Final Mas e P ojec
Mas e in Neu oenginee ing and Rehabili a ion
3D essel econs uc ion based on in a-ope a i e
in a ascula ul asound o obo ic au onomous
ca he e na iga ion
THESIS
Au ho : Ma ia Mon se a Ainchil Cayuela
Di ec o : P o . d . Jos Vande Slo en
Co-di ec o : P o . d . Emmanuel Vande Poo en
Supe iso : Miguel Angel Mañanas Villanue a
Summoning: Ap il 2023
Page 2 Thesis
3D essel econs uc ion based on in a-ope a i e IVUS o obo ic au onomous ca he e na iga ion Page 3
Abs ac
In ecen yea s, obo ic echnology has imp o ed ins umen na iga ion p ecision and
accu acy, and helped dec ease he complexi y o minimally in asi e su ge y. S ill, he
inhe en es ic ed access o he ana omy o he pa ien s se e ely complica es many
p ocedu es. In e en ionis s equen ly depend on ex e nal echnologies o isual
guidance, usually employing ionizing adia ion, due o he limi ed iew upon he su gical
scene. In he case o endo ascula p ocedu es, luo oscopy is he common imaging
modali y used o isualiza ion. This modali y is based on X- ays and only o e s a wo-
dimensional (2D) iew o he su gical scene.
Ha ing a eal- ime, up- o-da e unde s anding o he su ounding en i onmen o he
su gical ins umen s wi hin he ascula u e and no depending on using ionizing adia ion
would no only be e y help ul o in e en ionis s, bu also pa amoun o he na iga ion o
an in aluminal obo . The e o e, he aim o his hesis is o de elop an algo i hm able o
do an in a-ope a i e and eal- ime h ee-dimensional (3D) essel econs uc ion.
The algo i hm is di ided in o wo pa s: he econs uc ion and he me ging. In he i s
one, i is ob ained he 3D essel econs uc ion o a sec ion o he essel and in he
second one, he di e en sec ions o 3D essel econs uc ion a e combined. A eal essel
mesh is used o calcula e he i ing e o s o he econs uc ed essel which a e e y
small.
Page 4 Thesis
Resumen
En los úl imos años, la ecnología obó ica ha mejo ado la p ecisión y iabilidad de la
na egación de ins umen os y ha ayudado a disminui la complejidad de la ci ugía
mínimamen e in asi a. Aún así, el acceso es ingido inhe en e a la ana omía de los
pacien es complica g a emen e muchos p ocedimien os. Los in e encionis as dependen
con ecuencia de ecnologías ex e nas pa a la guía isual, gene almen e empleando
adiación ionizan e, debido a la isión limi ada de la escena qui ú gica. En el caso de los
p ocedimien os endo ascula es, la luo oscopia es la modalidad de imagen común
u ilizada pa a la isualización. Es a modalidad se basa en ayos X y solo o ece una is a
bidimensional (2D) de la escena qui ú gica.
Pode sabe en iempo eal y de o ma ac ualizada como es el en o no al ededo de los
ins umen os qui ú gicos que se encuen an den o de la ascula u a y no depende del
uso de adiación ionizan e no solo se ía muy ú il pa a los in e encionis as, sino ambién
undamen al pa a la na egación de un obo in aluminal. Po lo an o, el obje i o de es a
esis es desa olla un algo i mo capaz de ealiza una econs ucción idimensional (3D)
del aso sanguíneo de o ma in aope a o ia y en iempo eal.
El algo i mo se di ide en dos pa es: la econs ucción y la unión. En la p ime a se ob iene
la econs ucción 3D de una sección del aso sanguíneo y en el segundo se combinan las
di e en es secciones ob enidas de asos sanguíneos econs uidos en 3D. Se u iliza una
malla de un aso sanguíneo eal pa a calcula los e o es de ajus e del aso sanguíneo
econs uido, son e o es muy pequeños.
3D essel econs uc ion based on in a-ope a i e IVUS o obo ic au onomous ca he e na iga ion Page 5
Resum
En els úl ims anys, la ecnologia obò ica ha millo a la p ecisió i la iabili a de la
na egació dels ins umen s i ha ajuda a disminui la complexi a de la ci u gia
mínimamen in asi a. To i així, l'accés es ingi inhe en a l'ana omia dels pacien s
complica g eumen mol s p ocedimen s. Els in e encionis es so in depenen de
ecnologies ex e nes pe a la guia isual, no malmen emp an adiacions ioni zan s, a
causa de la isió limi ada de l'escena qui ú gica. En el cas dels p ocedimen s
endo ascula s, la luo oscòpia és la modali a d'ima ge comuna u ili zada pe a la
isuali zació. Aques a modali a es basa en aigs X i només o e eix una isió
bidimensional (2D) de l'escena qui ú gica.
Pode sabe en emps eal i de o ma ac uali zada com és l'en o n al ol an dels
ins umen s qui ú gics que es oben dins de la ascula u a i no depèn de l'ús de adiació
ioni zan no només se ia mol ú il pe als in e encionis es, sinó ambé onamen al pe a la
na egació d'un obo in aluminal. Pe an , l'objec iu d'aques a esi és desen olupa un
algo isme capaç de e una econs ucció idimensional (3D) del as sanguini de o ma
in aope a ò ia i en emps eal.
L'algo isme es di ideix en dues pa s: la econs ucció i la usió. En la p ime a s'ob é la
econs ucció en 3D d'una secció del as sanguini i en la segona, es combinen les
di e en s seccions ob ingudes de asos sanguinis econs uï s en 3D. S'u ili za una malla
d’un as sanguini eal pe calcula els e o s d'ajus del as sanguini econs uï , els e o s
son mol pe i s.

Page 6 Thesis
Con en s
ABSTRACT _________________________________________________ 3
RESUMEN __________________________________________________ 4
RESUM ____________________________________________________ 5
CONTENTS _________________________________________________ 6
LIST OF FIGURES ___________________________________________ 8
1. GLOSSARY ____________________________________________ 11
2. INTRODUCTION ________________________________________ 13
2.1. Endo ascula ca he e iza ion ................................................................... 13
2.2. Th ee-dimensional essel econs uc ion ................................................. 15
2.3. Thesis objec i es ...................................................................................... 18
2.3.1. Speci ic objec i es ...................................................................................... 18
2.4. Thesis scope ............................................................................................ 18
3. THREE-DIMENSIONAL CYLINDER-BASED GLOBAL LUMEN
RECONSTRUCTION _____________________________________ 19
3.1. Da a .......................................................................................................... 19
3.1.1. O igin o he da a ........................................................................................ 19
3.1.2. P epa a ion o he da a ............................................................................... 21
3.1.3. Cylinde model ............................................................................................ 22
3.2. P oposed econs uc ion me hod ............................................................. 24
3.2.1. P imi i e shape ........................................................................................... 24
3.2.2. Dis ance es ima ion .................................................................................... 25
3.2.3. Mo ing nodes ............................................................................................. 28
3.2.4. Ou lie s ....................................................................................................... 29
3.3. Me ging me hod ....................................................................................... 30
4. EXPERIMENTAL VALIDATION ____________________________ 32
4.1. Highe adius cylinde ............................................................................... 32
4.2. F us um ................................................................................................... 33
4.3. In-silico ..................................................................................................... 33
5. RESULTS & DISCUSSION ________________________________ 35
5.1. Highe adius cylinde ............................................................................... 35
5.2. F us um ................................................................................................... 36
3D essel econs uc ion based on in a-ope a i e IVUS o obo ic au onomous ca he e na iga ion Page 7
5.3. In-silico ..................................................................................................... 37
6. LIMITATIONS AND FUTURE WORK ________________________ 45
CONCLUSIONS ____________________________________________ 48
ACKNOWLEDGMENTS ______________________________________ 49
BIBLIOGRAPHY ____________________________________________ 50
ANNEX - ALGORITHM _______________________________________ 53
Page 8 Thesis
Lis o igu es
Figu e 1. Robo ic ca he e wi h one EM senso and an IVUS p obe embedded (wi hin he
o ange ci cle) used in [9]. ................................................................................................ 19
Figu e 2. IVUS c oss-sec ion in he xy-plane o he IVUS ame {i} ................................. 20
Figu e 3. IVUS poin s om a slice in he IVUS ame {i} ................................................. 20
Figu e 4. Cylinde ep esen a ion in {cyl} ame and in {i} ame. .................................... 20
Figu e 5. (1) Cylinde wi h he cen e o he coo dina e ame a he cen e poin o he
bo om base (2) Cylinde wi h he cen e o he coo dina e ame a he cen e o he
cylinde ............................................................................................................................ 23
Figu e 6. (1) Cylinde wi h he x axis pa allel o he longi udinal axis (2) Cylinde wi h he z
axis pa allel o he longi udinal axis. ................................................................................ 23
Figu e 7. P oposed econs uc ion me hod. .................................................................... 24
Figu e 8. Example o cylinde o N=12 nodes. ................................................................ 25
Figu e 9. Example o a cylinde o N=12 nodes di ided in o L=6 le els. ......................... 25
Figu e 10. IVUS poin s pe le el. .................................................................................... 26
Figu e 11. IVUS poin s pe slice in le el 1 (noisy). .......................................................... 26
Figu e 12. T iangles in a ace (1) Bo om iangle (2) Top iangle. ................................. 27
Figu e 13. T iangle wi hou poin s associa ed and i s adjacen (blue) iangles. .............. 27
Figu e 14. T a el dis ance calcula ion o a node ( ed poin ) based on he a e aged
dis ance o he adjacen (blue) iangles. ......................................................................... 28
Figu e 15. Mo ing nodes ................................................................................................ 28
Figu e 16. Ou lie s de ec ion wi h Boxplo [25]. ............................................................... 29
Figu e 17. Example o cylinde 60 and mesh 10. ............................................................ 30
Figu e 18. Example o cylinde 60 and mesh 10 a e applying he condi ion. ................. 31
Figu e 19. New mesh and he non-o e lapping selec ed cylinde poin s. ........................ 31
3D essel econs uc ion based on in a-ope a i e IVUS o obo ic au onomous ca he e na iga ion Page 9
Figu e 20. P imi i e shape and highe adius cylinde (mesh). ....................................... 32
Figu e 21. P imi i e shape and highe adius cylinde (sca e ed)................................... 32
Figu e 22. P imi i e shape and us um (mesh). ............................................................ 33
Figu e 23. P imi i e shape and us um (sca e ed). ...................................................... 33
Figu e 24. Pa ien -speci ic ao ic model .......................................................................... 34
Figu e 25. De o med p imi i e shape and bigge cylinde . .............................................. 35
Figu e 26. De o med p imi i e shape a e 3 i e a ions and us um. .............................. 36
Figu e 27. Adjacen (blue) iangles o a node ( ed poin ) on he op and on he bo om
le el. ............................................................................................................................... 37
Figu e 28. De o med p imi i e shape a e 10 i e a ions and us um. ............................ 37
Figu e 29. Fi ing e o o each de o med cylinde no me ged – Noisy s Noiseless. ..... 38
Figu e 30. Fi ing e o o iginal s de o med cylinde - Noisy da a .................................. 39
Figu e 31. Fi ing e o o iginal s de o med cylinde s - Noiseless da a .......................... 40
Figu e 32. Fi ing e o de o med cylinde s – Noisy da a s Noiseless da a .................... 41
Figu e 33. Violin plo o he Fi ing e o - Noisy da a ...................................................... 42
Figu e 34. Violin plo o he Fi ing e o - Noiseless da a ............................................... 43
Figu e 35. Fi ing e o ep esen a ion and dis ibu ion – Noisy da a ............................... 44
Figu e 36. Fi ing e o ep esen a ion and dis ibu ion – Noiseless da a ........................ 44
Figu e 37. Example o poin s o mesh wi h N=12 and L=5. ............................................. 46
Page 16 Thesis
usion be ween IVUS imaging and EM acking o ealize ully au oma ic p ocessing o
IVUS imaging and 3D econs uc ion in eal ime o endo ascula ao ic s en g a ing, as
well as b anch de ec ion o alignmen and deploymen o he s en g a ing wi h he
ascula u e b anches. In his case, Compu ed Tomog aphic (CT) da a is used o
complemen a y na iga ion allowing an e icien ca he e ad ancemen and assis an
clinical judgmen [13]. In June 2016 was published a second me hod ha p oposes a
echnique o endo ascula na iga ion based on IVUS imaging and EM sensing called
Simul aneous Ca he e and En i onmen Modelling (SCEM). Vessel s uc u e in o ma ion
om p e-ope a i e CT/Magne ic Resonance (MR) imaging is used o a oid adia ion
exposu e and con as agen s. This me hod elies on p ecise egis a ion be ween EM and
p e-ope a i e da a o eco e he 3D s uc u e o he ascula u e oge he wi h he posi ion
o he ca he e ip in aope a i ely, allowing o he p o ision o knowledge abou he
in e ac ions be ween he ca he e and i s su oundings [14]. A mon h la e , in July 2016, is
published SCEM+, a mo e obus me hod han SCEM, ha p oposes o o mula e he 3D
essel econs uc ion as a nonlinea op imiza ion p oblem based on he p e-ope a i e
da a. This allows essel econs uc ion in eal- ime and deals wi h measu emen e o s
om bo h EM senso s and IVUS images [15]. SCEM and SCEM+ ely on accu a e
egis a ion be ween EM and p e-ope a i e da a. In Oc obe 2016, was published an
app oach ha sugges s a egis a ion- ee essel econs uc ion me hod ha combined
wi h he 3D essel econs uc ion using IVUS, EM, and p e-ope a i e da a, es ima es and
upda es EM-CT egis a ion in a-ope a i ely. This amewo k imp o es SCEM+ because i
can handle global mo ion and pe iodic ascula de o ma ion b ough on by he ca diac
cycle and does no equi e any p io knowledge o EM-CT egis a ion [16].
Deep lea ning uses da a p ocessing and ad anced pa e n lea ning o ackle 3D
econs uc ion. Two app oaches a e sugges ed u ilizing a ious so s o inpu da a. The
i s app oach p oposes a ou -ocula ision sys em o he 3D econs uc ion o la ge-
scale conc e e- illed s eel ube (CFST) unde complex es ing condi ions. To sample he
la ge-scale CFST, a ou -ocula ision sys em is buil . A 3D poin cloud o he specimen
su ace is ob ained by using poin cloud cap u e, poin cloud il e ing, and poin cloud
s i ching echniques. A poin cloud co ec ion algo i hm based on geome ic ea u es and a
deep lea ning algo i hm a e u ilized, espec i ely, o co ec he coo dina es o he s i ched
poin cloud. This aises he 3D model accu acy o use in eal- ime complica ed su ace
moni o ing, imp o ing he ision measu emen accu acy in complex si ua ions [17] The
second app oach p oposes a pa allel agg ega ion ne wo k wi h a newly c ea ed global

3D essel econs uc ion based on in a-ope a i e IVUS o obo ic au onomous ca he e na iga ion Page 17
laye o ex ac ing spa ial ea u es om a andom walk no malized ma ix o eco e a
human mesh om a single image. This me hod wan s o sol e one p oblem ha equen ly
a ises when u ilizing G aph Neu al Ne wo ks (GNNs) o econs uc a single-image human
mesh, which is he absence o global in o ma ion in he spa ial ea u e agg ega ion o he
cu en GNNs. The es o ed human mesh migh end up wi h an undesi able de o mi y and
being inaccu a e as a esul . By applying his me hod, he human ea u e may be added o
he mesh using he coa se body mesh (head, hand, oo , e c.) o e ed by he coa sening
ne wo k. The local and global spa ial ea u es a e agg ega ed o upda e e ex
coo dina es [18].
A me hod ha uses de o mable model p oposes o econs uc he su ace o IVUS
co ona y a e ial walls using a simpli ied e sion o a de o mable model known as he 3D
opologically adap able snake model [19].
The e a e wo adi ional app oaches o 3D econs uc ion me hods based on images.
The i s one is Mul i-View S e eo (MVS) and i s goal is o econs uc a comple e 3D
objec model om a collec ion o images aken om known came a iewpoin s [20]. The
second app oach is S uc u e om Mo ion (S M) and consis s o he p ocess o
econs uc ing 3D s uc u e om i s p ojec ions in o a se ies o images aken om di e en
iewpoin s [21]. These me hods equi e a su icien numbe o pho os wi h a small
baseline iewpoin di e ence. Mo eo e , hey ei he need o compu e hese came a
a ibu es o depend on known came a calib a ion (in e nal and ex e nal). To e en ually
calcula e he ep esen a ion o he 3D o m and li hese pho os collec i ely om 2D o
3D, hey mus also compu e a co espondence be ween images. Howe e , he ype o
images needed o S M a e e y di e en om IVUS images.
Se e al a emp s ha e been made o pe o m a mesh econs uc ion om poin clouds.
The echnique a ies i one is wo king wi h an uns uc u ed poin cloud gene a ed by
mul iple image ma ching o a s uc u ed one, gene a ed by one image. S. Kim e al.
p opose a me hod o es ima e su ace no mals o he e ical poin s wi hin an uns uc u ed
poin cloud conside ing ha he p ocess o su ace econs uc ion depends on de e mining
p ecise su ace no mals, which a e occasionally calcula ed inaccu a ely [22]. X. Qin e al.
sugges he cons uc ion o an oc ee s uc u e ha sea ches o la a eas and con ols
edge g owing based on compulsi e es ic ion and op imiza ion c i e ia o ob ain an
op imal mesh su ace [23]. K. Kwon e al. p opose an i e a i e o se -based me hod o
econs uc ing a mesh model om he poin cloud o a pig by c ea ing a p imi i e shape in
Page 18 Thesis
he o m o a mesh. This mesh is de o med based on he dis ance om he p imi i e
shape o he poin s om he poin cloud. This p ocedu e is epea ed o eshape he mesh
model o i he shape o he co esponding poin cloud [24].
2.3. Thesis objec i es
The aim o his hesis is o de elop a me hod o do in a-ope a i e eal- ime 3D essel
econs uc ion. The me hod mus a oid exposing he pa ien and clinician o ionizing
adia ion. Hence, he da a used o de elop he me hod is IVUS and EM da a. The goal o
he algo i hm is o allow a cu en awa eness o he en i onmen wi hin he ascula u e o
imp o e he si ua ional awa eness o he clinician.
2.3.1. Speci ic objec i es
The speci ic objec i es o his hesis a e:
 In es iga e IVUS-based me hods using EM pose sensing and/o shape sensing o
eal- ime 3D essel econs uc ion.
 De elop a me hod o do in a-ope a i e eal- ime 3D essel econs uc ion.
 P o ide ools o isualize he ob ained econs uc ion.
 Ve i y and alida e he p oposed me hod.
2.4. Thesis scope
The algo i hm de eloped is di ided in o wo pa s: he econs uc ion and he me ging. In
he i s one, i is ob ained he 3D essel econs uc ion o a sec ion o he essel and in
he second one, he di e en sec ions o 3D essel econs uc ion a e combined. A eal
essel mesh is used o calcula e he i ing e o s o he econs uc ed essel which a e
e y small.
3D essel econs uc ion based on in a-ope a i e IVUS o obo ic au onomous ca he e na iga ion Page 19
3. Th ee-dimensional cylinde -based global lumen
econs uc ion
3.1. Da a
The da a ha ha e been used o his wo k a e IVUS da a, EM da a and cylinde model
da a.
3.1.1. O igin o he da a
The ca he e used o ga he he needed measu emen s om IVUS and EM acking is a
obo ic ca he e wi h a dis al ac i e segmen . The design o he ca he e and he senso s
used a e de ailed in [9] as he ca he e used o ga he he da a is he same one used o
es ima e an in a-ope a i e local 3D essel ep esen a ion.
Figu e 1. Robo ic ca he e wi h one EM senso and an IVUS p obe embedded (wi hin he o ange
ci cle) used in [9].
The IVUS measu emen s a e he con ou poin s o he essel. Figu e 2, which shows a
c oss-sec ional 2D US iew o he essel a he le el o he IVUS p obe, clea ly illus a es
hese aspec s. Since his senso is aligned wi h he longi udinal axis o he ca he e , he
c oss-sec ion is hus pe pendicula o his longi udinal axis and is isible in he xy-plane o
he IVUS coo dina e ame {i} and is igidly a ached o he cen e o he IVUS p obe. The
EM pose sensing in o ma ion a e he h ee EM posi ion alues: x, y and z; and he ou
EM o ien a ion qua e nion alues: x, y, z and w.
Page 20 Thesis
Figu e 2. IVUS c oss-sec ion in he xy-plane o he IVUS ame {i}
The con ou o he essel lumen can be ex ac ed om he IVUS slice and is ep esen ed
by a se o M consecu i e 2D poin s 𝑐
 spaced e e y 
 adians.
Figu e 3. IVUS poin s om a slice in he IVUS ame {i}
F om he IVUS and EM da a men ioned, a local model o he geome y o he ascula u e
is gene a ed om an algo i hm desc ibed in [9]. The model has a cylinde shape, as he
algo i hm es ima es he essel geome y and i s own coo dina e ame, {cyl} ame. This
cylinde model is also used o his wo k.
Figu e 4. Cylinde ep esen a ion in {cyl} ame and in {i} ame.
3D essel econs uc ion based on in a-ope a i e IVUS o obo ic au onomous ca he e na iga ion Page 21
3.1.2. P epa a ion o he da a
The da a used a e IVUS da a, EM da a and cylinde models. In his pa icula case, as
da a ha e hei own coo dina e ame, hey mus be in he same ame be o e aking any
u he s ep. Fou coo dina e ames a e used: {i} ame ha co esponds o he IVUS
ame, {e} ame ha co esponds o he EM ame, {cyl} ame ha co esponds o he
cylinde ame and he {w} ame ha co esponds o he wo ld ame, a ixed ca esian
coo dina e ame o he en i onmen , no o he mo ing ca he e .
The IVUS p obe and obo ic ca he e ip poses a e de e mined by measu ing he EM
senso 6-DOFs posed when posi ioned in a known elec omagne ic ield. The IVUS p obe
pose is ep esen ed by he homogeneous ans o ma ion ma ix wTi, desc ibing he pose o
he {i} ame in he {w} ame. The IVUS p obe pose is de e mined om he EM senso
pose wTe and om he cons an pose eTi o he IVUS p obe ela i e o he EM senso . eTi is
cons an because he ca he e is designed so he EM and IVUS senso s a e in he same
posi ions wi h espec o each o he when he da a is being collec ed.
These ela ions a e summa ized as:
wTi = wTe· eTi
Equa ion 1. Rela ion be ween he {i}, {e} and {w}.
IVUS da a a e ans o med in o he {w} using he ans o ma ion ma ix wTi and a e also
ans o med in o he {cyl} using a ans o ma ion ma ix: cylTw. EM da a a e ans o med
in o he {w} using he ans o ma ion ma ix wTe.
𝑇=𝑅
 𝑡

0 1

Equa ion 2. Homogeneous ans o ma ion ma ix o ame {i} wi h espec o ame {w}.
𝑇=𝑅
 𝑡

0 1

Equa ion 3. Homogeneous ans o ma ion ma ix o ame {e} wi h espec o ame {w}.
wRi and wRe a e he o a ion ma ices o ames {i} and {e} wi h espec o he ame {w} and
w i and w e a e he ansla ion ec o o ames {i} and {e} wi h espec o he ame {w}.

Page 22 Thesis
The e is a ela ionship be ween he {cyl} and {i} ame (see Equa ion 4) because he
cylinde model is c ea ed as mo e IVUS da a a e collec ed. iTcyl is he ans o ma ion
ma ix o ame {cyl} wi h espec o he exp ess o he ame {i}.
𝑇=cos (𝜃) −𝑠𝑖𝑛 (𝜃) 0 𝑖𝑝
sin (𝜃) ∙ cos (𝜑) cos (𝜃) ∙ cos (𝜑) −sin (𝜑) 𝑖𝑝
sin (𝜃) ∙ sin (𝜑)
0cos (𝜃) ∙ sin (𝜑)
0cos (𝜑) 0
0 1 

Equa ion 4. Homogeneous ans o ma ion ma ix o ame {cyl} wi h espec o ame {e}.
The posi ion ec o o he cylinde , ip, is de ined so ha i always lies on he xy plane o
ame {i}.
IVUS da a a e ans o med om he ame {w} in o he ame {cyl} o each cylinde using
cylTw.
wTcyl = wTe • eTcyl → cylTw = (wTcyl )-1
Equa ion 5. Homogeneous ans o ma ion ma ix o ame {cyl} wi h espec o ame {w}.
3.1.3. Cylinde model
Cylinde models a e gene a ed by s a ing wi h a ci cle o N nodes and a adius R, hen
adding L-1 le els o nodes o c ea e a cylinde . The cylinde model c ea ed does no
ma ch he local model desc ibed in [9]. The bo om base cen e poin o he cylinde model
is loca ed a he cen e o coo dina e ame (0,0,0). Howe e , he local model p esen s
some di e ence wi h he cylinde c ea ed.
Fi s , he local model is de ined aking in o accoun ha he cen e o he cylinde is on he
cen e o coo dina es o he ame. Fo his eason, a ans o ma ion ma ix is applied o
he cylinde model conside ing zz he heigh o he cylinde (see Figu e 5).
𝑇=1 0 0 0
0 1 0 0
0000 1 −𝑧𝑧/2
0 1 

Equa ion 6. Homogeneous ans o ma ion ma ix ha ansla es he cen e o he cylinde o he
cen e coo dina e ame {cyl}.
3D essel econs uc ion based on in a-ope a i e IVUS o obo ic au onomous ca he e na iga ion Page 23
Figu e 5. (1) Cylinde wi h he cen e o he coo dina e ame a he cen e poin o he bo om base
(2) Cylinde wi h he cen e o he coo dina e ame a he cen e o he cylinde .
Second, he longi udinal axis o he cylinde model is pa allel wi h z axis, whe eas in he
local model is pa allel wi h x axis (see Figu e 6).
Figu e 6. (1) Cylinde wi h he x axis pa allel o he longi udinal axis (2) Cylinde wi h he z axis
pa allel o he longi udinal axis.
As he equa ions being used a e om [9] and x axis is de ined o be pa allel o he
longi udinal axis, all IVUS da a need o be o a ed 𝛼= adians a ound he y axis using a
o a ion ma ix (Equa ion 7) in o de o ma ch he way da a is desc ibed.
𝑅(𝛼)=cos (𝛼) 0 sin (𝛼) 0
0 1 0 0
−sin (𝛼)
000cos (𝛼) 0
0 1
Equa ion 7. Ro a ion ma ix a ound he y axis.
The ca esian coo dina e sys em is used o de ine he sou ce da a, IVUS da a and
cylinde model da a. Howe e , hese da a ha e been con e ed in o cylind ical
coo dina es using hese equa ions (Equa ion 8) in o de o be able o pe o m he
econs uc ion calcula ions mo e e ec i ely.
𝑟=𝑥+𝑦 𝜃= an 𝑧=𝑧
Equa ion 8. Ca esian (x,y,z) o Cylind ical ( ,θ,z) coo dina es ans o ma ion.
Page 24 Thesis
3.2. P oposed econs uc ion me hod
The econs uc ion me hod p oposed in his hesis is inspi ed by he i e a i e o se -based
me hod in oduced by K. Kwon e al. [24]. This app oach was chosen because he inpu
da a sha es simila cha ac e is ics o he da a used in his hesis, IVUS: bo h a e poin
clouds, and he app oach uses a p imi i e shape, whe eas he cylinde model is employed
in his hesis. The basic p inciples o he o iginal app oach o mesh-model econs uc ion
p ocess a e as ollows. Fi s , a p imi i e shape is c ea ed in he o m o a mesh and he
dis ance om each node o he poin s om he poin cloud is calcula ed. The nodes a e
mo ed acco ding o he dis ance calcula ed. This p ocedu e is epea ed R imes o
eshape he mesh model o i he shape o he co esponding poin cloud (Figu e 7). The
econs uc ion me hod applied ollows only he i s h ee s eps: c ea ing a p imi i e shape,
es ima ing he dis ance o mo e and mo ing nodes.
Figu e 7. P oposed econs uc ion me hod.
3.2.1. P imi i e shape
The p imi i e shape is ob ained by es ima ing cylinde models (see Figu e 8) using he
algo i hm desc ibed in [9]. These models a e used o ha e a be e app oxima ion o how
he essel su ace eally is. As one o he goals o his app oach is o be eal- ime, as he
ca he e mo es and mo e IVUS da a is being ga he ed, new cylinde s will be c ea ed. As
new cylinde s a e c ea ed, he ame {cyl}k is no s a iona y and changes a each ime s ep
k.
3D essel econs uc ion based on in a-ope a i e IVUS o obo ic au onomous ca he e na iga ion Page 25
Figu e 8. Example o cylinde o N=12 nodes.
3.2.2. Dis ance es ima ion
In o de o es ima e he dis ance om he p imi i e shape mesh o he poin s om he
poin cloud, K. Kwon e al. p opose 4 s eps:
1. Finding he nea es iangle o a gi en poin .
To p ope ly dis o he mesh, iangles a e used o build each o i s aces. To
de e mine which poin in he poin cloud is close o e e y iangle o he mesh model
and calcula e he dis ance be ween hem, he cylinde model is spli in o L le els
ha ing hen N slices pe le el (see Figu e 9).
Figu e 9. Example o a cylinde o N=12 nodes di ided in o L=6 le els.
Page 32 Thesis
4. Expe imen al alida ion
One way o measu e he e ec i eness o an algo i hm is o alida e an algo i hm wi hou
elying on he o iginal da a ha helped o de elop he algo i hm. The algo i hm is es ed
using known geome ies such as cylinde and a us um, and in-silico. A use ul ool o
e alua ing he accu acy o a econs uc ion me hod is o look a he i ing e o wi h
espec o a g ound u h. In his chap e , he se -up o each alida ion is explained.
4.1. Highe adius cylinde
The algo i hm is es ed using a cylinde wi h a highe adius, 30mm, ins ead o using he
IVUS poin s. The cylinde sha es he same opology as he p imi i e shape. In his case,
he g ound u h is a 30 mm adius cylinde .
Figu e 20. P imi i e shape and highe adius cylinde (mesh).
Figu e 21. P imi i e shape and highe adius cylinde (sca e ed).

3D essel econs uc ion based on in a-ope a i e IVUS o obo ic au onomous ca he e na iga ion Page 33
4.2. F us um
The algo i hm is es ed using a us um ins ead o using he IVUS poin s. The us um
also sha es he same opology as he p imi i e shape. In his case, he g ound u h is he
us um.
Figu e 22. P imi i e shape and us um (mesh).
Figu e 23. P imi i e shape and us um (sca e ed).
4.3. In-silico
The alida ion is conduc ed by doing an in-silico expe imen . The main componen s o he
simula ion en i onmen a e a pa ien -speci ic ao ic model, syn he ically gene a ed EM
and IVUS da a, and a simula ed i ual ca he e . The pa ien -speci ic ao ic model (see
Page 34 Thesis
Figu e 24) was de i ed om segmen ed CT scans o an ao a o a pa ien . Fo he
pu pose o modeling EM noise o ealis ic syn he ic da a, Gaussian noise wi h ze o mean
and 0.3 mm and 0.5 mm s anda d de ia ions o he ansla ional and o a ional sec ions
o he wis , espec i ely, was added. Simila o his, he coo dina es o he syn he ic IVUS
da a had Gaussian noise added o hem wi h a ze o mean and a s anda d de ia ion o 1
mm. The ca he e was ins uc ed o epea edly ollow a p e-de ined ajec o y along he
essel du ing ca he e inse ion o ca he e bending du ing he in-silico es s. This p e-
de e mined ajec o y included a o wa d ansla ion o 20 mm a a speed o 2.4 mm/s, as
well as a sequence o bending ins uc ions a a speed o 4.8 °𝑠
, including a 30° bend o
he ca he e ip in a single bending plane (BP), a 360° bend o he BP, and a -30° bend o
he ca he e ip in he o iginal BP [9]. In his case, he g ound u h is a essel mesh.
Figu e 24. Pa ien -speci ic ao ic model
Since he IVUS and he EM senso a e aligned poin s, i can be de ined ha he cons an
pose o he IVUS p obe ela i e o he EM senso , eTi, is equal o he iden i y ma ix.
The e o e, Equa ion 1 can be also de ined as Equa ion 11.
wTi = wTe· eTi
eTi = I → wTi = wTe
Equa ion 11. New ela ion be ween he {i}, {e} and {w}.
3D essel econs uc ion based on in a-ope a i e IVUS o obo ic au onomous ca he e na iga ion Page 35
5. Resul s & Discussion
The de elopmen o a eal- ime 3D econs uc ion app oach o a essel has been he
p ima y goal o his hesis. The me hod employs i e a ions o modi y he mesh model in
he bes way possible o ma ch he shape o he poin cloud o IVUS da a.
The esul s ob ained by he expe imen al alida ion using known geome ies such as
cylinde and a us um, and in-silico will be discussed in his chap e .
5.1. Highe adius cylinde
The econs uc ion s ep is pe o med h ee imes, howe e as shown in Table 1, he
p imi i e shape expe iences i s maximum de o ma ion (see Figu e 25) in he i s i e a ion
ob aining a e y small e o .
Table 1. Fi ing e o o he de o med cylinde wi h espec o he bigge cylinde .
Figu e 25. De o med p imi i e shape and bigge cylinde .
I e a ion 0
I e a ion 1
I e a ion 2
I e a ion 3
20,0039 4,92∙10-16 4,92∙10-16 4,92∙10-16
Page 36 Thesis
5.2. F us um
Ini ially, he econs uc ion s ep is pe o med h ee imes, howe e as shown in Table 2
he i ing e o dec eases bu i is no as small as he one ob ained when using he bigge
cylinde . As can be seen in Figu e 26, he de o med cylinde does no comple ely ma ch
he us um as i does wi h he cylinde .
Table 2. Fi ing e o o he de o med cylinde wi h espec o he us um – 3 i e a ions.
Figu e 26. De o med p imi i e shape a e 3 i e a ions and us um.
As he esul s a e no he expec ed ones, he econs uc ion s ep is epea ed en imes o
s udy he de o ma ion e ec on he us um.
Table 3. Fi ing e o o he de o med cylinde wi h espec o he us um – 10 i e a ions.
As mo e i e a ions a e pe o med, he i ing e o educes as indica ed in Table 3, bu he
e o does no each ze o. Obse ing whe e he i ing e o is highe in he nodes, i can
be seen ha is in he nodes ha a e on he op and bo om le els. This is as a esul o he
way he a el dis ance o each node is calcula ed.
I e a ion 0
I e a ion 1
I e a ion 2
I e a ion 3
4,9406 0,5180 0.0869 0.0751
I e a ion 0
I e a ion 1
I e a ion 2
I e a ion 3
I e a ion 4
I e a ion 5
4,9406 0,5180 0.0869 0.0751 0.0585 0.0465
I e a ion 6
I e a ion 7
I e a ion 8
I e a ion 9
I e a ion 10
0.0390 0.0326 0.0283 0.0248 0.0224
3D essel econs uc ion based on in a-ope a i e IVUS o obo ic au onomous ca he e na iga ion Page 37
Figu e 27. Adjacen (blue) iangles o a node ( ed poin ) on he op and on he bo om le el.
As i can be seen in Figu e 27, he nodes o he op and bo om le els ha e less iangles
adjacen o he node. The e o e, as he nodes o he op and bo om le els ha e less da a,
he e o does no each ze o. An imp o ed de o ma ion ha ma ches be e he us um
is shown in Figu e 28.
Figu e 28. De o med p imi i e shape a e 10 i e a ions and us um.
5.3. In-silico
The algo i hm was un using cylinde models wi h N=12 slices and L=6 le els. The
me hod is spli in o wo pa s: he econs uc ion phase, which de o ms he p imi i e
shape, and he me ging phase, which combines he de o med p imi i e shape wi h he
nex de o med p imi i e shape. As he cylinde s models a e es ima ed a 12 ames pe
second, models om consecu i e ime s eps show a la ge o e lap. The e o e, only
cylinde s ha a e mul iples o 10 a e me ged. The i ing e o is calcula ed in bo h s eps
conside ing he essel mesh as he g ound u h.

Page 38 Thesis
 Noisy and noiseless da a
The algo i hm is un on syn he ically gene a ed IVUS da a wi h added noise and wi hou i .
The i ing e o o each one wi h espec o he essel mesh is calcula ed o illus a e how
he added noise a ec s he algo i hm.
Figu e 29. Fi ing e o o each de o med cylinde no me ged – Noisy s Noiseless.
On Figu e 29, i can be obse ed ha , wi h a ew excep ions, he i ing e o o he
de o med cylinde s p oduced om noisy and noiseless da a ollow he same pa e n.
Excep o cylinde nº120, noisy and noiseless ha e peaks a he same cylinde s, al hough
usually he peaks om noisy da a a e g ea e . Wi h cylinde nº120, bo h de o med
cylinde s ha e he same peak heigh and i ing e o . This may be he esul o an
e ec i e elimina ion o noisy ou lie s.
The cylinde has unde gone h ee de o ma ions in o de o p oduce he inal de o med
cylinde . To de e mine i he pa e n is he esul o he de o ming p ocess, he i ing e o
in each i e a ion and i s median ha e been compu ed.
Table 4. Median o he Fi ing e o s o de o med cylinde s ob ained in i e a ion 0, 1, 2 and 3.
Noisy
I e a ion 0
0.6503
Noiseless
I e a ion 0
0.6381
I e a ion 1
0.4774
I e a ion 1
0.4716
I e a ion 2
0.4646
I e a ion 2
0.4555
I e a ion 3
0.4722
I e a ion 3
0.4572
3D essel econs uc ion based on in a-ope a i e IVUS o obo ic au onomous ca he e na iga ion Page 39
The median in bo h columns o Table 4 ollows he same pa e n, dec easing om
i e a ion 0 o i e a ion 2 and sligh ly inc easing om i e a ion 2 o i e a ion 3. These
indings lead o he conclusion ha he e is a clea ela ion be ween he en i onmen and
wha is happening o he e o ; when he p imi i e shape is de o med based on noisy da a,
he e o is bigge .
 Compa a ion o i ing e o s
As he i ual ca he e mo es, mo e IVUS da a a e being ga he ed. The p oposed me hod
de o ms he p imi i e shape o i he shape o he IVUS poin s and me ges he de o med
cylinde wi h p e ious ones. The e o e, he i ing e o has been calcula ed as new
cylinde s we e being me ged.
 O iginal cylinde s De o med cylinde
The algo i hm uses as p imi i e shape a cylinde ha was es ima ed in [9]. Tha
p imi i e shape is men ioned as he o iginal cylinde . To e alua e he accu acy o
he me hod, he i ing e o o he o iginal cylinde s me ged, and he de o med
cylinde s me ged a e compa ed.
Figu e 30. Fi ing e o o iginal s de o med cylinde - Noisy da a
Page 40 Thesis
Figu e 31. Fi ing e o o iginal s de o med cylinde s - Noiseless da a
As can be seen on he igu es abo e, bo h wi h noiseless and noisy da a, he
de o med cylinde s p esen a lowe i ing e o han he o iginal cylinde s. In bo h
igu es, cons an peaks can be obse ed as he i ing e o slowly inc eases in
bo h cases bu he i ing e o om he o iginal cylinde p esen s mo e highe
peaks. These peaks can be ela ed o he o ien a ion o he p imi i e shape. As he
o iginal cylinde s mo e and change hei o ien a ion, he i ing e o inc eases.
Addi ionally, i is appa en he o al i ing e o ises. This may be as a esul o
handling mo e da a as he cylinde s a e combined.
 De o med cylinde wi h noisy da a s noiseless da a
To e alua e how he da a a ec s he accu acy o he me hod, he i ing e o o he
de o med cylinde s me ged c ea ed om noisy and noiseless da a a e compa ed.
3D essel econs uc ion based on in a-ope a i e IVUS o obo ic au onomous ca he e na iga ion Page 41
Figu e 32. Fi ing e o de o med cylinde s – Noisy da a s Noiseless da a
Looking a he Figu e 32, i can be seen ha o e all, he i ing e o o he
cylinde s de o med is e y small, especially o noisy da a which he algo i hm
achie es a e y compa able i ing e o . As expec ed, he i ing e o om
noiseless da a is smalle . These esul s suppo he heo y ha cylinde s c ea ed
om noiseless da a ha e a lowe i ing e o as hey a e c ea ed om pe ec da a.
Howe e , om cylinde nº 102 o 116, he i ing e o om he noiseless da a is
highe han he noisy da a. Checking he algo i hm e eals ha i could be because
he e is less da a when using noiseless da a, c i ical da a ha would ha e been
miscons ued o an ou lie has been dele ed. Compa ing he Figu e 32 and Figu e
29, can be seen ha in bo h igu es he i ing e o a nº 120 p esen s he same
beha io , same i ing e o in noisy and noiseless da a.
 Fi ing e o s o me ged cylinde s s no -me ged cylinde s
I would be alse o assume ha he a e age o he i ing e o s o all he cylinde s
ha ha e no been me ged equals he i ing e o o all he cylinde s combined
since some poin s a e cu -o when me ging cylinde s. Howe e , i is expec ed ha
bo h e o s will ha e simila esul s (see Table 5).
Page 48 Thesis
Conclusions
Being awa e o he su ounding en i onmen when na iga ing a ca he e wi hin he
ascula u e is e y use ul o in e en ionis s. The inhe en es ic ed access o he
ana omy o he pa ien s se e ely complica es many endo ascula p ocedu es. To his
end, an algo i hm able do an in a-ope a i e and eal- ime h ee-dimensional (3D) essel
econs uc ion has been de eloped.
The da a gi en o de elop his algo i hm consis ed o IVUS poin s and EM posing da a.
The e o e, me hods, based on IVUS da a using EM pose o eal- ime 3D essel
econs uc ion, ha e been esea ched. Howe e , he me hod ha inspi ed he algo i hm is
a me hod ha wo ks wi h speci ically poin cloud da a. I was conside ed he mos
adequa e me hod o his case as IVUS da a is o med by poin s and he me hod also
uses a p imi i e shape.
The algo i hm is di ided in o wo pa s: he econs uc ion and he me ging. In he i s
one, i is ob ained he 3D essel econs uc ion o a sec ion o he essel and in he
second one, he di e en sec ions o 3D essel econs uc ion a e combined.
The MATLAB command imesh has been used o isualize he econs uc ion, and he
algo i hm was es ed in-silico and using well-known geome ies like a cylinde and a
us um. The i ing e o be ween a mesh ep esen ing a genuine essel and he
econs uc ion o he essel was las ly compu ed o e i y he e ec i eness o he code.
Small econs uc ion e o s o mean 0.4722 mm and 0.4572 mm we e achie ed o
simula ed IVUS and EM da a wi h added noise and wi hou i .
Howe e , he in- i o alida ion was skipped because o a lack o ime. As he e would be
mo e noise and measu emen e o s, i would ha e been easonable o an icipa e sligh ly
la ge i ing e o s han hose achie ed in-silico. Fu u e wo k will in ol e doing in- i o
alida ion and upda ing he algo i hm o make i possible o econs uc when he essel
con ains ex a b anches.

3D essel econs uc ion based on in a-ope a i e IVUS o obo ic au onomous ca he e na iga ion Page 49
Acknowledgmen s
I would like o s a by hanking Ka holieke Uni e si ei Leu en (KU Leu en) and P o . d .
Jos Vande Slo en and P o . d . Emmanuel Vande Poo en o he oppo uni y o wo k on
his p ojec . I would like o exp ess my deepes app ecia ion o my supe iso s a KU
Leu en, Bea iz Fa ola Ba a a and Wim-Alexande Becke s, who ha e guided and
ad ised me h ough he whole p ojec .
Secondly, I would like o hank Uni e si a Poli ècnica de Ca alunya (UPC), i s p o esso s
and my classma es who ha e accompanied me du ing he mas e ’s deg ee in
Neu oenginee ing and Rehabili a ion.
Special hanks o Hospi al Uni e si a i de Bell i ge and my o me cowo ke s, o making i
possible o wo k and pu sue a mas e 's deg ee a he same ime.
Since e hanks also o my beau i ul iends, o hei unwa e ing lo e, suppo and o
making he wo ld a joy ul and a mo e lo ing place.
Wo ds canno exp ess my g a i ude o my amily, hei uncondi ional lo e, daily
encou agemen and o he us hey ha e in me.
Finally, I would like o hank God. To Him be he glo y and hono and powe .
Page 50 Thesis
Bibliog aphy
[1] Wo ld Heal h O ganiza ion, “Ca dio ascula diseases (CVDs),” 2021.
h ps://www.who.in /news- oom/ ac -shee s/de ail/ca dio ascula -diseases-
(c ds) (accessed Jan. 12, 2023).
[2] H. Ra ii-Ta i, C. J. Payne, and G. Z. Yang, “Cu en and eme ging obo -
assis ed endo ascula ca he e iza ion echnologies: A e iew,” Annals o
Biomedical Enginee ing, ol. 42, no. 4. Kluwe Academic Publishe s, pp.
697–715, 2014. doi: 10.1007/s10439-013-0946-8.
[3] Uni e si y o Cali o nia San F ancisco, “Endo ascula Su ge y | Condi ions &
T ea men s | UCSF Heal h.”
h ps://www.ucs heal h.o g/ ea men s/endo ascula -su ge y (accessed Jan.
12, 2023).
[4] F oed e & Medical College o Wisconsin, “Endo ascula The apy,
Ca he e iza ion P ocedu es.” h ps://www. oed e .com/hea -
ca e/ ea men /endo ascula - he apy (accessed Oc . 13, 2022).
[5] L. Da, D. Zhang, and T. Wang, “O e iew o he ascula in e en ional
obo ,” The In e na ional Jou nal o Medical Robo ics and Compu e Assis ed
Su ge y, ol. 4, no. 4, pp. 289–294, Dec. 2008, doi: 10.1002/RCS.212.
[6] J. Bona i, G. Ve o ec, C. Riga, O. Wazni, and P. S adle , “Robo ic
echnology in ca dio ascula medicine,” Na u e Re iews Ca diology, ol. 11,
no. 5. Na u e Publishing G oup, pp. 266–275, 2014. doi:
10.1038/n ca dio.2014.23.
[7] P. T. T an, “Ca he e and Vessel Shape Es ima ion o Guidance o Robo ic
Ca he e s in Endo ascula Su ge y,” Scha ing an de ka he e - en
bloed a o m oo begeleiding an obo ische ka he e s in endo asculai e
chi u gie, no. Ma ch, 2018.
[8] S. James Chen and J. D. Ca oll, “3-D econs uc ion o co ona y a e ial ee
o op imize angiog aphic isualiza ion,” IEEE T ans Med Imaging, ol. 19, no.
4, pp. 318–336, 2000, doi: 10.1109/42.848183.
[9] B. Fa ola Ba a a e al., “IVUS-Based Local Vessel Es ima ion o Robo ic
In a ascula Na iga ion,” IEEE Robo Au om Le , ol. 6, no. 4, pp. 8102–
8109, 2021, doi: 10.1109/l a.2021.3102307.
3D essel econs uc ion based on in a-ope a i e IVUS o obo ic au onomous ca he e na iga ion Page 51
[10] F. Bellocchio, N. A. Bo ghese, S. Fe a i, and V. Piu i, “3D Su ace
Recons uc ion,” 3D Su ace Recons uc ion, 2013, doi: 10.1007/978-1-4614-
5632-2.
[11] G. Hichem, F. Chouchene, and H. Belmab ouk, “3D Model Recons uc ion o
Blood Vessels in The Re ina wi h Tubula S uc u e,” In e na ional Jou nal on
Elec ical Enginee ing and In o ma ics, ol. 7, no. 4, 2015, doi:
10.15676/ijeei.2015.7.4.14.
[12] P. T. T an, P. Chang, J. ande Slo en, and D. S oyano , “3D Ca he e
Shape Recons uc ion Using Elec omagne ic and Image Senso s 3D
Ca he e Shape Recons uc ion using Elec omagne ic and Image Senso s,”
no. Ma ch, 2017, doi: 10.1142/S2424905X17400098.
[13] C. Shi e al., “Real- ime in i o in a ascula econs uc ion and na iga ion
o endo ascula ao ic s en g a ing,” In J Med Robo , ol. 12, no. 4, pp.
648–657, Dec. 2016, doi: 10.1002/RCS.1736.
[14] L. Zhao, S. Gianna ou, S.-L. Lee, R. Me i ield, and G. Z. Yang, “In a-
ope a i e Simul aneous Ca he e and En i onmen Modelling o
Endo ascula Na iga ion Based on In a ascula Ul asound,
Elec omagne ic T acking and P e-ope a i e Da a”.
[15] L. Zhao, S. Gianna ou, S. L. Lee, and G. Z. Yang, “SCEM+: Real-Time
Robus Simul aneous Ca he e and En i onmen Modeling o Endo ascula
Na iga ion,” In a ascula Ul asound: F om Acquisi ion o Ad anced
Quan i a i e Analysis, ol. 1, no. 2, pp. 185–197, 2020, doi: 10.1016/B978-0-
12-818833-0.00011-4.
[16] L. Zhao, S. Gianna ou, S. L. Lee, and G. Z. Yang, “Regis a ion- ee
simul aneous ca he e and en i onmen modelling,” Lec u e No es in
Compu e Science (including subse ies Lec u e No es in A i icial In elligence
and Lec u e No es in Bioin o ma ics), ol. 9900 LNCS, pp. 525–533, 2016,
doi: 10.1007/978-3-319-46720-7_61/TABLES/1.
[17] Y. Tang e al., “Vision-Based Th ee-Dimensional Recons uc ion and
Moni o ing o La ge-Scale S eel Tubula S uc u es,” Ad ances in Ci il
Enginee ing, ol. 2020, 2020, doi: 10.1155/2020/1236021.
[18] S. Li, Y. Liu, and W. Su, “Single-image human mesh econs uc ion by
pa allel spa ial ea u e agg ega ion,” Compu Anima Vi ual Wo lds, ol. 33,
no. 3–4, pp. 1–11, 2022, doi: 10.1002/ca .2084.
Page 52 Thesis
[19] F. Sun, “Su ace econs uc ion o he co ona y a e ial walls om
in a ascula ul asound images,” J Elec on Imaging, ol. 16, no. 4, p.
043016, 2007, doi: 10.1117/1.2804172.
[20] S. M. Sei z, B. Cu less, J. Diebel, D. Scha s ein, and R. Szeliski, “A
compa ison and e alua ion o mul i- iew s e eo econs uc ion algo i hms,” in
P oceedings o he IEEE Compu e Socie y Con e ence on Compu e Vision
and Pa e n Recogni ion, 2006, pp. 519–526. doi: 10.1109/CVPR.2006.19.
[21] J. L. Schonbe ge and J. M. F ahm, “S uc u e- om-Mo ion Re isi ed,”
P oceedings o he IEEE Compu e Socie y Con e ence on Compu e Vision
and Pa e n Recogni ion, ol. 2016-Decembe , pp. 4104–4113, Dec. 2016,
doi: 10.1109/CVPR.2016.445.
[22] S. Kim, H. G. Kim, and T. Kim, “Mesh modelling o 3D poin cloud om UAV
images by poin classi ica ion and geome ic cons ain s,” In e na ional
A chi es o he Pho og amme y, Remo e Sensing and Spa ial In o ma ion
Sciences - ISPRS A chi es, ol. 42, no. 2, pp. 507–511, 2018, doi:
10.5194/isp s-a chi es-XLII-2-507-2018.
[23] X. J. Qin, Z. T. Hu, H. B. Zheng, and M. Y. Zhang, “Su ace econs uc ion
om uno ganized poin clouds based on edge g owing,” Ad Manu , ol. 7,
no. 3, pp. 343–352, 2019, doi: 10.1007/s40436-019-00262-5.
[24] K. Kwon and D. Mun, “I e a i e o se -based me hod o econs uc ing a
mesh model om he poin cloud o a pig,” Compu Elec on Ag ic, ol. 198,
no. Ap il, 2022, doi: 10.1016/j.compag.2022.106996.
[25] “Ou lie de ec ion wi h Boxplo s. In desc ip i e s a is ics, a box plo … | by
Vishal Aga wal | Medium.” h ps://medium.com/@aga wal. ishal819/ou lie -
de ec ion-wi h-boxplo s-1b6757 a a21 (accessed Ap . 13, 2023).
3D essel econs uc ion based on in a-ope a i e IVUS o obo ic au onomous ca he e na iga ion Page 53
Annex - Algo i hm
clc; clea all;
% load cyl& o a ion_noiselessda a.ma
% load cyl& o a ion_noiseda a.ma
o i=10:10:leng h(da a_cyl)
C_w=[]; I_w=[];
o j=1:i
w_Te=[ o m(:,:,j);[0 0 0]]; w_Te(:,4)=[Ep(j,:),1];
IVUS=[x_da a(j,:);y_da a(j,:);ze os(1,M_cyl);ones(1,M_cyl)]; I_w=[I_w w_Te*IVUS];
cyl_pos=[cyl_px(j,:) cyl_py(j,:) 0 1]; cyl_pos=cyl_pos';
C_w=[C_w w_Te*cyl_pos];
end
% T ans o ma ion o all IVUS da a o one cylinde in o he cyl ame om he wo ld ame
w_Te=[ o m(:,:,i);[0 0 0]]; w_Te(:,4)=[Ep(i,:),1];
e_Tcyl=[cos( he a(i,:)), -sin( he a(i,:)),0,cyl_px(i,:);sin( he a(i,:))*cos(phi(i,:)),
cos( he a(i,:))*cos(phi(i,:)),-sin(phi(i,:)),cyl_py(i,:);
sin( he a(i,:))*sin(phi(i,:)), cos( he a(i,:))*sin(phi(i,:)),cos(phi(i,:)),0; [0,0,0,1]];
w_Tcyl=w_Te*e_Tcyl; cyl_Tw=in (w_Tcyl);
% T ans o ma ion & o a ion in o he cylinde ame
alpha=-pi/2; Ry=[cos(alpha) 0 sin(alpha) 0;0 1 0 0; -sin(alpha) 0 cos(alpha) 0; 0 0 0 1];
m=Ry*cyl_Tw;
I_cyl= m*I_w;I_cyl=I_cyl([1:3],:);
% CYLINDER MAKING
heigh =10;
le els=5;
N =1; N =12; zz=0:(heigh /le els):heigh ;
[Nodes, T iangles, Quads]=Ci cle_Mesh( ad(i),N ,N );
[Nodes3D,P isms,B icks] = Mesh2D_ o_Mesh3D(Nodes,T iangles,Quads,zz);
% TRANSFORMATION INTO THE CENTER OF THE COORDINATE FRAME
=[0; 0; -max(zz)/2]; TF_c=[1 0 0; 0 1 0; 0 0 1; 0 0 0];TF_c(:,4)=[ ; 1];
N=[Nodes3D(:,1),Nodes3D(:,2),Nodes3D(:,3),ones(leng h(Nodes3D),1)];N=N';
Nodes3D=TF_c*N;Nodes3D(4,:)=[]; Nodes3D=Nodes3D';
cyl_mesh=Nodes3D';

Page 54 Thesis
%TRIANGLE CONNECTIVITY MATRIX (my cylinde )
cyl_TCM=[];
cyl_TCM=[cyl_TCM ; [P isms(:,1) P isms(:,2) P isms(:,5)]];
cyl_TCM=[cyl_TCM ; [P isms(:,1) P isms(:,5) P isms(:,4)]];
% DEFINE SECTION OF IVUS DATA INSIDE THE CYLINDER IN Z AXIS
Cz=cyl_mesh(3,:);
I_sec ion_cyl=[];
o nI=1:leng h(I_cyl)
i I_cyl(3,nI)>=min(Cz) & I_cyl(3,nI)<=max(Cz)
I_sec ion_cyl=[I_sec ion_cyl I_cyl(:,nI)];
end
end
% TRANSFORM IVUS in {cyl} INTO THE CYLINDRICAL COORDINATES
I_cyl_CC=[];
o cc=1:leng h(I_sec ion_cyl)
angle=a an(I_sec ion_cyl(2,cc)/I_sec ion_cyl(1,cc));
i I_sec ion_cyl(1,cc)<0
angle=angle+pi;
else
i angle<0
angle=angle+2*pi;
end
end
I_cyl_CC(:,cc)=[sq (I_sec ion_cyl(1,cc)^2+I_sec ion_cyl(2,cc)^2) angle I_sec ion_cyl(3,cc)];
end
% TRANSFORM CYL NODES INTO THE CYLINDRICAL COORDINATES [x y z] --> [ angle z]
cyl_mesh_CC=[];
o cc=1:leng h(cyl_mesh)
angle=a an(cyl_mesh(2,cc)/cyl_mesh(1,cc));
i cyl_mesh(1,cc)<0
angle=angle+pi;
else
i angle<0
angle=angle+2*pi;
3D essel econs uc ion based on in a-ope a i e IVUS o obo ic au onomous ca he e na iga ion Page 55
end
end
cyl_mesh_CC(:,cc)=[sq (cyl_mesh(1,cc)^2+cyl_mesh(2,cc)^2) angle cyl_mesh(3,cc)];
end
% DEFINE SECTION OF IVUS DATA AROUND THE CYLINDER in he xyplane
I_sec ion_CC=[];index_i us=[];
o nI=1:leng h(I_cyl_CC)
i ad(i)*1.5>=I_cyl_CC(1,nI) && I_cyl_CC(1,nI)>= ad(i)*0.5
I_sec ion_CC=[I_sec ion_CC I_cyl_CC(:,nI)];
index_i us=[index_i us nI] ;
end
end
% SANITY CHECK - IVUS & CYL NODES IN CARTESSIAN COORDINATES SO WE CAN SEE
IF THEY ARE PLOTTED CORRECTLY
o hc=1:leng h(index_i us)
I_sec ion_HC(:,hc)=[I_sec ion_cyl(:,index_i us(hc))];
end
% DISTANCE CALCULATION USING CYLINDRICAL COORDINATES
angles=[]; Dis _le =[];cyl_nodes=[];I e a ion_nodes=[];
o i e a ion=1:4 %i e a ion 1 es i e a ion 0
leng h_d=[]; l_d=[];
i i e a ion~=1
DD=[];
i i e a ion==2
o n=1:N
angles(n,:)=[(2*pi/N )*(n-1)];
end
angles(leng h(angles)+1)=2*pi;
cylinde =cyl_mesh_CC';
else
cylinde =cyl_all;
cyl_nodes=[];
end
z_limi =unique(cylinde (:,3)); %g id in z
Page 56 Thesis
o le =1:le els
o l=1:(leng h(angles)-1)
I_a ea1=[];I_a ea2=[];Dis ance1=[];Dis ance2=[];
o k=1:leng h(I_sec ion_CC)
i z_limi (le )<=I_sec ion_CC(3,k) & I_sec ion_CC(3,k)<=z_limi (le +1)
i angles(l)<=I_sec ion_CC(2,k) & I_sec ion_CC(2,k)<=angles(l+1)
n_ i1=[P isms(N *(le -1)+l,1) P isms(N *(le -1)+l,2) P isms(N *(le -1)+l,5)];
n_ i2=[P isms(N *(le -1)+l,1) P isms(N *(le -1)+l,5) P isms(N *(le -1)+l,4)];
TRI1=[cylinde (n_ i1(1),:);cylinde (n_ i1(2),:);cylinde (n_ i1(3),:)];
TRI2=[cylinde (n_ i2(1),:);cylinde (n_ i2(2),:);cylinde (n_ i2(3),:)];
i l==N
TRI1(2,2)=angles(N +1);TRI1(3,2)=angles(N +1);
TRI2(2,2)=angles(N +1);
end
[dis 1,pp1]=poin T iangleDis ance(TRI1,I_sec ion_CC(:,k));
[dis 2,pp2]=poin T iangleDis ance(TRI2,I_sec ion_CC(:,k));
i dis 1>dis 2
B= aceNo mal( iangula ion([1,2,3],TRI2(:,1),TRI2(:,2),TRI2(:,3)));
A=I_sec ion_CC(:,k)'-pp2;
C=do (A,B);
i C<0
dis 2=-dis 2;
end
I_a ea2=[I_a ea2 I_sec ion_HC(:,k)];
Dis ance2=[Dis ance2 dis 2];
else
B= aceNo mal( iangula ion([1,2,3],TRI1(:,1),TRI1(:,2),TRI1(:,3)));
A=I_sec ion_CC(:,k)'-pp1;
C=do (A,B);
i C<0
dis 1=-dis 1;
end
I_a ea1=[I_a ea1 I_sec ion_HC(:,k)];
Dis ance1=[Dis ance1 dis 1];
end
end
end
3D essel econs uc ion based on in a-ope a i e IVUS o obo ic au onomous ca he e na iga ion Page 57
end
% emo e noise
%PLOTBOX OUTLIERS REMOVAL
D1=[];
Dis ance1=so (Dis ance1);n1=leng h(Dis ance1);
i n1==1 || n1==0
D1=Dis ance1;
else
q2= ound((1/2)*(n1+1));
q1= ound((1/4)*(n1+1));
q3= ound((3/4)*(n1+1));
iq 1=Dis ance1(q3)-Dis ance1(q1); low_lim1=Dis ance1(q1)-1.5*iq 1;
up_lim1=Dis ance1(q3)+1.5*iq 1;
D1=[];
o d=1:leng h(Dis ance1)
i low_lim1<Dis ance1(d) && Dis ance1(d)<up_lim1
D1=[D1 Dis ance1(d)];
end
end
end
D2=[];
Dis ance2=so (Dis ance2);n2=leng h(Dis ance2);
i n2==1 || n2==0
D2=Dis ance2;
else
q2= ound((1/2)*(n2+1));
q1= ound((1/4)*(n2+1));
q3= ound((3/4)*(n2+1));
iq 2=Dis ance2(q3)-Dis ance2(q1); low_lim2=Dis ance2(q1)-1.5*iq 2;
up_lim2=Dis ance2(q3)+1.5*iq 2;
D2=[];
o d=1:leng h(Dis ance2)
i low_lim2<Dis ance2(d) && Dis ance2(d)<up_lim2
D2=[D2 Dis ance2(d)];
end
Page 64 Thesis
l_mesh1(mm)=leng h(mesh1_s );
i mm==1 || l_mesh1(mm)>l_mesh1(mm-1)
%add new ows o he TCM2
me g_mesh_TCM=[]; nw_TCM_m2=[];
i mm==1
nmax=leng h(me g_mesh)-leng h(mesh2_ );
else
nmax=l_mesh1(mm)-l_mesh1(mm-1);
end
o le =1:nmax/N
i le ==1
az=TCM1(leng h(TCM1),1);
cm=TCM1;
else
az=nw_TCM_m2(leng h(nw_TCM_m2),1);
cm=nw_TCM_m2;
end
o ln=1:2
o c=1:N
a1=az+ c;
i ln==1
a3=a1+13;
a2=a1+1;
else
a2=a1+13;
a3=a2-1;
end
cm_m2=[a1 a2 a3];
i c==N
cm_m2(2)= cm(leng h( cm),2*ln-1)+1;
i ln==1
cm_m2(3)=TCM1(leng h(TCM1),3)+1+N *(le -1);
end
end
nw_TCM_m2=[nw_TCM_m2; cm_m2];
end

3D essel econs uc ion based on in a-ope a i e IVUS o obo ic au onomous ca he e na iga ion Page 65
end
end
me g_mesh_TCM=[TCM1; nw_TCM_m2];
elsei l_mesh1(mm)==l_mesh1(mm-1)
me g_mesh_TCM=TCM1;
else
cmmax=l_mesh1(mm-1)-l_mesh1(mm);
me g_mesh_TCM=TCM1([1:(leng h(TCM1)- cmmax*2)],:);
end
% ans o m in o he {w}
mesh1_w=w_Tcylm2*([mesh1_m2 ones(leng h(mesh1_m2),1)])';mesh1_w=mesh1_w([1:3],:)';
me g_mesh_w=w_Tcylm2*([me g_mesh
ones(leng h(me g_mesh),1)])';me g_mesh_w=me g_mesh_w([1:3],:)';
%PLOT
i mm==1
igu e
imesh(TCM1,mesh1_w(:,1),mesh1_w(:,2),mesh1_w(:,3),'edgecolo ','k')
end
imesh(me g_mesh_TCM,me g_mesh_w(:,1),me g_mesh_w(:,2),me g_mesh_w(:,3),' acecolo ',' ','
edgecolo ','k')
hold on
imesh(me g_mesh_TCM([1:leng h(mesh1_s )*2],:),me g_mesh_w(:,1),me g_mesh_w(:,2),me g_
mesh_w(:,3),'edgecolo ','k')
hold o
end
Page 66 Thesis