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Poin PCA+: A ull- e e ence Poin Cloud Quali y Assessmen me ic wi h
PCA-based ea u es
Xuemei Zhou a,c,∗, E angelos Alexiou b, I ene Viola a, Pablo Cesa a,c
aCen um Wiskunde & In o ma ica, Ams e dam, The Ne he lands
bTNO Ne he lands O ganiza ion o Applied Scien i ic Resea ch, The Hague, The Ne he lands
cTU Del , Del , The Ne he lands
ARTICLE INFO
MSC:
41A05
41A10
65D05
65D17
Keywo ds:
Poin cloud
Pe cep ual Quali y Assessmen
PCA
Full- e e ence
Fea u e selec ion
Random o es
ABSTRACT
This pape in oduces an enhanced Poin Cloud Quali y Assessmen (PCQA) me ic, e med Poin PCA+, as an
ex ension o Poin PCA, wi h a ocus on compu a ional simplici y and ea u e ichness. Poin PCA+ e ines he
o iginal PCA-based desc ip o s by employing P incipal Componen Analysis (PCA) solely on geome y da a;
addi ionally, he ex u e desc ip o s a e e ined h ough a di ec applica ion o he unc ion on YCbC alues,
enhancing he e iciency o compu a ion. The me ic combines geome y and ex u e ea u es, cap u ing local
shape and appea ance p ope ies, h ough a lea ning-based usion o gene a e a o al quali y sco e. P io o
usion, a ea u e selec ion module is inco po a ed o iden i y he mos e ec i e ea u es om a p oposed
supe -se . Expe imen al esul s demons a e he high p edic i e pe o mance o Poin PCA+ agains subjec i e
g ound u h sco es ob ained om ou publicly a ailable da ase s. The me ic consis en ly ou pe o ms s a e-
o - he-a solu ions, o e ing aluable insigh s in o he design o simila i y measu emen s and he e ec i eness
o handc a ed ea u es ac oss a ious dis o ion ypes. The code o he p oposed me ic is a ailable a
h ps://gi hub.com/cwi-dis/poin pca_sui e/.
1. In oduc ion
Poin cloud is p e ailing among he a ailable 3D imaging o ma s
in ecen yea s. I is essen ially a collec ion o poin s, whe e each poin
has a ibu es o geome y, colo , e lec ance, e c. Howe e , h ough
acquisi ion, comp ession, ansmission, and ende ing, he quali y o
a poin cloud can be deg aded, which necessi a es e ec i e and e i-
cien Poin Cloud Quali y Assessmen (PCQA) me ics. These me ics
p o ide a guide on he design, op imiza ion, and pa ame e uning o
poin cloud p ocessing pipelines. PCQA me ics ha e been ex ensi ely
u ilized in a ious applica ions, including benchma king isual asks
such as es o a ion [1,2], comp ession [3–5], supe - esolu ion [6,7], as
well as o quali y moni o ing in a ious sys ems [8–11].
Based on he a ailabili y o e e ence poin cloud da a, PCQA can
be gene ally di ided in o h ee ca ego ies, namely Full Re e ence (FR),
Reduced Re e ence (RR) and No Re e ence (NR). Compa ed wi h RR
and NR, FR equi es he ully a ailable e e ence du ing he execu ion,
which mimics he way he Human Vision Sys em (HVS) pe cei es qual-
i y as a compa ison o di e ences be ween a deg aded and a p is ine
e sion [12]. F om a me hodology s andpoin , PCQA is composed o
wo main componen s: ea u e ex ac ion and ea u e eg ession [13–
16]. Resea che s ha e u ilized bo h hand-c a ed and lea ning-based
∗Co esponding au ho .
E-mail add ess: [email p o ec ed] (X. Zhou).
ea u es, usually combined wi h a non-linea unc ion o lea ning-based
eg esso [17,18]. End- o-end schemes can signi ican ly imp o e he
p edic ion pe o mance by i ing he g ound u h well. Howe e , he
HVS mechanisms behind hem a e di icul o explain [19] . In addi-
ion, one o he mos challenging issues o end- o-end lea ning-based
app oaches is hei equi emen o la ge amoun s o labeled da a o
aining [20–22]. The lea ning model may ha e di icul ies in handling
a ious con en s and dis o ions i he aining se is no su icien ly
la ge o ails o adequa ely ep esen eal-wo ld con en s [23]. Besides,
he sho age o da a may p obably cause se ious o e - i ing p oblems.
In ac , only e y size-limi ed, dis o ion- ype unbalanced poin cloud
da ase s a e a ailable in he PCQA ield.
In p e ious esea ch, he pe cep ual quali y o poin clouds unde
he FR amewo k has been explo ed using mul iple geome ic ea u es,
ex u al ea u es, o a combina ion o bo h. Howe e , hese s udies
ypically compu e geome ic o ex u al simila i y measu emen s om
he e e enced and dis o ed poin clouds, independen ly [24–26]. This
is achie ed by iden i ying co espondences among poin s based on
geome y. Conside ing he a o emen ioned limi a ions and d awing
inspi a ion om Poin PCA [25], ou emphasis in his pape is on
non-deep-lea ning-based FR PCQA me ics. To his aim, we desc ibe
h ps://doi.o g/10.1016/j.image.2025.117262
Recei ed 30 Decembe 2023; Recei ed in e ised o m 16 Sep embe 2024; Accep ed 9 Janua y 2025
Signal P ocessing: Image Communica ion 135 (2025) 117262
A ailable online 17 Janua y 2025
0923-5965/© 2025 Published by Else ie B.V.
X. Zhou e al.
Fig. 1. Poin PCA+ a chi ec u e: bo h he e e ence and he dis o ed poin cloud a e passing om e e y s age o compu e a quali y sco e. Ope a ions in he blue box a e applied
only o he geome y da a o poin clouds. Only he e e ence poin cloud se es as a e e ence o iden i y neighbo hoods.
Poin PCA+ and ex end ou p io analysis [27], inco po a ing esul s
and discussions ha ake in o accoun dis o ion ypes and ea u e
impo ance. The con ibu ions o he pape a e h ee old:
•We ex end he Poin PCA amewo k by pe o ming PCA on he
geome y da a o he e e ence poin cloud and ans o ming
bo h he e e ence and dis o ed poin clouds on o he new basis.
This way we can cap u e di e ences in hei shape p ope ies
e ec i ely.
•We u ilize 𝑘𝑛𝑛 algo i hm o de e mine he neighbo hood, which is
as e and e u ns a consis en numbe o poin s, he e o e u he
dec easing he compu a ional cos o subsequen p ocessing s eps.
•We pe o m ex ensi e expe imen a ion on ou publicly a ailable
da ase s, demons a ing ha Poin PCA+ consis en ly achie es su-
pe io pe o mance ac oss ou dis inc da ase s. A ho ough anal-
ysis in es iga es he e ec i eness o di e en handc a ed ea u es
conce ning speci ic dis o ion ypes, aiming o disce n which ea-
u es a e mo e impac ul o di e en dis o ion ype ca ego ies.
2. Rela ed wo ks
2.1. G ound- u h labeling and subjec i e da ase cons uc ion
In he de elopmen o objec i e PCQA me ics, subjec i e quali y as-
sessmen da ase s a e he basis o hei design and alida ion. G ound-
u h a ings o isual impai men s in s imuli, namely Mean Opinion
Sco e (MOS) o Di e en ial MOS (DMOS), a e ob ained h ough sub-
jec i e quali y assessmen expe imen s [28,29]. These sco es p ima ily
indica e he deg ee o deg ada ion a ec ing he con en s wi h li le in-
o ma ion abou he ep esen a ions o dis o ion. Exis ing syn hesized
PCQA da ase s, gene a ed ei he by pe o ming a es in a con olled
labo a o y en i onmen o by mimicking i wi h poin cloud p ocessing
algo i hms, a e size-limi ed and dis o ion- ype and dis o ion-le el
unbalanced, o en by design [30–33]. Fo example, when using es
me hods such as absolu e ca ego y a ing, he dis o ion le el o
a ce ain dis o ion ype mus be isually dis inguishable o ob ain
meaning ul MOS alues and o a oid a iguing subjec s. Rega ding he
comp ession dis o ion o PCQA, ecen esea ch indica es a mono onic
ela ionship wi h bi a e when e alua ing comp ession quali y [11,34].
Howe e , i is c ucial o emphasize ha subjec i e quali y e alua ion
some imes does no ollow a mono onic beha io . This is pa icula ly
e iden in cases whe e he balance be ween geome y and colo quali y
in poin cloud con en is challenging o es ablish [35]. This complexi y
adds di icul y o disce ning be ween di e en poin cloud coding mod-
ules. The e o e, i becomes impe a i e o in eg a e bo h geome y and
ex u e dis o ions in assessing he pe cep ual quali y o poin clouds
o PCQA. The u iliza ion o e ec i e geome y- and ex u e- ela ed
ea u es can enhance he op imiza ion o a ious algo i hms associa ed
wi h pe cep ion.
2.2. Objec i e quali y assessmen o poin cloud
Objec i e PCQA me ics can be di ided in o poin -based, p ojec ion-
based, and ea u e-based models based on he way o p ocess he poin
clouds. Poin -based me ics such as poin - o-poin , poin - o-plane, and
hei a ian s [36–39] measu e deg ada ions be ween he o iginal and
dis o ed poin clouds pe poin , mainly based on Euclidean o colo
space dis ances [40]. Alexiou e al. [41] p opose he angula simila i y
o angen planes among co esponding poin s, which conside s neigh-
bo hood in o ma ion. These me ics a e compu a ionally e icien bu
su e om a c ude co espondence o ma ching be ween poin s.
P ojec ion-based app oaches adap exis ing Image Quali y Assess-
men (IQA) me ics o PCQA. The i s a emp is epo ed in [42],
which desc ibes a amewo k o p edic ing poin cloud quali y by
employing 2D IQA me ics on 6 o hog aphic p ojec ed iews. This
me hodology was u he ex ended in [43] by assigning non-uni o m
weigh ing on each iew, he weigh s o a s imulus a e compu ed as
he a io o he du a ion o inspec ion on co esponding iews, di ided
by he o al ime. Liu e al. [44] p o ide a PCQA model based on
he p inciple o in o ma ion con en weigh ed s uc u al simila i y (IW-
SSIM) [45]. Icosphe e and a se ies o ans o ma ions a e employed o
gene a e iewpoin s. PQA-Ne [46] akes 6 o hog aphic p ojec ions o
poin clouds as inpu s, ea u es a e ex ac ed a e con olu ion neu al
ne wo k blocks, and hey sha e a dis o ion iden i ica ion and a quali y
p edic ion module ha assis in ob aining inal quali y sco es. PQA-
Ne adop s a wo-s ep s a egy o ain he mul i- ask neu al ne wo k.
Howe e , he p ojec ion p ocess and he numbe o iewpoin s ha e a
non-negligible impac on he inal p edic ion accu acy; besides, how o
combine he quali y sco e on each iewpoin in o a sco e is also no
s aigh o wa d.
Fea u e-based me ics conside pe cep ual loss om bo h geome y
and ex u e p ope ies. Viola e al. [47] ex ac he colo s a is ics,
his og am, and co elog am o assess he le el o impai men and
combine he colo -based me ics wi h geome y-based me ics o o m
a global quali y sco e. Alexiou e al. [26] employ he local dis ibu ions
o poin clouds o p edic pe cep ual deg ada ions om opology and
colo . Yang e al. [48] cons uc a local g aph cen e ed a esampled
key poin s o bo h e e ence and dis o ed poin clouds, wi h he
colo g adien on he local g aph being used o measu e dis o ions.
Diniz e al. [49] in oduced a ex u e desc ip o based on pe cep ual
colo dis ance pa e ns, which is scale and o a ion in a ian [50].
Meyne e al. [24] u ilize an op imally-weigh ed linea combina ion
o cu a u e-based and colo -based ea u es o e alua e isual quali y.
Diniz e al. [51] adop he s a is ical in o ma ion o he ex ac ed
geome y/colo ea u es and eed hem in o a eg ession model.
Deep lea ning-based modules ha e also been used o ex ac pe cep-
ual ea u es. An ex ension using coa se- o- ine p og essi e knowledge
ans e based on HVS is gi en in [52]. Zhang e al. [53] make use
Signal P ocessing: Image Communica ion 135 (2025) 117262
2
X. Zhou e al.
o mul i-modal in o ma ion o add ess he PCQA p oblem; he quali y-
awa e encode ea u es a e op imized wi h he assis ance o symme ic
c oss-modali y a en ion. They i s spli poin clouds in o wo sub-
models, wi h a poin cloud encode o ex ac he geome y ea u e,
and an image encode o ob ain he ex u e ea u e. Subsequen ly, he
quali y-awa e encode ea u es a e op imized wi h he assis ance o
symme ic c oss-modali y a en ion. Zhang e al. [54] u ilize na u al
scene s a is ics and en opy on he quali y- ela ed geome y and colo
ea u e domains, which a e p ojec ed om 3D space, and suppo
ec o eg ession is employed o ob ain quali y sco es. IT-PCQA [55]
u ilizes he ich p io knowledge in images and builds a b idge be ween
2D and 3D pe cep ion in he ield o quali y assessmen . Speci ically,
a hie a chical ea u e encode and a condi ional disc imina i e ne -
wo k is p oposed o ex ac e ec i e la en ea u es and minimize
he domain disc epancy. pmBQA [56] p oposes a p ojec ion-based
blind quali y indica o ia mul imodal lea ning by using ou ho-
mogeneous modali ies (i.e., ex u e, no mal, dep h and oughness).
In e es ed eade s may e e o [40] o a mo e comp ehensi e e iew
o he li e a u e.
In summa y, poin -based schemes may neglec he high-dimensional
p ope ies o poin clouds and he in e play among hese dimensions,
he eby limi ing hei e ec i eness. P ojec ion-based me hods o en
ely on 2D IQA, which may no adequa ely cap u e he in insic cha -
ac e is ics o poin clouds. Fea u e-based schemes end o ha e a high
le el o complexi y, while he in e p e abili y o deep lea ning-based
me hods is a d awback wi h aining equi ing a huge amoun o da a.
3. P oposed me hod
In Fig. 1, he Poin PCA+ amewo k is illus a ed, which is spli in o
h ee modules, namely, (a) p e-p ocessing, (b) ea u e ex ac ion, and
(c) quali y eg ession which a e in oduced in he ollowing subsec-
ions. No e ha a FR me ic ypically uses ei he he p is ine o he
impai ed con en as a e e ence, o bo h. In ou me ic design, only he
p is ine poin cloud se es as a e e ence.
3.1. P e-p ocessing
To ensu e cohe en geome y and colo in o ma ion wi hou edun-
dancies, poin s wi h iden ical coo dina es ha belong o he same poin
cloud a e me ged [37]. The colo o a me ged poin is ob ained by
a e aging he colo o co esponding poin s sha ing he same coo di-
na es. Fo an FR PCQA me ic, iden i ying ma ches be ween e e ence
and dis o ed poin clouds is c ucial o compa ing co esponding lo-
cal p ope ies. In ou me hod, we use he 𝑘𝑛𝑛 algo i hm o iden i y
neighbo hood pai s be ween wo poin clouds. In pa icula , o each
poin ha belongs o a e e ence poin cloud , we ind i s 𝑁nea es
e e ence poin s, and i s 𝑁nea es dis o ed poin s om he dis o ed
poin cloud , in e ms o Euclidean dis ance.
3.2. Fea u e ex ac ion
To cap u e local pe cep ual quali y deg ada ions o a dis o ed poin
cloud, we compu e geome y and ex u e desc ip o s based on he
iden i ied neighbo hoods. S a is ics based on hese desc ip o s a e sub-
sequen ly calcula ed and se e as p edic o s o isual quali y. Fea u es
a e inally ob ained ia pooling o e hese p edic o s. As men ioned
ea lie , ou me hod uses only he p is ine poin cloud as a e e ence o
ind he ma ches in he dis o ed poin cloud.
Table 1
De ini ion o desc ip o s.
Desc ip o De ini ion Dis ance
Geome ic
E o ec o 𝒆= (𝝎
𝑖−𝝎
𝑖)𝑟𝛼
E o along axes 𝜖𝑚= (𝝎
𝑖−𝝎
𝑖)𝑇⋅𝐮𝑚𝑟𝛽
E o om o igin 𝜺=𝝎
𝑖𝑟𝛼,𝑟𝛽
Mean 𝝁=1
𝑁∑𝑛𝝎
𝑛𝑟𝛼,𝑟𝛽
Va iance 𝝀=1
𝑁∑𝑛(𝝎
𝑛−𝝁)2𝑟𝛿
Sum o a iance 𝛴=∑𝑚𝜆
𝑚𝑟𝛿
Co a iance 𝜮=1
𝑁∑𝑛(𝝎
𝑛−𝝁)⋅(𝝎
𝑛−𝝁)T𝑟𝛾
Omni a iance O=3
√∏𝑚𝜆
𝑚𝑟𝜆
Eigenen opy E= −∑𝑚𝜆
𝑚
⋅log 𝜆
𝑚𝑟𝛿
Aniso opy A= (𝜆
1−𝜆
3)∕𝜆
1𝑟𝛿
Plana i y P= (𝜆
2−𝜆
3)∕𝜆
1𝑟𝛿
Linea i y L= (𝜆
1−𝜆
2)∕𝜆
1𝑟𝛿
Sca e ing S=𝜆
3∕𝜆
1𝑟𝛿
Change o cu a u e C=𝜆
3/∑𝑚𝜆
𝑚𝑟𝛿
Pa alleli y P𝑚= 1 −𝐮𝑚⋅𝐯
𝑚–
Angula simila i y 𝜃= 1 −2⋅a ccos(cos(𝐮𝑚,𝐯
𝑚))
𝜋–
Tex u al
Mean
𝝁=1
𝑁∑𝑛𝒑𝑡,
𝑛𝑟𝛿
Va iance
𝒔=1
𝑁∑𝑛(𝒑𝑡,
𝑛−
𝝁)2𝑟𝛿
Sum o a iance
𝛴=∑𝑚𝑠
𝑚𝑟𝛿
Co a iance
𝜮=1
𝑁∑𝑛(𝒑𝑡,
𝑛−
𝝁)⋅(𝒑𝑡,
𝑛−
𝝁)T𝑟𝛾
Omni a iance
O=3
√∏𝑚𝑠
𝑚𝑟𝛿
En opy
H= −∑𝑚𝑠
𝑚
⋅log 𝑠
𝑚𝑟𝛿
3.2.1. Geome y desc ip o s
Gi en a que y poin 𝐩𝑖o , he subsc ip 𝑖deno es he poin index,
1≤𝑖≤||, and ||is he ca dinali y. The coo dina es o 𝐩𝑖’s 𝑁nea es
neighbo s in a e indica ed as 𝒑𝑔 ,
𝑛= (𝑥𝑛, 𝑦𝑛, 𝑧𝑛)T, wi h 1≤𝑛≤𝑁and
∈ {,}. The geome y o 𝐩𝑖is deno ed as 𝒑𝑔 ,
𝑖, and he geome y
o i s closes neighbo in is deno ed as 𝒑𝑔 ,
𝑖. Ini ially, he co a iance
ma ix 𝜮
𝑖is compu ed as
𝜮
𝑖=1
𝑁∑𝑁
𝑛=1 (𝒑𝑔 ,
𝑛−
𝒑𝑔 ,
𝑖)⋅(𝒑𝑔 ,
𝑛−
𝒑𝑔 ,
𝑖)T
,(1)
whe e
𝒑𝑔 ,
𝑖indica es he cen oid, gi en as
𝒑𝑔 ,
𝑖=1
𝑁∑𝑁
𝑛=1 𝒑𝑔 ,
𝑛.(2)
Then, eigen-decomposi ion is applied o 𝜮
𝑖, o ob ain he eigen ec-
o s which o m an o hono mal basis 𝐕composed o eigen ec o s
𝐯
𝑚, whe e 𝑚= 1,2,3. Nex , we map he e e ence and dis o ed
neighbo hoods o he new o hono mal basis, deno ed as 𝝎
𝑛= (𝒑𝑔 ,
𝑛−
𝒑𝑔
𝑖)⋅𝐕. Finally, we apply PCA o he co a iance ma ix o 𝝎
𝑛and
compu e he eigen ec o s 𝐯
𝑚. This p ocess is isually demons a ed in
Fig. 2, showcasing he dis inc ion be ween he wo bases.
The me i inhe en in p ojec ing he geome y o bo h he e e ence
and dis o ed poin clouds on o a sha ed o hono mal basis, es ab-
lished by he e e ence poin cloud, lies in he capaci y o uni y he
ep esen a ion o geome y deg ada ion wi hin a common space. This
enables a mo e p ecise measu emen o geome y simila i y wi hin he
amewo k o he FR PCQA pa adigm.
The mapped coo dina es o he e e ence and dis o ed poin s 𝝎
𝑛,
he eigen ec o s 𝐯
𝑚and he uni ec o s 𝐮𝑚, wi h 𝐮1= [1,0,0]T,
𝐮2= [0,1,0]Tand 𝐮3= [0,0,1]T, a e used o cons uc he geome ic
desc ip o s de ined in Table 1.
3.2.2. Tex u e desc ip o s
The colo space is i s con e ed om RGB o YCbC [57]. This
con e sion is mo i a ed by he ac ha he human eye is mo e sensi i e
o changes in b igh ness han changes in colo acco ding o HVS. We
deno e he ex u e in o ma ion o 𝐩𝑖’s 𝑁nea es neighbo s in as
𝒑𝑡,
𝑛= (𝑌𝑛, 𝐶 𝑏𝑛, 𝐶 𝑟𝑛)T. The p oposed 6 ex u e desc ip o s a e de ined
in Table 1.
Signal P ocessing: Image Communica ion 135 (2025) 117262
3
X. Zhou e al.
Fig. 2. The o hono mal basis o med by bo h e e ence (longd ess) and dis o ed (longd ess_Oc ee-Li ing_R04) poin clouds. The o ange colo ep esen s he geome y a ound one
poin (2130 h poin ) o he e e ence poin cloud and he co esponding basis a e PCA ope a ion; he pu ple colo ep esen s he geome y a ound he ma ched poin o he
dis o ed poin cloud and he co esponding basis a e PCA ope a ion.
Fig. 3. The poin cloud longd ess and s a is ical ea u es using mean o linea i y (Figs. 3(b)–3(c)), plana i y (Figs. 3(d)–3(e)). The ampli udes o s a is ical ea u es a e colo -mapped,
wi h ed indica ing highe and blue lowe alues. I can be no iced ha he mean o linea i y 3(b) and plana i y 3(d) o Poin PCA/Poin PCA+ cap u e high- and low- equency
geome ic egions, espec i ely. Addi ionally, Poin PCA+ has lowe complexi y as he neighbo hood is de e mined h ough knn.
3.2.3. Explana ion o desc ip o s
Each geome y desc ip o ep esen s an in e p e able shape p op-
e y inside he neighbo hood. Speci ically, 𝒆deno es he e o ec o
be ween he mapped coo dina es o he e e ence que y poin and i s
nea es neighbo , and 𝜖𝑚is he p ojec ed dis ance o he e o ec o
ac oss he 𝑚 h axis. The 𝜺is used o cap u e he Euclidean and p ojec ed
dis ances o he mapped e e ence que y poin o i s nea es dis o ed
neighbo om he cen oid and p incipal axes, espec i ely. 𝝁,𝝀,
𝛴and 𝜮 e eal local s a is ics. Ep o ides an es ima ion o he
space unce ain y on he p ojec ed su aces. Addi ionally, P𝑚and 𝜃𝑚
assess he pa alleli y and he angula dispe sion o he dis o ed plane.
The emaining geome y desc ip o s explo e he opology o a local
egion om di e en aspec s, elying on he spa ial dispe sion along
di e en p incipal axes.
𝝁,
𝒔and
𝛴o he YCbC channel exp ess
he in insic dis ibu ion o luminance and ch oma ic componen s.
𝜮
and
Oshow he a iabili y o colo in o ma ion.
𝐇p o ides an
es ima ion o colo unce ain y o he local egion. E e y desc ip o is
compu ed pe poin 𝐩𝑖.
3.2.4. P edic o s
P edic o s a e de ined as he e o samples ob ained by compu ing a
dis ance o e desc ip o alues. We de ine di e en dis ance unc ions
o di e en desc ip o s. We use he Euclidean dis ance o measu e he
Fig. 4. The p edic o s o linea i y (Fig. 4(b)) and plana i y (Fig. 4(c)) o poin cloud
longd ess-Oc ee-Li ing-R02 (Fig. 4(a)). The ampli udes o p edic o s a e colo -mapped,
wi h ed indica ing highe and blue lowe alues. No ably, he ela i e di e ences in
linea i y and plana i y o Poin PCA+ e ec i ely highligh egions ha can o m linea
s uc u es and de ec bulges, such as w inkles in clo hing, in he longd ess.
poin - o-poin dis ances be ween que y poin pai s unde he new basis
𝑟𝛼=√∑𝑚𝒅𝟏2,(3)
Signal P ocessing: Image Communica ion 135 (2025) 117262
4
X. Zhou e al.
whe e 𝒅𝟏is he di e ence be ween wo poin s. We use he absolu e
alue o measu e he poin - o-plane dis ance, as
𝑟𝛽=|𝒅𝟐|,(4)
whe e 𝒅𝟐indica es he p ojec ed dis ance be ween a poin and he
e e ence axes. We use he ollowing de ini ion o ela i e di e ence
o he co a iance ea u es
𝑟𝛾=|𝒒⊙𝒒−𝑸|
𝒒⊙𝒒,(5)
whe e {𝒒=𝝀,𝐐=𝜮}and {𝒒=
𝒔,𝐐=
𝜮}, o geome y and
ex u e a ibu es, espec i ely, ⊙is o elemen -wise p oduc . We use
he ela i e di e ence o mula [26], o he emaining desc ip o s
𝑟𝛿=|𝜙−𝜙|
||𝜙||+||𝜙||+𝜀,(6)
whe e 𝜀is a small cons an o a oid unde ined ope a ions. Finally, he
de ini ions o pa alleli y and angula simila i y desc ip o s inco po a e
a dis ance unc ion. Fo no a ional pu poses only, we de ine dis ances
𝑟𝜌and 𝑟𝜃 o be iden ical o he de ini ions o P𝑚and 𝜃𝑚, espec i ely.
Table 1enlis s dis ance unc ion(s) used pe desc ip o .
3.2.5. Fea u es
Fea u es a e de ined by pooling o e p edic o alues. Speci ically,
p edic o s 𝜓𝑖,𝑗 ,𝑘 a e ob ained pe poin 𝐩𝑖, desc ip o 𝑗, and dis ance
unc ion 𝑟𝑘,𝑘∈ {𝛼 , 𝛽 , 𝛾 , 𝛿 , 𝜌, 𝜃}. This is done o all desc ip o s 𝑗in
Table 1, using he co esponding dis ances 𝑟𝑘. Th ough pooling, we
ob ain a ea u e 𝑓𝑗 ,𝑘 o e e y p edic o :
𝑓𝑗 ,𝑘 =1
||∑||
𝑖=1 𝜓𝑖,𝑗 ,𝑘.(7)
3.3. Quali y eg ession
To ob ain a quali y sco e ha is well-aligned wi h he HVS, he
Recu si e Fea u e Elimina ion (RFE) algo i hm is used o selec he
mos ele an p edic o se among all he p oposed p edic o s. RFE [58]
imp o es model accu acy, and e iciency, and educes o e i ing. Ma-
chine lea ning-based eg ession models ha e been ex ensi ely used
o ackle he quali y eg ession p oblem in he domain o quali y
assessmen , we hen use he andom o es algo i hm o eg ess he
selec ed p edic o s o he inal quali y sco e.
3.4. Di e ences wi h Poin PCA
In compa ison o Poin PCA, ou p e-p ocessing me hodology in-
ol es solely u ilizing he p is ine poin cloud as a e e ence, dispensing
wi h he need o bo h p is ine and dis o ed poin clouds. Rega ding
geome ic ea u es, we ans o m he 𝑥𝑦𝑧 alues o bo h he p is-
ine and dis o ed poin clouds in o he basis o med by he p is ine
poin cloud, elimina ing he necessi y o sepa a e bases o dis inc
poin cloud se s. Fo ex u al ea u es, we di ec ly apply s a is ical
unc ions o he colo alues in he YCbC space wi hou eso ing
o PCA decomposi ion. The decision o o ego PCA on ex u e s ems
om he lack o physical signi icance pos -decomposi ion o YCbC
channel alues, as obse ed in geome y. Simul aneously, his app oach
aids in educing compu a ional complexi y. Addi ionally, Poin PCA+
adop s dis inc dis ance unc ions o a ious desc ip o s, elimina ing
cons ain s on he compu a ion o mean and s anda d de ia ion alues.
We illus a e he dispa i ies be ween Poin PCA and Poin PCA+ o a
speci ic poin cloud, longd ess, in Fig. 3. No ably, we isualize he
linea i y and plana i y geome ic desc ip o s be o e compa ison. F om
Fig. 3, he geome ic dissimila i y measu emen s di e when using 𝑘𝑛𝑛
and 𝑟-𝑠𝑒𝑎𝑟𝑐 ℎme hods. Fo Poin PCA, we employed he 𝑟-𝑠𝑒𝑎𝑟𝑐 ℎme hod
wi h 𝑟= 0.008 ×𝐵, whe e 𝐵 ep esen s he maximum leng h o he
bounding box o he e e ence poin cloud. In con as , o Poin PCA+,
we used he 𝑘𝑛𝑛 algo i hm wi h 𝑘= 81. While o he s a is ical ea u es
𝜇, he 𝑘𝑛𝑛 algo i hm wi h 𝑘= 9was applied. Bo h he linea i y and
plana i y a e dec eased compa ed wi h Poin PCA. We also isualize he
p edic ions co esponding o linea i y and plana i y in Fig. 4. We can
see ha he p edic o s exac ly desc ibe he line and he une en egion
o poin cloud longd ess.
4. Expe imen al esul s
In his Sec ion, we epo he e alua ion esul s o he p oposed
Poin PCA+ me ic unde h ee public da ase s in Sec ion 4.2 wi h
o he 8 s a e-o - he-a me ics. Mo eo e , we epo he pe o mance
achie ed in he ICIP 2023 Poin Cloud Visual Quali y Assessmen
(PCVQA) g and challenge1in Sec ion 4.3. Speci ically, he challenge
consis s o 5 acks, which co espond o di e en use cases in which
quali y me ics a e ypically used. The i s wo acks aim o as-
sess he pe cep ual ideli y o dis o ed con en s wi h/wi hou espec
o he o iginals o any le el o dis o ion, espec i ely. This is he
mos gene ic and adi ional se -up o quali y me ics. The nex wo
acks ocus on me ics o high-end quali y wi h/wi hou access o he
o iginal con en . These a e desi able in applica ions such as con en
p oduc ion, high-quali y s eaming, digi al wins, e c. The las ack
should be sensible o quali y di e ences wi hin di e en p ocessed
e sions o he same poin cloud con en , which is sui able o op i-
miza ion scena ios. We pa icipa ed in T ack#1 FR b oad- ange quali y
es ima ion, T ack#3 FR high- ange quali y es ima ion, and T ack#5 FR
in a- e e ence quali y es ima ion. Addi ional analysis ela ed o c oss-
da ase alida ion and ea u e impo ance is ca ied ou ac oss all he
a o emen ioned da ase s, as de ailed in Sec ion 4.4 and Sec ion 4.5.
These sec ions aim o demons a e he gene alizabili y o he p oposed
Poin PCA+.
4.1. Se up
4.1.1. Da ase s
Th ee publicly a ailable da ase s we e ec ui ed o pe o mance
e alua ion, namely, M-PCCD, SJTU, and WPC. The M-PCCD [60] con-
sis s o 8 poin clouds whose geome y and colo a e encoded using
V-PCC and G-PCC a ian s, esul ing in 232 dis o ed s imuli. De ailed
dis o ion ypes include Oc ee-Li ing, Oc ee-RAHT, T iSoup-Li ing,
T iSoup-RAHT and V-PCC. The con en s in M-PCCD depic ei he hu-
man igu es o objec s. The SJTU [61] includes 9 e e ence poin
clouds wi h each poin cloud co up ed by se en ypes o dis o ions
unde six le els, gene a ing 378 dis o ed s imuli. De ailed dis o ion
ypes include Oc ee-based comp ession, Colo Noise (CN), Geome -
ic Gaussian Noise (GGN), downsampling, and combina ions o he
CN, GGN and downsampling. SJTU includes 5 human body models
and 4 inanima e objec s. The WPC [44] con ains 20 e e ence poin
clouds wi h each poin cloud deg aded unde i e ypes o dis o -
ions and di e en le els, leading o 740 dis o ed s imuli. De ailed
dis o ion ypes include Oc ee-LPCC, T iSoup-SPCC, V-PCC, Gaussian
noise and downsampling. WPC da ase only collec s objec s including
snacks, ui s and ege ables, e c. The B oad Quali y Assessmen o
S a ic Poin Clouds (BASICS) [34] is used in he ICIP 2023 PCVQA
g and challenge, and comp ises 75 poin clouds om 3 di e en se-
man ic ca ego ies: (i) Humans & Animals, (ii) Inanima e Objec s, and
(iii) Buildings & Landscapes. Each poin cloud is comp essed wi h 3
comp ession me hods om he MPEG s anda diza ion ield, i.e., Oc ee-
RAHT, Oc ee-P edli and V-PCC; 1 lea ning-based algo i hm, i.e.,
GeoCNN, a a ying comp ession le els, esul ing in 1494 p ocessed
poin clouds. BASICS da ase is aimed o p o ide a ounda ion o e-
sea ch ha suppo s he elep esence applica ions, in e ms o comp es-
sion and quali y assessmen . Table 3summa ized he cha ac e is ics o
he ou da ase s.
1h ps://si es.google.com/ iew/icip2023-pc qa-g and-challenge
Signal P ocessing: Image Communica ion 135 (2025) 117262
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X. Zhou e al.
Table 2
SROCC pe o mance on M-PCCD, SJTU and WPC da ase s.
Me ic Poin PCA+ Poin PCA [25] PCQM [24] Poin SSIM [26] Bi Dance [59] Plane2Plane [41] P2Plane_MSE [40] P2P_MSE [40] PSNR Y [40]
M-PCCD 0.943±0.022 0.941±0.032 0.940 ±0.032 0.925 ±0.024 0.859 ±0.061 0.847 ±0.076 0.901 ±0.025 0.896 ±0.042 0.798 ±0.162
SJTU 0.865±0.064 0.890±0.056 0.862 ±0.030 0.708 ±0.070 0.748 ±0.077 0.761 ±0.039 0.578 ±0.155 0.612 ±0.157 0.743 ±0.083
WPC 0.857±0.040 0.866±0.036 0.749 ±0.036 0.465 ±0.059 0.451 ±0.054 0.454 ±0.069 0.452 ±0.065 0.563 ±0.071 0.614 ±0.061
Table 3
O e iew o M-PCCD, SJTU, WPC and BASICS da ase s.
Da ase s Con en s Dis o ion ypes Dis o ion
le els
To al
M-PCCD Humans & Inanima e Objec s 8 Oc ee-Li ing, Oc ee-RAHT, T iSoup-Li ing,
T iSoup-RAHT, V-PCC
5 G-PCC: 6
V-PCC: 5
232
SJTU Humans & Inanima e Objec s 9 Oc ee-based comp ession, CN, GGN, downsampling, CN
+ GGN, CN + downsamplin, GGN + downsampling
7 6 378
WPC Inanima e Objec s 20 Oc ee-LPCC, T iSoup-SPCC, V-PCC, Gaussian noise,
downsampling
5 Geome y: 3
Tex u e:1/3/4
740
BASICS 1. Humans & Animals 2. Inanima e Objec s
3. Buildings & Landscapes
75 Oc ee-RAHT, Oc ee-P edli , V-PCC, GeoCNN 4 G-PCC: 5
V-PCC: 6
1494
4.1.2. E alua ion me ics
Fo he PCVQA G and Challenge, all submissions unde go es ing
on a designa ed es se cu a ed by he o ganize s. The e alua ion o
pe o mance elies on i e s anda d c i e ia p o ided by he o ganiz-
e s: including Pea son Linea Co ela ion Coe icien (PLCC), Spea -
man Rank O de Co ela ion Coe icien (SROCC), Di e ence/Simila
Analysis quan i ied by A ea Unde he Cu e (D/S𝐴𝑈 𝐶), Be e /Wo se
Analysis quan i ied by Co ec Classi ica ion pe cen age (B/W𝐶 𝐶) [62],
and he Run ime Complexi y (RC). No ably, no unc ion is employed o
sco e mapping. Addi ionally, o he assessmen o pe o mance me ics
on h ee o he commonly used da ase s, he c i e ia include SROCC,
PLCC, Kendall Rank O de Co ela ion Coe icien (KROCC), and Mean
Squa e E o (MSE) a e chosen. Highe alues o PLCC, SROCC, and
KROCC indica e be e pe o mance in e ms o co ela ion wi h human
opinion while lowe RMSE indica es be e consis ency.
4.1.3. Implemen a ion de ails
We use RFE o selec he bes ea u e se among all he p edic o s,
wi h he bes SROCC pe o mance on he PCVQA g and challenge es
se . In he in e ence s age, he de aul con igu a ion o sciki -lea n ( e -
sion 1.2.2) in Py hon is used. Rega ding he neighbo hood size o he
compu a ion o desc ip o s, 𝐾= 81 is chosen conside ing complexi y
and pe o mance, a e expe imen ing wi h 𝐾∈ {9,25,49,81,121}.
4.2. Pe o mance e alua ion on M-PCCD, SJTU and WPC
We compa e Poin PCA+ wi h exis ing FR poin -based quali y me -
ics, he esul s a e shown in Table 2. The bes pe o mance among
hese me ics is highligh ed in bold ace, wi h he second bes unde -
lined. Speci ically, each da ase is spli in o wo pa i ions ha con ain
80% and 20% o he con en s o aining and es ing, espec i ely,
wi h all he dis o ed e sions o a speci ic con en placed in one
pa i ion. Fo M-PCCD, SJTU, and WPC, we use 6/2, 7/2, and 16/4
con en s o aining/ es ing, espec i ely. Then, a quali y p edic ion
model is ained on he aining da a and es ed on he co esponding
es ing da a o he same da ase , o wi hin-da ase alida ion. his
p ocess is epea ed o all possible 80%–20% spli s o each da ase ,
leading o 28, 36, and 4845 es ing pa i ions and an equal numbe o
co esponding quali y p edic ion models o M-PCCD, SJTU, and WPC
espec i ely. Finally, he a e age and he s anda d de ia ion o SROCC
index compu ed ac oss all es ing spli s o each da ase , a e epo ed.
F om Table 2we can see ha PCA-based me ics a e compe i i e wi h
he highes SROCC on he h ee da ase s, especially he pe o mance o
Poin PCA on WPC is inc eased by 15.62% in e ms o SROCC hough
he pe o mance o Poin PCA+ is a sligh ly lowe han Poin PCA (0.866
VS 0.857).
Table 4
T ack#1 (FR b oad ange): op 4 pe o mance compa ison on he o icial PCVQA g and
challenge es se , e alua ed by he challenge o ganize s. Bes in bold and second bes
unde lined. Ou submission is anked in 2nd place.
Submission SROCC PLCC D/S𝐴𝑈 𝐶B/W𝐶 𝐶RC(s)
KDDIUSCJoin 0.875 0.917 0.888 0.970 42.80
Poin PCA+ 0.874 0.909 0.871 0.961 1000.00
SJTU MMLAB 0.871 0.896 0.832 0.955 8.60
SlowHand 0.791 0.825 0.805 0.924 130.47
Table 5
T ack#3 (FR high ange): op 4 pe o mance compa ison on he o icial PCVQA g and
challenge es se , e alua ed by he challenge o ganize s. Bes in bold and second bes
unde lined. Ou submission is anked in 3 d place.
Submission SROCC PLCC D/S𝐴𝑈 𝐶B/W𝐶 𝐶RC(s)
SJTU MMLAB 0.630 0.592 0.665 0.909 8.60
KDDIUSCJoin 0.551 0.516 0.642 0.872 42.80
Poin PCA+ 0.603 0.479 0.625 0.886 1000.00
SlowHand 0.377 0.423 0.565 0.780 130.47
Table 6
T ack#5 (FR in a- e e ence): op 4 pe o mance compa ison on he
o icial PCVQA g and challenge es se , e alua ed by he challenge
o ganize s. Bes in bold and second bes unde lined. Ou submission
is anked in 3 d place.
Submission D/S𝐴𝑈 𝐶B/W𝐶 𝐶RC(s)
SJTU MMLAB 0.808 0.947 8.60
KDDIUSCJoin 0.822 0.933 42.80
Poin PCA+ 0.811 0.938 1000.00
SlowHand 0.753 0.854 130.47
4.3. Pe o mance e alua ion on BASICS
We spli BASICS in o aining– alida ion- es wi h 60%-20%–20%
ollowing he ules om he PCVQA g and challenge [63]. Table 4 o
Table 6show he o icial e alua ion esul s o T ack#1, T ack#3 and
T ack#5, espec i ely.
Re e encing Tables 5–6, se e al no able obse a ions eme ge om
he compe i ion esul s ac oss all h ee FR acks. (1) Despi e s ong
pe o mances in T ack 1 and T ack 5, none o he eams a ained
sa is ac o y esul s in T ack 3 o in PCVQA, highligh ing he challenges
associa ed wi h ine-g ained PCQA. (2) Examining Poin PCA+, i is
e iden ha he ex ac ed ea u es wi hin a neighbo hood size o 81,
combined wi h he applica ion o s a is ical unc ions (e.g., mean and
a iance) on geome y, may ail o cap u e sub le di e ences be ween
wo poin clouds. This highligh s he limi a ions o using s a is ical
ea u es o cap u e sub le di e ences.
Signal P ocessing: Image Communica ion 135 (2025) 117262
6
X. Zhou e al.
Table 7
C oss-da ase alida ion among M-PCCD, SJTU, WPC and BASICS da ase s. Bo h he aining and es ing used all he con en among he da ase s. Bes in bold.
Tes
M-PCCD SJTU WPC BASICS
T ain PLCC SROCC KROCC RMSE PLCC SROCC KROCC RMSE PLCC SROCC KROCC RMSE PLCC SROCC KROCC RMSE
M-PCCD – – – – 0.726 0.725 0.541 3.148 0.500 0.469 0.328 4.003 0.847 0.777 0.589 0.899
SJTU 0.855 0.881 0.708 2.578 – – – – 0.578 0.608 0.442 2.575 0.732 0.717 0.523 1.946
WPC 0.731 0.878 0.703 4.767 0.610 0.604 0.435 2.049 – – – – 0.848 0.726 0.536 3.675
BASICS 0.832 0.880 0.692 1.057 0.579 0.645 0.472 2.810 0.500 0.490 0.347 3.202 – – – –
4.4. C oss-da ase alida ion
To e i y he gene aliza ion and obus ness o he p oposed Poin -
PCA+, we conduc c oss-da ase expe imen s among all 4 da ase s. We
ain he model using he en i e con en o one da ase and hen es
i sepa a ely using he en i e con en o he o he h ee da ase s. The
expe imen al esul s a e shown in Table 7. F om Table 7, we can d aw
he ollowing obse a ions:
1. Poin PCA+ pe o ms well in gene aliza ion and obus ness, pa -
icula ly when ained on he small M-PCCD da ase and es ed
on he la ge BASICS da ase . Combined wi h Table 2, he c oss-
da ase e alua ion pe o mance is e en highe han ce ain FR
PCQA me ics, o example Bi Dance [59], PSNR_Y [40], e c.
2. Compa ed wi h M-PCCD, SJTU and BASICS da ase s, he WPC
da ase has he wo s pe o mance among all he e alua ion me -
ics. SROCC and PLCC o Poin PCA+ on WPC ained on M-PCCD
and BASICS achie e he same accu acy as andom guessing, his
may be because he con en s in WPC only con ain objec s, and
he dis o ion ypes o WPC a e mo e complex compa ed wi h
he o he h ee da ase s.
3. Poin PCA+ shows be e SROCC pe o mance on he SJTU da a-
se compa ed o he WPC da ase . This is likely because SJTU
sha es speci ic human igu es wi h he M-PCCD da ase and
includes bo h human and objec ca ego ies o M-PCCD and
BASICS, while SJTU and WPC ha e no o e lapping con en .
In conclusion, he c oss-da ase pe o mance o Poin PCA+ is p om-
ising bu i s gene aliza ion depends on da ase composi ion. T aining
on la ge, di e se da ase s and es ing on smalle ones no mally yields
be e esul s, while he e e se leads o poo gene aliza ion. Howe e ,
his canno hold i he e exis s a domain shi (i.e., in ou case, con en s
and dis o ion ype) be ween he es ing se and he aining se .
4.5. Pe o mance on indi idual dis o ion ype
To u he explo e he e ec i eness o he designed geome y and
ex u e ea u es o a speci ic dis o ion ype, we es he pe o mance
pe dis o ion ype pe da ase , wi h he esul s lis ed in Table 8. We
can d aw he ollowing obse a ions.
1. When assessing comp ession dis o ion, V-PCC eme ges as he
mos challenging dis o ion ype o which o e alua e pe cep ual
quali y, aligning wi h indings om a p io s udy [46]. P edic -
ing he pe cep ual quali y o comp ession dis o ions om G-PCC
and lea ning-based me hods p o es o be mo e manageable, wi h
Oc ee-Li ing exhibi ing a sligh ad an age o e Oc ee-RAHT
on M-PCCD and BASICS da ase s.
2. Fo CN and Gaussian noise dis o ions, CN has he poo es
pe o mance. Howe e , p edic ion accu acy imp o es by 16.06%
o CN+GGN in e ms o SROCC on he SJTU da ase , indi-
ca ing ha geome y- ela ed ea u es help cap u e hese dis o -
ions. Gaussian noise pe o ms wo s on WPC, as i a ec s bo h
geome y and ex u e, c ea ing a compounded dis o ion.
3. Fo downsampling dis o ion ypes, he pe o mance o Poin -
PCA+ is no ably high on he SJTU da ase bu ela i ely lowe
on he WPC da ase . This implies ha downsampling on objec s
p esen s a challenge o he HVS o disce n, as i may exe a
masking e ec on objec s mo e p ominen ly han on humans.
Table 8
Pe o mance compa ison o Poin PCA+ me ics o di e en dis o ion ypes pe da ase .
DT e e s o dis o ion ype and NC deno es he numbe o con en s.
Da ase DT NC PLCC SROCC KROCC RMSE
M-PCCD
Oc ee-Li ing 48 0.938 0.991 0.962 0.826
Oc ee-RAHT 48 0.962 0.984 0.931 0.704
T iSoup-Li ing 48 0.951 0.965 0.879 0.597
T iSoup_RAHT 48 0.970 0.963 0.870 0.561
V-PCC 40 0.823 0.815 0.674 1.266
SJTU
CN 54 0.621 0.741 0.545 2.594
CN + GGN 54 0.894 0.860 0.697 0.825
Downsampling 54 0.969 0.944 0.848 0.562
Downsampling+CN 54 0.946 0.937 0.788 1.371
Downsampling+GGN 54 0.981 0.965 0.879 0.736
GGN 54 0.955 0.958 0.848 0.810
Oc ee (PCL) 54 0.975 0.965 0.879 0.797
WPC
Downsampling 60 0.802 0.795 0.594 1.177
Oc ee (LPCC) 80 0.916 0.881 0.708 0.850
T isoup (SPCC) 240 0.987 0.923 0.818 0.594
Gaussian noise 180 0.628 0.650 0.417 1.826
V-PCC 180 0.737 0.756 0.566 2.054
BASICS
GeoCNN 294 0.971 0.941 0.787 0.305
Oc ee-P edli 375 0.975 0.937 0.792 0.289
Oc ee-RAHT 375 0.895 0.876 0.693 0.441
V-PCC 450 0.787 0.690 0.514 0.371
In summa y, Poin PCA+ exhibi s p o iciency in p edic ing comp es-
sion dis o ions. Howe e , i s e ec i eness diminishes when con on ed
wi h dis o ion ins ances p ima ily mani es ing in colo alues, as
obse ed o CN dis o ions on he SJTU da ase . Addi ionally, when
he equilib ium be ween geome ic and colo is dis up ed, as exem-
pli ied by Gaussian noise on he WPC da ase , Poin PCA+ s uggles o
accu a ely gauge he ex en o deg ada ion.
4.6. Fea u e impo ance o Poin PCA+ o di e en dis o ion ypes pe
da ase
We e alua ed he e ec i eness o he 40 selec ed ea u es a e RFE.
The model was ained on 80% o he da ase , and ea u e impo ance
was calcula ed on he emaining 20% o each dis o ion ype. This was
done using he pe mu a ion impo ance echnique [64] based on MSE.
Pe mu a ion impo ance shows how c ucial a ea u e is o a speci ic
model, a he han i s s andalone p edic i e alue, helping o assess he
gene aliza ion abili y o he ea u es ac oss di e en dis o ion ypes.
The ea u e impo ance o Poin PCA+ ac oss he ou da ase s is shown
in Fig. 5. The ea u e impo ance o each dis o ion ype pe da ase
is illus a ed in Fig. 6. Combining Fig. 5and Fig. 6, we can d aw he
ollowing conclusions:
1. The ea u e impo ance anking a ies ac oss di e en da ase s,
p ima ily due o dis inc ions in con en and dis o ion ypes
among he ou da ase s. The a iance on he 𝑧axis (𝑓𝑧
𝜆,𝛿) wi hin
he geome ic ea u es ob ained he lowes impo ance anking
on bo h M-PCCD and BASICS, anked 29 h and 38 h on SJTU
and WPC da ase s, espec i ely.
2. Geome ic ea u es consis en ly exhibi supe io ea u e impo -
ance ankings when compa ed o ex u al ea u es, as obse ed
in he op-5 ea u es ac oss all ou da ase s. In M-PCCD, SJTU,
Signal P ocessing: Image Communica ion 135 (2025) 117262
7
X. Zhou e al.
Fig. 5. The ea u e impo ance o all he ex ac ed geome y and ex u e ea u es wi hin poin PCA+ me ic o M-PCCD, SJTU, WPC and BASICS da ase s. The numbe s a e ob ained
by anking he 40 ea u es based on he impo ance sco e pe da ase .
Fig. 6. Fea u e impo ance o Poin PCA+ pe dis o ion ype o M-PCCD, SJTU, WPC, and BASICS da ase s, sepa a ely. The numbe s a e ob ained by anking he 40 ea u es
based on he pe mu a ion ea u e impo ance sco e pe dis o ion ype.
and WPC, he op-3 ankings comp ise a combina ion o ex u e
and geome y ea u es. Howe e , in BASICS, only geome y
ea u es a e ep esen ed in he op-3 anking.
3. The poin - o-poin dis ance (𝑓𝒆,𝛼) and he mean alue o 𝑣chan-
nel (𝑓𝑣
𝝁,𝛿) demons a e s ong pe o mance ac oss a ious dis o -
ion ypes in M-PCCD da ase . No ably, in T iSoup-Li ing, he
mean alue o 𝑦channel (𝑓𝑦
𝝁,𝛿) excels bu pe o ms less op imally
in he case o V-PCC dis o ion. In SJTU da ase , he cosine
simila i y o he 𝑦axis (𝑓𝑦
𝜃) ou pe o ms o he ea u es o all
dis o ion ypes, excep o CN+GGN dis o ion. Simila ly, he
co a iance o he 𝑢channel (𝑓𝑢
𝜮) excels o all dis o ion ypes,
wi h he excep ion o Gaussian noise in WPC. Meanwhile, in
BASICS, he p ojec ed dis ances o he dis o ed cen oid om
e e ence planes on he 𝑧axis (𝑓𝑧
𝝎𝐵,𝛽 ) consis en ly yield high
ankings ac oss all dis o ion ypes.
4.7. Discussion
A he da ase le el, pe o mance is signi ican ly in luenced by
he o al numbe o poin clouds. In ex ensi e da ase s encompassing
di e se con en , p edic ion accu acy ends o be lowe compa ed o
smalle da ase s wi h ewe a ia ions, e en when hei dis o ion
ypes a e simila . Fu he mo e, dis o ion le els play a c ucial ole
in impac ing p edic ion accu acy, wi h ine-g ained dis o ion p o ing
mo e challenging han coa se di ision. In he con ex o poin clouds,
compound dis o ion does no necessa ily esul om he mix u e o
mul iple dis o ion ypes, e en a single dis o ion ype can concu en ly
comp omise ex u e and geome y. Hand-c a ed geome y and ex u e
ea u es exhibi dis inc s eng hs and weaknesses ac oss a ious dis o -
ion ypes. Combining bo h ypes o ea u es adap i ely wi h dis o ions
may enhance p edic ion accu acy.
Signal P ocessing: Image Communica ion 135 (2025) 117262
8
X. Zhou e al.
5. Conclusion and u u e wo k
This pape p oposes a PCA-based FR PCQA me ic, namely Poin -
PCA+, which elies on an en iched se o lowe complexi y desc ip o s
wi h espec o i s Poin PCA p edecesso . A e a p e-p ocessing s ep,
ea u es a e ex ac ed om bo h geome ic and ex u al domains. A
subse o ea u es is selec ed o enhance he s abili y o he model, and a
lea ning-based ea u e usion based on ensemble lea ning is applied o
he ea u e subse , o p o ide a quali y sco e o a dis o ed poin cloud.
Ou expe imen al esul s demons a e ha Poin PCA+ ou pe o ms he
majo i y o exis ing PCQA me ics, eaching second place in T ack#1
and hi d place in T ack#3 and T ack#5 o he ICIP 2023 PCVQA g and
challenge.
Compa ed o o he eams in he PCVQA g and challenge, Poin PCA+
has he highes compu a ional complexi y, wi h a p ocessing ime
o 1000 ms, while he lowes epo ed is 8.6 ms. This ine iciency
s ems om he poin -based FR PCQA amewo k, especially he PCA
decomposi ion applied o each poin . One solu ion o educe he com-
pu a ional load is o downsample he poin cloud be o e p ocessing,
while main aining i s o e all s uc u e. Addi ionally, bo h Poin PCA
and Poin PCA+ mainly ocus on local ea u es, neglec ing he b oade
geome ic and ex u e con ex o he poin cloud. To imp o e, inco -
po a ing global ea u es ha cap u e mo e comp ehensi e in o ma ion
is essen ial. This will lead o a mo e e icien and holis ic cha ac-
e iza ion o poin clouds, mee ing he demands o he PCQA ield.
These addi ions a e poised o con ibu e o a mo e holis ic and e icien
cha ac e iza ion o he poin cloud, aligning wi h he igo ous demands
o he PCQA ield.
CRediT au ho ship con ibu ion s a emen
Xuemei Zhou: W i ing – e iew & edi ing, W i ing – o iginal d a ,
Me hodology, In es iga ion, Da a cu a ion. E angelos Alexiou: W i -
ing – e iew & edi ing, Valida ion, Supe ision, Me hodology. I ene
Viola: W i ing – e iew & edi ing, Visualiza ion, Valida ion, Supe i-
sion, Funding acquisi ion. Pablo Cesa : W i ing – e iew & edi ing,
Supe ision, Funding acquisi ion.
Decla a ion o compe ing in e es
The au ho s decla e ha hey ha e no known compe ing inan-
cial in e es s o pe sonal ela ionships ha could ha e appea ed o
in luence he wo k epo ed in his pape .
Acknowledgmen s
This wo k was suppo ed h ough he NWO WISE g an and he
Eu opean Commission Ho izon Eu ope p og am, unde he g an ag ee-
men 101070109, TRANSMIXR h ps:// ansmix .eu/. Funded by he
Eu opean Union.
Da a a ailabili y
Da a will be made a ailable on eques .
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