci. Ins um. 79 013711
[133] Huo D, Pini R and Benson S M 2016 A calib a ion- ee
app oach o measu ing ac u e ape u e dis ibu ions
using x- ay compu ed omog aphy Geosphe e
12 558–71
[134] Coope D, Ma yas J, Ka zenbe g M and Hallg imsson B
2004 Compa ison o mic ocompu ed omog aphic and
mic o adiog aphic measu emen s o co ical bone po osi y
Calci . Tissue In . 74 437–47
[135] Viei a P and Pacio nik S 2001 Unce ain y e alua ion o
me allog aphic measu emen s by image analysis and
he modynamic modeling Ma e . Cha ac . 47 219–26
[136] Panig ahi S K and Gup a S 2018 Au oma ic anking o image
h esholding echniques using consensus o g ound u h
T ai . Signal 35 121–36
[137] Kalaso ´
a D, Zikmund T, Spu ný P, Haloda J, Bo o iˇ
cka J and
Kaise J 2020 Chemical and physical p ope ies o Žd’´
a
nad s´
aza ou l chond i e and po osi y di e en ia ion using
compu ed omog aphy Me eo i . Plane . Sci.
55 1073–81
[138] Du Plessis A, Olawuyi B J, Bosho W P and Le Roux S G
2016 Simple and as po osi y analysis o conc e e using
x- ay compu ed omog aphy Ma e . S uc . 49 553–62
[139] B edemann J and Schmi R H 2018 Task-speci ic
unce ain y es ima ion o medical CT measu emen s J.
Sens. Sens. Sys . 7627–35
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