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Special Sec ion on 3DOR 2025
SHREC 2025: Pa ial e ie al benchma kI
Ba I e an Blokland a,∗, Isaac Agui e b, I an Sipi an b, Benjamin Bus os c, Sil ia Biaso i d,
Gio gio Palmie i d
aNTNU, Depa men o Compu e Science, Sem Sælands ei 9, T ondheim, 7034, T øndelag, No way
bUni e si y o Chile, Depa men o Compu e Science, A . Beauche 851, San iago, 8370456, Me opoli an Region, Chile
cUni e si y o Chile, Depa men o Compu e Science & IMFD, A . Beauche 851, San iago, 8370456, Me opoli an Region, Chile
dIs i u o di Ma ema ica Applica a e Tecnologie In o ma iche ‘‘E. Magenes’’ IMATI - CNR, Via de Ma ini 16, Geno a, 16149, I aly
A R T I C L E I N F O
Keywo ds:
SHREC 2025
3D local shape desc ip o s
ShapeBench
Benchma k
A B S T R A C T
Pa ial e ie al is a long-s anding p oblem in he 3D Objec Re ie al communi y. I s main di icul ies a ise
om how o de ine 3D local desc ip o s in a way ha makes hem e ec i e o pa ial e ie al and obus
o common eal-wo ld issues, such as occlusion, noise, o clu e , when dealing wi h 3D da a. This SHREC
ack is based on he newly p oposed ShapeBench benchma k o e alua e he ma ching pe o mance o local
desc ip o s. We p opose an expe imen consis ing o h ee inc easing le els o di icul y, whe e we combine
di e en il e s o simula e eal-wo ld issues ela ed o he pa ial e ie al ask. Ou main indings show ha
classic 3D local desc ip o s like Spin Image a e obus o se e al o he es ed il e s (and hei combina ions),
bu mo e ecen lea ned local desc ip o s like GeDI can be compe i i e o some speci ic il e s. Finally, no 3D
local desc ip o was able o success ully handle he ha des le el o di icul y.
1. In oduc ion
Finding simila o ele an objec s o a gi en que y inpu is a
undamen al ask in mul imedia da abases. An exac sea ch in his
con ex is, in gene al, meaningless because wo objec s in he da ase
a e iden ical only in he case whe e hey a e digi al copies. Two
models ob ained om he same sou ce (e.g., by 3D scanning he same
objec wice) will esul in di e en bu simila models. In addi ion
o e ie al, simila i y sea ch algo i hms can be used o implemen
mul imedia mining asks such as clus e ing and classi ica ion. Thus, i
is ele an o s udy e ec i e me hods o ep esen ing and sea ching
mul imedia objec s.
Among simila i y sea ch p oblems, one o pa icula in e es is he
pa ial e ie al on 3D models. In his ask, usually he que y inpu is a
pa ial 3D iew, and he p oblem is o ind he co esponding pa in a
comple e o pa ial 3D model o 3D scene. Fig. 1 shows an example o
a pa ial scene. The pa ial e ie al ask is known o be di icul and
complex, as p e ious SHREC acks on his p oblem ha e shown [1,2].
P ac ically all eal-wo ld 3D cap u es con ain some deg ee o occlu-
sion, and i is as such one o he mos common challenges encoun e ed
by 3D shape e ie al and ecogni ion me hods. The ad en o lea ning-
based me hods o his ask has he oppo uni y o imp o e upon he
IThis a icle is pa o a Special issue en i led: ‘3DOR 2025’ published in Compu e s & G aphics.
This a icle has been ce i ied as Replicable by he G aphics Replicabili y S amp Ini ia i e: h p://www. eplicabili ys amp.o g.
∗Co esponding au ho .
E-mail add esses: [email p o ec ed] (B.I. an Blokland), [email p o ec ed] (I. Agui e), [email p o ec ed] (I. Sipi an),
[email p o ec ed] (B. Bus os), [email p o ec ed] (S. Biaso i), [email p o ec ed] (G. Palmie i).
s a e o he a , and has as o ye no ecei ed much a en ion om
he machine lea ning communi y. Thus, a sys ema ic benchma king
me hodology on his opic is bo h ele an and imely. Un o una ely,
es ing he obus ness o a gi en 3D shape e ie al me hod o a ious
scena ios unde which a ying deg ees o pa iali y occu is di icul
o accomplish using eal-wo ld 3D cap u es. These cap u es inhe en ly
con ain a ious ypes o noise and cap u ing a e ac s. I is u he mo e
di icul o achie e quan i a i e esul s due o he ime and s o age
equi emen s o such indi idual cap u es.
This SHREC ack builds upon he ShapeBench benchma k in o-
duced in p e ious wo k [3], which p oposed a eplicable and scalable
me hodology o e alua ing local 3D shape desc ip o s. While he o ig-
inal wo k ocused on con olled compa isons o desc ip o obus ness
using syn he ic a ia ions applied exclusi ely o he scene objec , ou
SHREC ack signi ican ly ex ends his e alua ion. Fi s , we simula e
mo e ealis ic and challenging e ie al scena ios by in oducing mul i-
il e pipelines and by applying dis o ions o bo h he model and he
scene. Second, we in oduce a s uc u ed no ion o di icul y le els,
enabling a p og essi e assessmen o desc ip o obus ness. Thi d, we
include and e alua e se e al new desc ip o s, including ecen lea ning-
based me hods, and analyze hei execu ion imes unde con olled
h ps://doi.o g/10.1016/j.cag.2025.104397
Recei ed 12 May 2025; Recei ed in e ised o m 18 Augus 2025; Accep ed 19 Augus 2025
Compu e s & G aphics 132 (2025) 104397
A ailable online 6 Sep embe 2025
0097-8493/© 2025 The Au ho s. Published by Else ie L d. This is an open access a icle unde he CC BY license ( h p://c ea i ecommons.o g/licenses/by/4.0/ ).
B.I. an Blokland e al.
Fig. 1. An example o a pa ial iew om a scene. No e he missing pa s on
he models.
geome ic condi ions. Finally, we adap and op imize he benchma k
in as uc u e o es ing Py hon-based me hods, hus b oadening ac-
cessibili y and enabling he inclusion o deep lea ning desc ip o s.
Toge he , hese ex ensions make ou benchma k a mo e comp ehensi e
and ealis ic es bed o he pa ial 3D e ie al ask.
Se en eams egis e ed o his SHREC ack, bu only h ee eams
submi ed esul s o e alua ion: I an Sipi an om U. o Chile [Team 1],
Isaac Agui e om U. o Chile [Team 2], and Ba I e an Blokland
om NTNU [Team 3].
2. The ShapeBench benchma k
This sec ion in oduces he ShapeBench benchma k, he da ase
used o he benchma k, he e alua ion me ic, and he combina ions
o il e s selec ed o his SHREC ack.
2.1. The benchma k
ShapeBench [3] is a ecen me hodology o e alua ing local 3D
shape desc ip o s. I e alua es he abili y o a desc ip o o de e mine
ha wo su ace poin s a e simila unde a ious eal-wo ld condi ions.
These include clu e , occlusion, and noise.
The benchma k measu es his by ma ching co esponding poin s
on wo copies o he same objec ( o his o ical easons e e ed o as
he ‘‘model’’ and ‘‘scene’’ objec ), whe e he a o emen ioned ad e se
condi ions a e simula ed by modi ying he scene objec using a se-
quence o il e s. Each il e applies a p ocedu al modi ica ion o he
objec . A es ed me hod mus subsequen ly co ec ly iden i y ma ching
pai s o co esponding model and scene poin s, whe e model poin s a e
hidden among a la ge se o andom poin s on o he objec s. All objec s
a e aken om a se o 790,635 iangle meshes om he Obja e se
da ase [4].
This ack ins ead applies il e s o bo h objec s, c ea ing a mo e
ealis ic es ing en i onmen . We u he ex end he benchma k by
in eg a ing suppo o me hods implemen ed in he Py hon language,
which simpli ies es ing me hods u ilizing machine lea ning. The es i-
ma ion o occlusion and clu e has also been ewo ked o be as e , in
some cases educing he o al execu ion ime o a single benchma k un
by se e al hou s.
The Desc ip o Dis ance Index (DDI) [3] is used as he p ima y
me ic o e alua e he e icacy o a gi en me hod in pe o ming hese
ecogni ion asks. Le 𝛿 be he dissimila i y unc ion de ined o e a
gi en 3D local desc ip o . Le 𝑚 be he ma ching poin in he model
objec , and le 𝑠 be he ma ching poin in he scene objec . Gi en a se
o 𝑅 andom su ace poin s om he da ase , he DDI accumula es he
numbe o poin s 𝑟∈𝑅 such ha 𝛿(𝑚, 𝑟)< 𝛿(𝑚, 𝑠), i.e., he DDI coun s
how many andom poin s we e conside ed a be e ma ch, i.e., a a
lowe dis ance, o 𝑚 han 𝑠, which is he known ma ch. The inal DDI
sco e o he 3D local desc ip o is he sum o all hese alues o all
selec ed pai s o poin s (𝑚, 𝑠). We also measu e he execu ion imes o
he e alua ed me hods.
Fig. 2. Illus a ion o he e ec s o indi idual il e s. The model objec is on
he le , and he scene is on he igh . F om op o bo om, he e ec s o he
occlusion, clu e , Gaussian noise, and e ex pe u ba ion il e s a e shown.
2.2. Fil e s
A il e is a ans o ma ion applied on an objec . As s a ed, he
pu pose o il e s is o simula e eal-wo ld issues while pe o ming
e ie al asks on digi ized objec s o scenes. Fi s , we de ine some
e ms ha will be used o desc ibing he il e s:
•Suppo olume: The egion (usually a cylinde o sphe e) ha
con ains all he shape in o ma ion used o compu e a local shape
desc ip o .
•Suppo adius: The size o he suppo olume o a local shape
desc ip o .
•Independen a iable: The a iable being a ied in each il e , o
es i s e ec on he DDI o a local desc ip o .
Fo he e alua ion o local 3D shape desc ip o s in his ack, we
use ShapeBench wi h combina ions o he ollowing il e s:
•Occlusion: This il e chooses a andom iewing di ec ion om
which he scene is iewed, and emo es all geome y ha is
no isible om ha poin o iew. The independen a iable
is he a ea o he emaining mesh ha in e sec s he suppo
olume di ided by he a ea o he unmodi ied mesh in e sec ing
he suppo olume. Fig. 2a shows an example o he applica ion
o his il e .
•Clu e : A physics simula o andomly places objec s on op o he
inpu scene, simula ing how hey collide wi h o he objec s and
how g a i y a ec s hem. The independen a iable is he a ea o
clu e objec s ha in e sec s he suppo olume, di ided by he
a ea in e sec ing he suppo olume ha belongs o he objec
Compu e s & G aphics 132 (2025) 104397
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B.I. an Blokland e al.
Table 1
Le els o il e ing, and hei es ed il e con igu a ions.
Le el # Ex. Fil e s applied on
model
Fil e s applied on scene
Le el 1 Ex. 1 Occlusion
Ex. 2 Clu e
Ex. 3 Gaussian noise
Le el 2 Ex. 4 Occlusion + Gaussian noise
Ex. 5 Occlusion Occlusion
Ex. 6 Occlusion + Fixed
Gaussian noise
Occlusion + Fixed Gaussian
noise
Ex. 7 Occlusion Clu e + Occlusion
Ex. 8 Occlusion + Fixed
Gaussian noise
Clu e + Occlusion + Fixed
Gaussian noise
Le el 3 Ex. 9 Two clu e objec s + Occlusion
+ Ve ex pe u ba ion + Fixed
Gaussian noise
being ecognized. Fig. 2b shows an example o he esul o his
il e .
•Gaussian noise: Simula es a ious sou ces o noise in oduced in
he cap u e p ocess. This il e displaces he posi ion o all e ices
by a dis ance ha ollows a no mal dis ibu ion, using a ixed
alue o he s anda d de ia ion. The independen a iable is
he s anda d de ia ion o he noise unc ion. Fig. 2c shows an
example o his il e .
•Ve ex Pe u ba ion: Simula es cap u ing he mesh mul iple imes
by displacing iangle e ices, while keeping he mesh’s o e all
shape in ac . The independen a iable is he dis ance o he
closes co esponding e ex in he modi ied mesh. An example
is shown in Fig. 2d.
2.2.1. Le els o di icul y
We de ine h ee di e en le els o inc easing di icul y o he
pa ial e ie al ask. Le el 1 es s common sou ces o ma ching in-
accu acies in isola ion. Le el 2 es s combina ions o hese ha a e
o en obse ed in p ac ical applica ions. Le el 3 aims o p esen a
combina ion o hese ha can be expec ed in cap u es o eal-wo ld
en i onmen s. Table 1 lis s he il e con igu a ion on each expe imen
ha is done a each di icul y le el. Fig. 3 isualizes Expe imen s 4 o
8, and Fig. 4 depic s he e ec s o applying he il e s as de ined in
Expe imen 9.
The expe imen s use a ia ions o he a o emen ioned il e s in
o de o educe he dimensionali y and in e p e abili y o he esul s.
Expe imen s 6, 8, and 9 apply Gaussian noise wi h a ixed s anda d
de ia ion ins ead o one chosen a andom. Expe imen 9 also applies
he clu e il e wi h only 2 clu e objec s ins ead o he usual 10.
Finally, when occlusion is applied o bo h he model and he scene, he
occlusion ac ion o he o e lapping a ea is used as he independen
a iable.
The Desc ip o Dis ance Index (DDI) me ic is used by Shapebench [3]
o measu e he e ec o each il e con igu a ion on he ma ching
pe o mance o a local 3D shape desc ip o .
2.3. Execu ion ime
We ha e also ex ended he benchma k wi h a new p ocess o
measu ing he execu ion ime o a es ed me hod. Deciding he op imal
me hod o use o 3D shape ecogni ion is o en a balance be ween i s
ma ching capabili ies, and i s execu ion ime. In cases whe e la ency
is essen ial, o p ocessing powe is limi ed, a as e me hod ha is less
capable may be desi able.
Recen wo k has p edominan ly measu ed he ime o gene a e
a single desc ip o o a gi en su ace as a unc ion o he suppo
Fig. 3. Illus a ion o he expe imen s a Le el 2. The model is on he le , and
he scene is on he igh . Re e o Table 1 o he il e con igu a ions used.
He e Figu es a) o e) co espond o expe imen s 4 o 8, espec i ely.
Fig. 4. Illus a ion o Expe imen 9, a Le el 3 (Occlusion + Two clu e
objec s + Fixed Gaussian noise + Ve ex pe u ba ion). The model is on he
le , and he scene is on he igh .
adius [5–9], hough he e ex o iangle coun [10–12], o case
s udies [13,14] ha e also been used.
Fig. 5 shows obse ed execu ion imes as a unc ion o he suppo
adius. Fig. 5(b) demons a es ha he execu ion ime can a y by
oughly a ac o o wo o he same adius. This a ia ion is caused
by ha he ime cos o p ocessing a poin o iangle ha lies wi hin
he suppo olume can be di e en o ha o one which lies ou side o
i . The loca ion o he suppo olume a ies he p opo ion o in- and
Compu e s & G aphics 132 (2025) 104397
3
B.I. an Blokland e al.
Fig. 5. Sca e plo s showing he a ia ion o execu ion imes when compu ing
he SHOT desc ip o 25 imes o a andomly selec ed e ex and suppo
adius. Each inpu poin cloud has 5M poin s. A hea map isualiza ion is used
o highligh clus e s o in o al 10k sample poin s.
excluded geome y o a gi en su ace, and hus he execu ion ime.
Fig. 5(a) shows ha his a ia ion disappea s when his p opo ion is
cons an , as is he case wi h su ace poin s on a sphe e.
Unde s anding he pe o mance cha ac e is ics o a me hod he e-
o e equi es measu ing he execu ion ime cos o geome y inside and
ou side he suppo olume sepa a ely. This app oach de ia es om
p e ious wo k, which has gene ally dis ega ded he cos o excluding
geome y as being some hing all me hods need o do, wi h he implici
assump ion ha his cos is app oxima ely he same o all me hods.
We use syn he ic meshes, which allow his p opo ion o be con olled.
The i s wo o hese ( ype a and b, as shown in Fig. 6) place meshes
a andomly chosen loca ions inside he suppo olume. Wha is being
a ied be ween hese is he dis ibu ion o he geome y. Type a sp eads
i ou uni o mly, while ype b concen a es i . Type c exclusi ely places
geome y ou side he suppo egion, wi h a uni o m dis ibu ion.
Finally, ype d (no pic u ed di ec ly) uses a mesh simila o ha o
ype a, bu does no eques he me hod o gene a e any desc ip o s.
This allows he es ima ion o he me hod’s o e head, assuming i s
implemen a ion does no ha e an explici check o his.
Fo measu ing he execu ion ime i sel , we limi he unning o
he desc ip o me hod o a single h ead. While desc ip o s would in
a p ac ical se ing p ima ily be compu ed in pa allel, we also wish o
be able o compa e agains me hods implemen ed in Py hon. These a e
inhe en ly single- h eaded. Boos ing o he CPU was disabled, and he
benchma k h ead was locked o a single co e h ough he ope a ing
sys em. The numbe o desc ip o s being gene a ed a a ime is ixed,
and a e compu ed in a single ba ch. This ensu es accele a ion s uc u es
(i he me hod uses hem) a e only compu ed once pe scene.
One no ewo hy conside a ion is he obse a ion ha iangle and
poin cloud esolu ion a e somewha independen o one ano he . As-
suming ha uni o m su ace sampling is used, only he a ea o a mesh
de e mines he poin cloud esolu ion, no he numbe o iangles ha
a e used o desc ibe i . The densi y o iangles can a y g ea ly ac oss
a gi en mesh, which makes i di icul o compa e he execu ion imes
o poin cloud and iangle based me hods di ec ly.
3. Me hods
Among he 3D local desc ip o s conside ed in ack, he GeDI (Sec-
ion 3.1) and COPS (Sec ion 3.2) me hods a e lea ning-based me hods,
while MICI (Sec ion 3.3) is a mo e adi ional his og am-based me hod.
In he e alua ion we include ou desc ip o s used in he o iginal
ShapeBench [3]: Spin Image [15], Radial In e sec ion Coun Image
(RICI) [11], Quick In e sec ion Coun Change Image (QUICCI) [12],
and Signa u e o His og ams o O ienTa ions (SHOT) desc ip o [9].
Fig. 6. Types o syn he ic meshes gene a ed by he benchma k.
3.1. Gene al and dis inc i e lea ned desc ip o s (GeDI) (I an Sipi an)
GeDi [16] in oduces a lea ned desc ip o o local 3D poin cloud
pa ches ha is compac and dis inc i e. A pa ch 𝑋 ⊂ 3 is de ined as
a se o 3D poin s wi hin a ixed adius 𝑟 om a cen al poin 𝑥 in he
o iginal poin cloud 𝑃. To accommoda e a ying poin densi ies and
ensu e uni o m inpu size o lea ning, he me hod pe o ms a andom
sampling o 𝑚 poin s pe pa ch, wi h esampling i ewe poin s a e
p esen . This p ocess yields a consis en s uc u e o ba ch p ocessing
and model aining. To achie e in a iance o ans o ma ions and
imp o e he obus ness o he desc ip o , he me hod es ima es a local
e e ence ame (LRF) using he TOLDI algo i hm [17]. Finally, he
me hod downsamples he pa h o 𝑛 < 𝑚 poin s o compu a ional
e iciency.
The canonicaliza ion s ep ans o ms hese sampled poin s o a
no malized coo dina e ame ela i e o he pa ch cen e and adius.
Speci ically, poin s a e i s o a ed in o he LRF and hen no mal-
ized o ansla ion and scale in a iance. The canonicalized poin se
se es as inpu o a deep ne wo k 𝛷𝛩, which lea ns o p oduce a
desc ip o 𝑓∈𝑑 wi h uni no m. The ne wo k design is based on
Poin Ne ++ [18], which uses hie a chical ecep i e ields o cap u e
geome ic pa e ns a mul iple spa ial scales.
To keep geome ic consis ency and sol e possible inaccu acies in
LRF es ima ion, he me hod in oduces QNe , a spa ial ans o me
ne wo k ha ou pu s a uni qua e nion ep esen ing a o a ion in
𝑆𝑂(3). Unlike ma ix-based ans o ma ion ne wo ks, QNe inhe en ly
p oduces alid o a ions wi hou equi ing addi ional egula iza ion
e ms o compu a ionally expensi e o hogonaliza ion s eps. QNe is
ained join ly wi h he main desc ip o ne wo k, p o iding an e icien
and in eg a ed solu ion o compensa e o canonicaliza ion noise while
p ese ing he spa ial p ope ies c i ical o geome ic lea ning.
The aining p ocedu e uses a siamese ne wo k a chi ec u e wi h
sha ed weigh s ac oss b anches, p ocessing pai s o co esponding
pa ches sampled om o e lapping egions o di e en poin clouds.
Desc ip o s a e lea ned using a ha d con as i e loss ha emphasizes
disc imina ion be ween ma ching and non-ma ching pa ches. Nega i e
sampling is conduc ed by excluding samples wi hin a p ede ined adius
a ound ancho poin s, ensu ing spa ial dis inc i eness. This aining
s a egy, combined wi h andomized pa ch sampling, p omo es o-
bus ness, suppo s la ge miniba ch aining, and leads o imp o ed
gene aliza ion ac oss a ying poin cloud con igu a ions.
3.2. Comp ehensi e model o pa s segmen a ion (Isaac Agui e)
COPS [19] in eg a es seman ics ex ac ed om isual concep s and
3D geome y o e ec i ely iden i y objec pa s. I ende s a 3D poin
cloud om mul iple iewpoin s, deli e ing he esul ing image ou pu s
Compu e s & G aphics 132 (2025) 104397
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B.I. an Blokland e al.
Fig. 7. In (a): isualiza ion o he poin p ojec ion and weigh ing p ocedu e,
and in (b) app oxima e isualiza ion o he weigh ing o poin samples o he
sum being accumula ed in each pixel bin o he MICI desc ip o .
Fig. 8. Desc ip o s gene a ed using he RICI and MICI me hodologies: despi e
di e ing inpu modali ies, app oxima ely equi alen desc ip o s a e p oduced.
in o DINO 2 [20] o ex ac high-le el ea u es. These ea u es a e hen
backp ojec ed on o he co esponding poin s in he o iginal poin cloud.
Finally, a geome y-awa e ea u e agg ega ion p ocess clus e s poin s
in o pa s and assigns hem labels.
This p ocedu e can also be used o compu e ea u es/desc ip o s o
each poin , and i is expec ed ha geome ically simila pa s will p o-
duce simila ou pu s. Fo he expe imen s, DINO 2 wi h egis e s [21]
is used, which is an imp o ed e sion o DINO 2, speci ically in i s
small a ian .
3.3. Mul imodal in e sec ion coun image (MICI) (Ba I e an Blokland)
The Mul imodal In e sec ion Coun Image (MICI) is an app oxima-
ion o he p e iously p oposed RICI [11] desc ip o . The RICI and MICI
me hods bo h aim o compu e he numbe o in e sec ions be ween a
ci cle desc ibed by each pixel in he image, and he su ace o an objec .
Whe e hey di e is ha while RICI equi es a iangle mesh as inpu ,
MICI uses a poin cloud ( his is he ‘‘MICI Poin Cloud’’ a ian ). The
combina ion o he RICI and MICI me hods allows iangle meshes and
poin clouds o be compa ed ac oss bo h modali ies in e changeably
( his is he ‘‘MICI T iangle’’ a ian ).
This can be ad an ageous in applica ion domains such as bin pick-
ing, whe e i may be necessa y o loca e a known CAD objec in a
3D scan. Because desc ip o s can be ex ac ed om he iangle mesh
di ec ly, he lossy s ep o uni o mly sampling he mesh in o a poin
cloud can be a oided. The ex ac ed desc ip o s can subsequen ly be
compa ed o hose compu ed om poin s in a poin cloud cap u ed by
a 3D scanne .
To es ima e he in e sec ion coun pe bin, MICI accumula es poin s
om he inpu poin cloud on o a plane subdi ided in o a g id o
pixels. A isual ep esen a ion o his p ocedu e is shown in Fig. 7(a).
A desc ip o is compu ed o he poin 𝑆 and su ace no mal 𝑆𝑛. A
poin 𝑃 wi h su ace no mal 𝑃𝑛 is p ojec ed in cylind ical coo dina e
space on o he desc ip o , yielding poin 𝐼 ha de e mines which pixel
𝑃 con ibu es o.
Two ac o s weigh he con ibu ion. The i s o which is a 2D
Gaussian unc ion whose mean is cen e ed in he co esponding pixel
and has a s anda d de ia ion o 0.1. This aims o ocus he con ibu ions
close o whe e he ci cles used by he o iginal RICI desc ip o s would
be. These Gaussian weigh s a e isualized in Fig. 7(b). The second
weigh ing ac o is he cosine o he angle 𝜃 be ween he ci cle angen
𝑇 and inpu poin cloud no mal ec o 𝑃𝑛. Fo a gi en su ace, as he
angle be ween hese ec o s dec eases, mo e poin s will be encoun e ed
in he p oximi y o he ci cle. Reducing he weigh o hese by he
cosine accoun s o his. The combina ion o hese ac o s esul s, unde
ideal condi ions, in a desc ip o ha is isually nea ly indis inguishable
om a simila one compu ed o a iangle mesh, as is shown in Fig. 8.
All poin con ibu ions a e accumula ed in a 2D his og am. The inal
s ep in he ea u e ex ac ion p ocess is o con e he accumula ed
loa ing poin alues in o a disc e e numbe o in e sec ions. This is
done by di iding he con en s o each bin by a cons an ac o 𝑐 ha
depends on he densi y o he inpu poin cloud, and hus he me hod
and se ings by which he poin cloud is acqui ed. Fo his benchma k,
we de e mined 𝑐 expe imen ally as he ac o ha minimizes he di e -
ence be ween all nonze o bins o he same desc ip o compu ed using
he MICI and RICI me hod o a la ge se o sample desc ip o s.
4. Resul s and discussions
The esul s o he expe imen s de ined in Table 1 a e now p e-
sen ed o all pa icipa ing me hods. Fo hese esul s, he ollowing
pa ame e s ha e been used:
•Pa ame e s o il e s:
–Fixed Gaussian noise: s anda d de ia ion o 0.001.
–Ve ex pe u ba ion (al e na e iangula ion in he o iginal):
same as o iginal ShapeBench [3].
–Mul i- iew occlusion: angle be ween iewpoin s a ies be-
ween 0 and 90 deg ees.
–Fo Expe imen 9, he numbe o clu e objec s was educed
o 2 ins ead o he usual 10 o a clu e il e .
•Pa ame e s o me hods:
–QUICCI: suppo adius 0.39.
–RICI: suppo adius 0.255.
–SHOT: suppo adius 0.15.
–COPS: suppo adius 0.5 ( o aining).
–GeDI: suppo adius 0.5 ( o aining).
–Spin image: suppo adius 0.81.
–MICI: Le el h eshold se o 166.6, suppo adius was 0.5
(MICI T iangle was also un a his suppo adius o be
able o compa e maximum achie able pe o mance s poin
cloud pe o mance).
One o he pa ame e o no e is ha e ex coun s o poin clouds
p o ided o GeDI and COPS by he benchma k we e scaled o 10%
and 5%, espec i ely. Running bo h o hese me hods a ull esolu ion
p o ed in ac ably slow. The e e ence desc ip o se o COPS was also
limi ed o 250,000 desc ip o s o a simila eason. The la e does
cause some p oblems wi h compa ing i s pe o mance o o he me hods.
Howe e , based on expe ience he DDI=0 line should app oxima ely be
co ec , bu o he subdi isions may shi had he ull esolu ion been
used ins ead. While his measu e p o ides hese me hods wi h less in-
o ma ion, we belie e any p ac ical applica ion o hem would equi e
simila measu es. Compa isons o o he me hods should he e o e be
possible.
4.1. Le el 1 expe imen s
The i s le el in es iga es he e ec o speci ic ad e se condi ions
in isola ion o o he s, whe e each expe imen applies a single il e .
Fo each expe imen , he obse ed e ec on he DDI me ic is shown
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Fig. 9. Resul s o Expe imen 1 (Occlusion). Fig. 9(i) shows he numbe o
sample poin s pe his og am bin.
Fig. 10. Resul s o Expe imen 2 (Clu e ). Fig. 10(i) shows he numbe o
sample poin s pe his og am bin.
o each es ed me hod. The colo s show he dis ibu ion o DDI alues,
wi h g een ep esen ing DDI = 0. A highe p opo ion o low DDI alues
co esponds o a mo e e ec i e local desc ip o . The e o e, he g eene
he cha , he mo e e ec i e he local desc ip o is. Each cha also
con ains he commonly used A ea unde P ecision-Recall cu es (AUC)
me ic.
The e ec s o occlusion a e shown in Fig. 9. The Spin Image, RICI,
and QUICCI ou pe o med he o he me hods. GeDI and SHOT ely on
poin cloud neighbo hoods o hei shape ep esen a ion, which a e
deg aded by he il e . Visual desc ip o s like COPS a e also no obus
o geome ical occlusion.
The esul s o clu e can be seen in Fig. 10. He e MICI T iangle
and RICI ou pe o m he o he me hods, ollowed by QUICCI. These
Fig. 11. Resul s o Expe imen 3 (Gaussian Noise). Fig. 11(i) shows he
numbe o sample poin s pe his og am bin.
Fig. 12. Hea maps o esul s o expe imen 4 (Occlusion + Gaussian noise).
desc ip o s we e speci ically designed o be obus o clu e , which
is e iden he e. The o he me hods show li le o no abili y o esis
clu e .
When subjec ed o no mally dis ibu ed e ex pe u ba ions, Fig.
11 shows ha he Spin Image is he mos obus in his es . This can
be explained by i s subdi ision o con ibu ions o incoming e ices
ha ing a smoo hing e ec , and la ge suppo adius. In con as , SHOT
has imp essi e pe o mance despi e i s small suppo adius. Lea ned
neu al ne wo ks wo k as smoo hed eg ession unc ions, which could
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Fig. 13. Line cu es o esul s o expe imen 4 (Occlusion + Gaussian noise).
Fig. 14. Resul s o Expe imen 5 (occlusion on bo h meshes). Fig. 14(i) shows
he numbe o sample poin s pe his og am bin.
explain hei obus ness o noise. COPS may also bene i he e om ha
isual ea u es a e independen o geome ical noise. Finally, QUICCI
and RICI a e mo e suscep ible o changes in he geome y, and hus
hey ob ain wo se esul s compa ed o he o he me hods.
4.2. Le el 2 expe imen s
The second le el expe imen s in es iga e he e ec o combina ions
o il e s. Two se s o plo s (hea maps and line cu es) a e compu ed o
Fig. 15. Resul s o Expe imen 6 (occlusion and Gaussian noise on bo h
meshes). Fig. 15(i) shows he numbe o sample poin s pe his og am bin.
Fig. 16. Resul s o Expe imen 7 (occlusion on bo h objec s, clu e in scene).
each expe imen , showing he same esul s om di e en pe spec i es.
To simpli y isualiza ion, hese cha s ocus on he ac ion o cases
whe e he DDI = 0. In he hea maps, his p opo ion is ep esen ed by
a colo map, whe e g een indica es a p opo ion equal o 1 ( he op imal
esul ). The line cha s g oup esul s by hei alues on he e ical axis.
When Occlusion is combined wi h Gaussian noise, Figs. 12 and 13
show ha he Spin Image ob ains he bes esul s, ollowed by MICI
(bo h e sions). As Spin Image beha es well in bo h il e s sepa a ely,
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Fig. 17. Resul s o Expe imen 7 (occlusion on bo h objec s, clu e in scene).
one would expec i o ha e good obus ness o bo h il e s. GeDI also
shows some obus ness o low le els o noise and occlusion, which is
also inhe i ed om i s obus ness o Gaussian noise.
Expe imen s 5 and 6 bo h apply an occlusion il e on he model
and scene objec s, bu ensu e he maximum angle be ween he iewing
di ec ions is a mos 90°. The occlusion ac o o he su ace isible
om bo h poin s o iew is used as he independen a iable. Whe e
he wo expe imen s di e is ha Gaussian noise wi h a ixed s anda d
de ia ion is applied in expe imen 6.
The esul s o expe imen 5 a e shown in Fig. 14, and hose o
expe imen 6 in Fig. 15. In he case o he o me , he conclusions
a e in line wi h hose om expe imen 1, al hough pe o mance he e
is gene ally be e . We conjec u e ha his is imp o emen caused
by he il e gene a ing occluded meshes om simila poin s o iew,
inad e en ly making he model and scene objec s mo e simila o one
ano he han co esponding objec s would be in expe imen 1. When
noise is added in expe imen 6, he me hods which we e ound o su e
mos om i s e ec s in expe imen 3 a e also hose mos a ec ed by i
he e.
The il e s applied in expe imen s 7 and 8 a e simila o hose o
5 and 6, excep o he addi ion o a clu e il e being o he scene
objec . The esul s o expe imen 7 a e shown in Figs. 16 and 17, and
hose o expe imen 8 in Figs. 18 and 19.
As was shown in expe imen 2, he COPS, SHOT, GeDI, MICI Poin -
Cloud, and o a lesse ex en he Spin Image, a e all a ec ed by clu e .
The me hods ha a e he leas obus o i a e also hose which su e
he mos in bo h o hese expe imen s. A e adding noise in expe imen
8, a simila d op is obse ed as o he one om expe imen 5 o 6. Ou
o all es ed me hods, MICI T iangle and RICI a e he only me hods ha
can handle all applied il e s.
4.3. Le el 3 expe imen
The hi d le el aims o simula e a combina ion o a e ac s com-
monly ound in eal-wo ld 3D cap u es. Tes ed me hods a e subjec ed
Fig. 18. Resul s o Expe imen 8 (occlusion and Gaussian noise on bo h
objec s, clu e in scene).
Fig. 19. Resul s o Expe imen 8 (occlusion and Gaussian noise on bo h
objec s, clu e in scene).
o a combina ion o occlusion, a ixed amoun o Gaussian noise, e ex
pe u ba ions, and a small amoun o clu e . The obse ed alues o
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Fig. 20. Resul s o Expe imen 9. DDI=0 cu es a e compu ed o all da a poin s ha all abo e o below h eshold alues o each o he h ee independen
a iables in his expe imen . Occlusion alues abo e 0.3 a e labeled as ‘high‘, and ‘low‘ o he wise. Clu e alues be ween 0 and 1 a e conside ed ‘low‘, and ‘high‘
be ween 1 and 2. Ve ex displacemen s be ween 0.07 and 0.15 a e conside ed ‘high‘.
Fig. 21. Th oughpu o desc ip o gene a ion o di e en syn he ic scenes. In Fig. 21(a) uni o m densi y geome y wi hin he suppo olume; In Fig. 21(b) high
densi y geome y wi hin he suppo olume; In Fig. 21(c) geome y ou side he suppo olume.
Fig. 22. Numbe o desc ip o s compa ed pe second o each es ed me hod.
hese esul s ha e been classi ied in o a ‘high‘ and ‘low‘ ca ego y o
easie in e p e a ion. The esul s a e shown in Fig. 20.
No single 3D local desc ip o could e ec i ely handle high le els
o all il e s combined. MICI-T iangle and he Spin Image pe o m bes
wi h high le els o clu e , al hough he o e all e ec i eness emains
low. GeDI pe o ms well when no much clu e is p esen .
4.4. Execu ion imes
The esul s o he measu ed execu ion imes a e shown in Figs. 21
and 22. I should be no ed ha hese cha s show esul s o iangle,
poin cloud, and lea ning based me hods. Lea ning based me hods u i-
lize he GPU, while he emainde we e un exclusi ely single- h eaded
on he CPU. Resul s o desc ip o gene a ion h oughpu o CPU and
GPU-based me hods can he e o e no be compa ed di ec ly.
All execu ion ime esul s we e measu ed on a sys em wi h an
AMD Ryzen 9 3900X CPU and an N idia Quad o P5000 GPU. CPU
equency boos ing was disabled o ensu e he p ocesso main ained
a cons an execu ion speed (3.8 GHz). Execu ion was u he limi ed o
a single co e h ough he ope a ing sys em o a oid slowdowns om
co e swi ching.
In e ms o he obse ed gene a ion speed, GEDI is clea ly he as es
o he lea ning-based me hods. The Spin Image is he as es o he CPU-
based implemen a ions. The only excep ion can be seen in Fig. 21(c),
whe e he SHOT desc ip o appea s o be much as e a disca ding
poin s ou side i s suppo olume. Cylind ical suppo olume me hods
such as he Spin Image and MICI mus pe o m mo e calcula ions o
de e mine whe he a poin o iangle in e sec s hei suppo egion,
and ecei e a compa a i ely small upli . Only he syn he ic meshes
we e used o measu ing execu ion ime.
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