Academic Edi o s: F ancesco
Ma inello, Chen Zhang and
Hao eng Zhao
Recei ed: 5 May 2025
Re ised: 26 June 2025
Accep ed: 11 July 2025
Published: 16 July 2025
Ci a ion: Kešelj, K.; S amenko i´c, Z.;
Kos i´c, M.; A´cin, V.; Teki´c, D.;
No ako i´c, T.; I aniše i´c, M.; I ezi´c,
A.; Magazin, N. Machine Lea ning
(Au oML)-D i en Whea Yield
P edic ion o Eu opean Va ie ies:
Enhanced Accu acy Using
Mul ispec al UAV Da a. Ag icul u e
2025,15, 1534. h ps://doi.o g/
10.3390/ag icul u e15141534
Copy igh : © 2025 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license
(h ps://c ea i ecommons.o g/
licenses/by/4.0/).
A icle
Machine Lea ning (Au oML)-D i en Whea Yield P edic ion o
Eu opean Va ie ies: Enhanced Accu acy Using Mul ispec al
UAV Da a
K s an Kešelj 1, Zo an S amenko i´c 1,* , Ma ko Kos i´c 1, Vladimi A´cin 2, D agana Teki´c 1,
Tihomi No ako i´c 1, Mladen I aniše i´c 1, Aleksanda I ezi´c 3and Nenad Magazin 1
1Facul y o Ag icul u e, Uni e si y o No i Sad, T g Dosi eja Ob ado i´ca 8, 21000 No i Sad, Se bia;
[email p o ec ed] (K.K.); [email p o ec ed] (M.K.); [email p o ec ed] (D.T.);
ihomi [email p o ec ed] (T.N.); [email p o ec ed] (M.I.);
[email p o ec ed] (N.M.)
2Ins i u e o Field and Vege able C ops, Maksima Go kog 30, 21000 No i Sad, Se bia;
ladimi [email p o ec ed]
3Cen e o Biosys ems, BioSense Ins i u e, Uni e si y o No i Sad, D . Zo ana Ðin ¯
di´ca 1,
21000 No i Sad, Se bia; aleksanda [email p o ec ed]
*Co espondence: [email p o ec ed]
Abs ac
Accu a e and imely whea yield p edic ion is aluable globally o enhancing ag icul u al
planning, op imizing esou ce use, and suppo ing ade s a egies. S udy add esses he
need o p ecision in yield es ima ion by applying machine-lea ning (ML) eg ession models
o high- esolu ion Unmanned Ae ial Vehicle (UAV) mul ispec al (MS) and Red-G een-Blue
(RGB) image y. Resea ch analyzes i e Eu opean whea cul i a s ac oss 400 expe imen al
plo s c ea ed by combining 20 ni ogen, phospho us, and po assium (NPK) e ilize ea -
men s. Yield a ia ions om 1.41 o 6.42 /ha s eng hen model obus ness wi h di e se
da a. The ML app oach is au oma ed using PyCa e , which op imized and e alua ed
25 eg ession models based on 65 ege a ion indices and yield da a, esul ing in 66 ea u e
a iables ac oss 400 obse a ions. The da ase , spli in o aining (70%) and es ing se s
(30%), was used o p edic yields a h ee g ow h s ages: 9 May, 20 May, and 6 June 2022.
Key models achie ed high accu acy, wi h he Suppo Vec o Reg ession (SVR) model
eaching R
2
= 0.95 on 9 May and R
2
= 0.91 on 6 June, and he Mul i-Laye Pe cep on
(MLP) Reg esso a aining R
2
= 0.94 on 20 May. The indings unde sco e he e ec i eness
o p ecisely measu ed MS indices and a igo ous expe imen al app oach in achie ing high-
accu acy yield p edic ions. This s udy demons a es how a p ecise expe imen al se up,
la ge-scale ield da a, and Au oML can ha ness UAV and machine lea ning’s po en ial
o enhance whea yield p edic ions. The main limi a ions o his s udy lie in i s ocus on
expe imen al ields unde speci ic condi ions; u u e esea ch could explo e adap abili y o
di e se en i onmen s and whea a ie ies o b oade applicabili y.
Keywo ds: yield p edic ion; whea ; machine lea ning; mul ispec al indices
1. In oduc ion
Ea ly p edic ion o whea yield is c ucial no only o es ima ing inal p oduc ion
quan i ies bu also o enabling a me s o op imize c op managemen p ac ices h ough
he imely applica ion o ag onomic measu es aimed a maximizing yield.
Ag icul u e 2025,15, 1534 h ps://doi.o g/10.3390/ag icul u e15141534
Ag icul u e 2025,15, 1534 2 o 32
In his pape , we ha e s udied he applica ion o machine-lea ning me hodologies,
pa icula ly using he PyCa e lib a y, in p ocessing da a acqui ed om UAVs equipped
wi h bo h MS and RGB came as. The goal was o de elop highly accu a e machine-lea ning
models o he es ima ion o whea yield based on d one images o he plan canopy, empha-
sizing achie ing high p ecision and a signi ican coe icien o de e mina ion. While he e
a e nume ous s udies on whea yield p edic ion, many su e om inadequa e p ecision
and lowe de e mina ion coe icien s, making hem less eliable o p ac ical applica ions.
This wo k aims o add ess hese issues by employing ad anced machine-lea ning ech-
niques and comp ehensi e UAV-based da a collec ion on i e Eu opean whea cul i a s,
which, in e ms o a ie al cha ac e is ics, a e simila o whea a ie ies g own ac oss
Eu ope. This s udy’s no el y lies in se ing a new benchma k o high p edic i e accu acy
in Eu opean whea yield es ima ion models by using machine-lea ning me hodologies and
UAV image y.
T adi ional c op yield p edic ion me hods—o en based on ield su eys, s a is ical
modeling, o sa elli e image y— equen ly lack he spa ial esolu ion, imeliness, and
adap abili y equi ed o mode n p ecision ag icul u e. These app oaches a e ypically
labo -in ensi e, delayed in esponse, o unable o cap u e sub le wi hin- ield a iabili y.
Hence, he e is a g owing in e es in in eg a ing UAV echnology and machine lea n-
ing o o e come hese limi a ions and deli e mo e accu a e, si e-speci ic, and imely
yield p edic ions.
Machine lea ning (ML) is a ield o a i icial in elligence ha ocuses on de eloping
algo i hms enabling compu e s o ecognize pa e ns and make da a-d i en p edic ions o
decisions wi hou being explici ly p og ammed o each ask. In ag icul u e, ML models,
pa icula ly eg ession models, a e widely used o p edic ou comes such as c op yield by
analyzing complex da ase s [
1
,
2
]. These models iden i y ela ionships be ween a iables
(e.g., soil p ope ies, en i onmen al ac o s, o plan cha ac e is ics) and a ge ou comes,
allowing o mo e accu a e and imely p edic ions.
A ecen ad ancemen in ML is Au oma ed Machine Lea ning (Au oML), which au o-
ma es he p ocess o selec ing, uning, and op imizing ML models. Au oML enables he
building o e ec i e p edic i e models by simpli ying he model selec ion and hype pa-
ame e uning p ocess [
3
]. In ou s udy, we used Au oML (PyCa e lib a y) o iden i y
he mos sui able ML models o p edic ing whea yield om UAV-collec ed MS and RGB
image y, enhancing he speed, accu acy, and ep oducibili y o he modeling p ocess. The
in eg a ion o Au oML in yield es ima ion o e s a powe ul app oach o maximize he
u ili y o ag icul u al da a, op imize esou ce alloca ion, and imp o e decision-making in
p ecision ag icul u e.
Unmanned ae ial ehicles (UAVs) ha e expe ienced a su ge in use o cap u ing ae ial
images ac oss nume ous sec o s. Thei applica ion has no ably ad anced in ag icul u e due
o ecen echnological de elopmen s [
4
]. These ad ancemen s ha e enabled he in eg a ion
o complex echnology such as MS and RGB came as in o UAVs, hus solidi ying hei ole
as emo e sensing sys ems in p ecision ag icul u e [5].
Thei p incipal unc ion is o cap u e images a mul iple wa eleng h bands beyond
he isible spec um. Among he mos employed indices a e he No malized Di e ence
Vege a ion Index (NDVI), No malized Di e ence Red Edge (NDRE), G een No malized
Di e ence Vege a ion Index (GNDVI), Lea Chlo ophyll Index (LCI), and Op imized Soil
Adjus ed Vege a ion Index (OSAVI) [6–8].
Beyond hese MS indices, he ole o RGB indices such as G een–Red Ra io Index
(GRRI), G een–Blue Ra io Index (GBRI), Red–Blue Ra io Index (RBRI), Excess G een (ExG),
Colou Index o Vege a ion (CIVE), and Vege a ion Index G een (VIg) should no be unde -
es ima ed [
3
]. While MS indices p o ide insigh s in o speci ic aspec s o c op heal h no
Ag icul u e 2025,15, 1534 3 o 32
isible o he naked eye, RGB indices can p o ide use ul insigh s ha a e mo e isually
in ui i e. They can p o ide da a abou he gene al heal h and igo o he c op based on
he isual colo , and hey can help de ec issues such as wil ing o isible pes s. Mo eo e ,
con empo a y li e a u e emphasizes he applica ion o high- esolu ion hype spec al and
RGB came as o es ima ing abo e-g ound biomass (AGB), which is a signi ican pheno-
ypic index o e alua ing pho osyn hesis capaci y, heal hy g ow h, and es ima ing c op
yield. Fu he insigh s in o his opic can be ound in he wo ks o Yang Liu e al. [9,10].
Despi e p omising esul s in p e ious s udies, many su e om limi ed scale, use o
low- esolu ion sa elli e image y, o na ow c op di e si y. Fo example, some s udies ocus
on suga cane o co n and use da ase s es ic ed o 48–80 small plo s, educing gene aliz-
abili y. In con as , his s udy le e ages UAV-acqui ed high- esolu ion da a ac oss 400 plo s
and i e whea cul i a s, e lec ing he he e ogenei y o Eu opean p oduc ion sys ems.
MS and RGB came as, hanks o hei abili y o cap u e high- esolu ion images ac oss
mul iple spec al bands, including he in a ed, nea -in a ed, ed, g een, and blue ange,
p o ide a weal h o da a. This da a is in aluable o assessing c op heal h, iden i ying
nu ien de iciencies, o acking pes in es a ions. The e o e, UAVs equipped wi h hese
came as ha e become pi o al in c op moni o ing, analysis, and yield es ima ion, which a e
undamen al asks o e icien and e ec i e p ecision ag icul u e. A combina ion o emo e
sensing sys ems and machine-lea ning echniques is a ac ing pa icula a en ion oday,
especially in he es ima ion o c op yields [
11
]. This in eg a ed app oach holds signi ican
p omise o imp o ing he accu acy and e iciency o c op yield p edic ion.
Re . [
12
] in es iga ed ea ly p edic ion o suga cane c op yield using high- esolu ion
MS image y om UAVs and h ee ad anced machine-lea ning echniques: Random Fo -
es Reg ession (RFR), SVR, and Nonlinea Au o eg essi e Exogenous A i icial Neu al
Ne wo k (NARX ANN). The s udy ocused on plo -le el p edic ion and add essed chal-
lenges such as high a ooning capaci y, limi ed high- esolu ion da a, and yield complexi y.
Resul s showed ha ege a ion indices exhibi ed s onge co ela ions wi h c op yield
du ing he middle g ow h s age. NARX ANN ou pe o med o he models wi h an R
2
o
0.96 and he lowes Roo Mean Squa e E o (RMSE) o 4.92 /ha. SVR and RFR showed
simila pe o mance, wi h R
2
alues o 0.52 and 0.48, and RMSE alues o 14.85 /ha and
11.20 /ha, espec i ely.
While his s udy demons a es he po en ial o machine-lea ning app oaches o plo -
le el suga cane yield p edic ion, a limi a ion lies in expe imen al scale, conduc ed o e
48 plo s, as well as he lowe esolu ion o sa elli e-acqui ed image y. Expanding he
expe imen al ield size and using highe - esolu ion image y cap u ed a op imal g ow h
s ages would enhance model accu acy and eliabili y.
Ano he s udy o es ima e co n g ain yield using a neu al ne wo k model based on
MS and RGB ege a ion indices, canopy co e , and plan densi y was conduc ed by [
13
].
The esul s showed high co ela ions be ween he es ima ed and obse ed co n g ain yield.
The a iables wi h he highes ela i e impo ance o yield es ima ion a ied depending
on he s age o c op de elopmen . Fo he ea ly s age (47 days a e sowing), wide dynamic
ange ege a ion index (WDRVI), plan densi y, and canopy co e exhibi ed he highes
co ela ion coe icien and he smalles e o s. A a la e s age (79 days a e sowing), a
combina ion o NDVI, NDRE, WDRVI, ExG, iangula g eenness index (TGI), plan densi y,
and canopy co e p o ided he bes es ima ion o co n g ain yield. The s udy highligh s
he e ec i eness o emo e sensing da a and machine-lea ning echniques o he accu a e
es ima ion o c op yield. While his s udy demons a es he e ec i eness o emo e sensing
da a and machine-lea ning echniques o yield es ima ion, i is limi ed by i s small plo
sizes, wi h each plo con aining only 15–20 plan s and a o al o 80 plo s o e all. Inc easing
Ag icul u e 2025,15, 1534 4 o 32
he numbe and size o plo s, along wi h mo e ex ensi e plan sampling, could u he
enhance model obus ness and gene alizabili y, leading o mo e eliable yield p edic ions.
Howe e , a common limi a ion ac oss hese s udies is he lack o di e se c op ypes
and insu icien es ing ac oss a ying e iliza ion o cul i a -speci ic esponses. The
cu en esea ch add esses hese gaps by applying a wide ange o ege a ion indices o a
he e ogeneous whea da ase , enabling g ea e model adap abili y and obus ness ac oss
eal- ield scena ios.
One o he mos used machine-lea ning sys ems is he PyCa e so wa e [
3
,
14
], which
can also be used o analyzing and in e p e ing MS and RGB indices in he con ex o
yield es ima ion. PyCa e , an open-sou ce Py hon lib a y, simpli ies complex machine-
lea ning asks o da a scien is s and analys s. In he ield o ag icul u e, PyCa e au oma es
yield es ima ion om MS and RGB came a da a h ough pa e n ecogni ion, s eamlining
end- o-end expe imen s.
Simila esea ch using he PyCa e machine-lea ning algo i hm models o es ima e
c op heal h was conduc ed by [
3
]. In he s udy, UAVs equipped wi h MS and RGB came as
we e used o cap u e images o sp ing whea (T i icum aes i um L.). Thei objec i e was o
emo ely es ima e he maximum quan um e iciency o he pho osys em (F
/F
m
), a key
indica o o pho osyn he ic heal h in plan s.
They cons uc ed 51 ege a ion indices and used 26 di e en machine-lea ning al-
go i hms in PyCa e o analyze hese indices. Thei esul s showed s ong co ela ions
be ween mos o he MS and hal o he RGB ege a ion indices wi h F /Fm.
A e compa ing he pe o mance o he algo i hms, he Au oma ic Rele ance De e -
mina ion (ARD) model p o ided he highes accu acy in es ima ing F
/F
m
when using a
combina ion o RGB and MS ege a ion indices. The esea ch unde sco es he po en ial
o using UAVs and machine lea ning o apid and p ecise moni o ing o pho osyn he ic
heal h in c ops, p o iding c i ical echnical suppo o ag icul u e.
Building on his po en ial, he p esen s udy in oduces an app oach o achie ing high
p edic ion accu acy in whea yield modeling by combining UAV-based MS and RGB da a
wi h Au oML. By applying an Au oML ool, 25 machine-lea ning models we e op imized
o assess he po en ial o 65 ege a ion indices o yield es ima ion. This esea ch s ands
ou o i s la ge-scale expe imen al design, which in ol ed di e se ea men s on mul i-
ple whea cul i a s ac oss 400 plo s, ep esen ing condi ions ypical o Eu opean whea
a ie ies. The me hodology and comp ehensi e da a collec ion o e a scalable ame-
wo k o yield p edic ion, ad ancing he in eg a ion o UAV and Au oML echnologies in
p ecision ag icul u e.
In summa y, his s udy builds upon he exis ing body o esea ch while add essing key
limi a ions ela ed o scale, da a esolu ion, c op di e si y, and expe imen al complexi y. I
in oduces a obus and scalable Au oML-based amewo k ha in eg a es MS and RGB
image y ac oss di e se geno ypes and ea men condi ions, aiming o push he bounda ies
o p edic i e accu acy in c op yield es ima ion.
2. Ma e ials and Me hods
The Wo k low Diag am o Whea Yield P edic ion Using UAV-Based Da a and
Machine-Lea ning Models is p esen ed in he Appendix Aas Figu e A1.
2.1. Expe imen al Field Design and Se up
The s udy was pa o a long- e m expe imen conduc ed by he Ins i u e o Field
and Vege able C ops, No i Sad, Voj odina, Se bia. I s p ecise geog aphic coo dina es a e
45
◦
19
′
58.0
′′
N, 19
◦
49
′
53.6
′′
E, and i s ands a an al i ude o 82 m (Figu e 1). The si e was
pa i ioned in o 400 sub-plo s, each spanning 5
×
10 m, me hodically o ganized in o a
Ag icul u e 2025,15, 1534 5 o 32
s uc u ed g id o 20 ×20. The soil a he si e is he domina ing soil ype in he Voj odina
egion, Haplic Che nozem A ic [
15
], and is cha ac e ized as highly e ile (app oxima ely
43% o he o al a able land).
Figu e 1. Geog aphic loca ion o he expe imen al ield.
Fi e dis inc whea cul i a s we e selec ed o he s udy: NS Ig a, NS Rajna, NS
Fu u a, NS Epoha, and NS Obala. The sowing densi y anged be ween 200 and 230 kg/ha,
con ingen upon he speci ic cul i a . C i ically, each cul i a was subjec ed o a di e se
a ay o ea men s, comp ising wen y di e en NPK mine al e ilize combina ions. I is
no ewo hy ha each o hese ea men s was eplica ed ou imes o ensu e obus ness in
he indings.
The expe imen aimed o c ea e a di e se se o condi ions, simila o he na u al
changes seen in a ming ields. This ma ix inco po a ed ou hund ed sub-plo s, each in-
e spe sed wi h one o he i e whea cul i a s, and was u he nuanced by wen y dis inc
NPK ea men a ia ions. This design allowed o a ia ion changes in spec al channels,
closely mimicking eal-wo ld a ming e en s. This design no only accen ua es he s udy’s
p ecision bu also enables he eplica ion o na u ally occu ing ag onomic phenomena in
a con olled se ing. Fo a de ailed b eakdown o NPK ea men combina ions and he
co esponding yields ac oss each whea cul i a , eade s a e di ec ed o Table 1.
Table 1. Comp ehensi e o e iew o NPK ea men combina ions and co esponding yields o each
whea cul i a .
Mine al Fe iliza ion Yield In e als/A e age Yield ( /ha)
Va ian N (kg/ha) P (kg/ha) K (kg/ha) NS Ig a NS Rajna
NS Fu u a
NS Epoha NS Obala
10001.63–2.93
(2.3)
1.41–2.85
(2.26)
1.93–2.76
(2.29)
1.90–2.63
(2.33)
2.02–4.51
(2.97)
2 100 0 0 3.53–5.46
(4.73)
3.11–5.19
(4.53)
3.27–5.00
(4.32)
3.67–5.20
(4.59)
4.34–5.67
(5.15)

Ag icul u e 2025,15, 1534 6 o 32
Table 1. Con .
Mine al Fe iliza ion Yield In e als/A e age Yield ( /ha)
Va ian N (kg/ha) P (kg/ha) K (kg/ha) NS Ig a NS Rajna
NS Fu u a
NS Epoha NS Obala
3 0 100 0 1.92–3.25
(2.53)
1.82–2.88
(2.46)
2.25–2.97
(2.60)
2.71–3.15
(2.96)
3.04–4.42
(3.63)
4 0 0 100 1.62–2.74
(2.21)
1.96–2.57
(2.16)
1.72–5.34
(2.97)
1.93–2.38
(2.22)
1.94–3.91
(2.66)
5 100 100 0 4.85–5.86
(5.38)
5.06–5.53
(5.34)
5.07–5.42
(5.25)
5.37–5.62
(5.48)
5.07–5.44
(5.29)
6 100 0 100 4.24–5.54
(4.82)
4.15–5.18
(4.72)
4.27–4.81
(4.49)
4.29–5.11
(4.73)
4.83–5.68
(5.16)
7 0 100 100 2.19–3.19
(2.72)
1.99–3.34
(2.69)
1.43–3.26
(2.47)
2.20–3.25
(2.81)
2.16–5.37
(3.70)
8 50 50 50 4.36–5.18
(4.83)
4.31–5.07
(4.64)
4.39–4.96
(4.67)
4.48–4.93
(4.66)
4.59–6.32
(5.23)
9 50 100 50 4.63–5.26
(5.03)
4.44–5.25
(4.91)
4.77–5.38
(5.06)
4.75–5.01
(4.88)
5.22–6.28
(5.54)
10 50 100 100 4.54–5.34
(4.91)
4.56–5.26
(4.94)
4.88–5.30
(5.13)
4.50–5.48
(4.97)
5.06–5.95
(5.42)
11 100 50 50 5.28–5.72
(5.46)
5.35–5.90
(5.62)
4.88–5.64
(5.35)
5.34–5.62
(5.48)
5.30–6.16
(5.62)
12 100 100 50 5.46–5.88
(5.65)
5.21–5.80
(5.53)
5.27–5.77
(5.61)
5.64–5.68
(5.66)
5.18–6.19
(5.64)
13 100 100 100 5.50–6.12
(5.73)
5.45–6.00
(5.82)
5.41–5.82
(5.66)
5.38–5.75
(5.52)
5.24–6.22
(5.67)
14 100 150 50 5.29–6.05
(5.70)
5.36–6.19
(5.79)
5.39–6.20
(5.78)
5.40–6.09
(5.73)
5.16–6.03
(5.50)
15 100 150 150 5.65–6.14
(5.89)
5.43–6.14
(5.86)
5.55–6.04
(5.81)
5.46–5.82
(5.68)
5.18–6.17
(5.62)
16 150 50 50 5.20–5.78
(5.38)
5.08–6.05
(5.63)
5.18–5.80
(5.47)
4.65–5.65
(5.12)
5.03–6.33
(5.46)
17 150 100 50 5.06–6.14
(5.64)
4.73–6.20
(5.48)
4.97–5.96
(5.49)
5.49–6.03
(5.74)
5.19–5.95
(5.52)
18 150 100 100 5.17–5.75
(5.50)
4.30–5.81
(5.34)
4.64–5.62
(5.36)
5.26–6.01
(5.67)
5.39–5.76
(5.51)
19 150 150 100 5.38–5.83
(5.64)
4.57–5.66
(5.19)
5.27–5.70
(5.50)
5.49–5.72
(5.65)
5.12–6.24
(5.65)
20 150 150 150 5.22–5.97
(5.46)
4.28–5.68
(4.92)
5.18–5.53
(5.28)
5.46–5.83
(5.69)
5.22–6.42
(5.65)
2.2. Unmanned Ae ial Vehicle (UAV) Da a Acquisi ion
Fo he pu poses o da a acquisi ion, high- esolu ion pho og aphic images we e cap-
u ed on he ollowing da es: 9 May 2022, du ing he Heading phase, 20 May 2022, du ing
he Flowe ing phase, and 6 June 2022, du ing he G ain illing phase. The DJI P4 Mul-
ispec al UAV, equipped wi h an MS came a, was u ilized o his pu pose. To ensu e
op imal ligh ing condi ions and minimize po en ial senso disc epancies, he ae ial su -
eys we e conduc ed unde clea sky condi ions, speci ically be ween 12:00 and 13:00 h,
co esponding o he local sola noon.
Ag icul u e 2025,15, 1534 7 o 32
To ensu e da a consis ency and ligh s abili y, all UAV missions we e conduc ed
unde wind speeds below 3 m/s, and iden ical ligh pa ame e s we e main ained ac oss
all sessions, including al i ude (30 m AGL), speed (3 m/s), and image o e lap (75% bo h
longi udinally and la e ally). An au onomous waypoin -based ligh plan was used in
each session, allowing o p ecise eplica ion o ligh pa hs. P io o e e y mission, he
UAV sys em unde wen a p e- ligh checklis o ensu e p ope senso calib a ion, ba e y
condi ion, and GPS connec i i y. Addi ionally, he same pilo ope a ed all missions o
educe a iabili y in execu ion.
The DJI P4 Mul ispec al, a quad o o UAV (DJI, Shenzhen, China), was equipped
wi h an in eg a ed RGB came a and i e dis inc monoch oma ic senso s. These senso s
encompass blue (B), g een (G), ed (R), ed edge (RE), and nea -in a ed (NIR) bands,
each ailo ed o speci ic spec al egions. Le e aging he da a om he collec ed MS and
RGB images, he s udy de i ed a se o 65 indices. This encompassed 40 MS and 25 RGB
indices, o e ing a holis ic pe spec i e on he heal h and g ow h dynamics o he c op. A
comp ehensi e speci ica ion o hese monoch oma ic senso s can be ound in Table 2.
Table 2. Pa ame e s o he monoch oma ic senso s o he mul ispec al came a.
Band Cen e Wa eleng h/nm Bandwid h/nm
Blue (B) 450 16
G een (G) 560 16
Red (R) 650 16
Red Edge (RE) 730 16
Nea -in a ed (NIR) 840 26
All ligh s we e planned and execu ed using he DJI GS P o so wa e (Ve sion: V2.0
2018.11, DJI, Shenzhen, China), ensu ing consis en na iga ion and image cap u e pa ame-
e s. The calib a ion o he senso s was e i ied p io o akeo using he in eg a ed sunligh
senso o no malize ligh in ensi y, ensu ing eliable spec al eadings ac oss di e en imes
and da es.
When deployed a an ope a ional al i ude o 30 m, he UAV achie ed a spa ial esolu-
ion o 1.6 cm pe pixel. To asce ain he d one’s geospa ial accu acy du ing i s ligh , we
employed he D-RTK 2 high-p ecision mobile s a ion (DJI, Shenzhen, China). The came a’s
exposu e se ing was calib a ed o 2 s wi h speci ied ligh ma gins se a 5 m. The image y
was sys ema ically cap u ed, wi h each mission co e ing an a ea o 2.7 hec a es.
Du ing ou s udy, high- esolu ion imaging gene a ed a subs an ial olume o da a,
culmina ing in a o al digi al oo p in o 36.484 GB o aw da a ac oss h ee sepa a e
imaging sessions co e ing a combined a ea o 8.1 hec a es. This yielded a digi iza ion
oo p in o app oxima ely 4.504 GB/ha pe session. Each session en ailed he acquisi ion
o mul ispec al da a ac oss i e spec al channels: blue, ed, g een, ed-edge, and nea -
in a ed, each con ibu ing an equal pa i ion o he o e all da a olume. Consequen ly,
he digi iza ion oo p in o each spec al channel amoun ed o oughly 0.901 GB/ha
pe session.
Fu he mo e, o homosaic images we e c ea ed o each spec al channel in each o he
h ee sessions, con ibu ing an addi ional 7.898 GB in o al o he digi al oo p in . When
his is no malized ac oss he o al su eyed a ea, i esul s in an added digi al oo p in o
app oxima ely 0.975 GB/ha o he o homosaic images.
Upon summing up he o al da a olume o all imaging sessions (36.484 GB) and he
o homosaic images (7.898 GB), a cumula i e digi al oo p in o 44.382 GB was calcula ed.
Ag icul u e 2025,15, 1534 8 o 32
When his o al digi al oo p in is no malized o e he su eyed a ea o 8.1 hec a es, an
o e all digi iza ion oo p in o app oxima ely 5.479 GB pe hec a e was ob ained.
In o al, he e we e 9375 aw images cap u ed ac oss all sessions, wi h an e en dis ibu-
ion ac oss he i e spec al channels, and he o e all digi iza ion oo p in pe session and
pe channel encompasses da a om hese indi idual images as well as om he compiled
o homosaic images.
The UAV’s ligh plan was algo i hmically gene a ed using he DJI GS P o so wa e
sui e (DJI, Shenzhen, China). To ensu e he UAV’s op imal na iga ional ajec o y, a sola
adia ion spec al senso was used. This acili a ed adap i e adjus men s o pho og aphic
pa ame e s such as ISO, whi e balance, and shu e speed based on eal- ime sola i adiance
da a, elimina ing he nuances o manual calib a ions. The d one could main ain ligh o
25 o 30 min on a single ba e y cycle.
2.3. Da a P ocessing
Upon success ul da a e ie al using he DJI P4 Mul ispec al d one, Pix4D (Pix4Dmap-
pe En e p ise 4.5.6, 2020, Pix4D, P illy, Swi ze land) so wa e o a p ocessing me hodology
was used, as delinea ed by [
16
]. This mul i ace ed wo k low en ailed he cons uc ion o an
o homosaic ep esen a ion, aligning and amalgama ing indi idual ames o a chi ec a
uni ied, geome ically cong uen depic ion o he expe imen al ac . O homosaic map-
pings o he en i e RGB and MS bandwid hs we e subsequen ly syn hesized, culmina ing
in an ensemble o GeoTi iles. These geo e e enced cons uc s no only summa ized
he aw image da a bu also p o ided ich me ada a de ailing he spa ial o ien a ion and
geoloca ion o each cons i uen pixel.
The p ep ocessing s eps included adiome ic co ec ion based on eal- ime sunligh
in ensi y measu emen s om he onboa d sunligh senso , ensu ing e lec ance no mal-
iza ion ac oss all spec al bands. Geome ic co ec ion was achie ed using he D-RTK
2 high-p ecision GNSS base s a ion, enabling accu a e alignmen o image coo dina es.
Fu he mo e, noise il e ing and shadow educ ion we e au oma ically pe o med wi hin
he Pix4D pipeline, based on poin cloud quali y and ex u e a ia ion.
In he subsequen phase, he syn hesized GeoTi da ase s we e in eg a ed in o he
A cGIS (A cGIS-A cMap 10.8.2, 2021, Es i Inc., 380 New Yo k S , Redlands, CA, USA)
pla o m o a g anula analy ical exe cise, inspi ed by me hodologies p esen ed by [
17
]. A
salien ea u e o his explo a ion was he de i a ion o nume ical me ics o he RGB and
MS spec a ac oss each delinea ed plo . Addi ionally, he ex ac ion o s a is ical desc ip o s
o each dema ca ed polygonal segmen wi hin he expe imen al expanse was conduc ed.
2.4. De elopmen o RGB and MS Indices Le e aging Ex ac ed Spec al Da a
This s udy dissec ed and analyzed he nume ical ep esen a ions associa ed wi h
he in ensi ies obse ed wi hin he ed, blue, and g een spec al sec ions, supplemen ed
by da a om he ed-edge domain and he nea -in a ed egion. A e ex ac ing hese
spec al da a, equa ions o RGB and MS indices we e de i ed, as speci ically ou lined
in
Tables A1 and A2, in he Appendix A
, based on he me hodologies p esen ed in he
scien i ic pape by [
3
]. The applica ion o such indices p o ides a p o ound comp ehension
o he spec al cha ac e is ics o he analyzed e ain, elucida ing de ails abou hei in insic
physical and op ical p ope ies. A he speci ic s ages o de elopmen and wi h he plan ing
densi y employed, he canopy o he whea plan s is closed such ha soil isibili y h ough
he canopy is almos nonexis en . The e o e, backg ound noise such as soil and shadows
was minimal and did no signi ican ly impac he analysis. This dense canopy ensu es ha
he measu emen s a e p ima ily om he whea plan s hemsel es, p o iding accu a e
canopy in o ma ion.
Ag icul u e 2025,15, 1534 9 o 32
2.5. Applying he PyCa e Lib a y o Yield P edic ion
PyCa e is an open-sou ce, high-le el machine-lea ning lib a y ha o e s e icien da a
p epa a ion and modeling h ough a simple and use - iendly API [
18
]. The key s ep o his
esea ch is applying he PyCa e so wa e on MS and RGB indices ob ained by using UAVs
o yield es ima ion. Fo ha pu pose, he co ela ion coe icien be ween he collec ed eg-
e a ion indices and he ac ual yield was examined. This s ep was necessa y o s a is ically
es ablish he ela ionship be ween he 65 calcula ed ege a ion indices and he ac ual yield.
A e ha , he no maliza ion o 65 nume ical ea u es o he da ase was pe o med using
he z-sco e me hod. This s ep is c ucial o machine-lea ning algo i hms sensi i e o ea u e
scales, as i ans o ms each ea u e o ha e a mean o ze o and a s anda d de ia ion o one.
No maliza ion o he ea u es esul ed in a quicke con e gence o he algo i hm, ul ima ely
leading o mo e gene alizable and obus p edic ions. These no malized indices we e hen
ma ched wi h co esponding yield da a collec ed manually om he ield. This app oach
led o he es ablishmen o a da abase con aining 400 obse a ions, each encompassing
66 ea u e a iables, including 65 ege a ion indices and whea yield, which was employed
in his esea ch. Upon ini ializa ion, a unique session iden i ie (Session ID: 4797) was
gene a ed o acili a e he ep oducibili y o he expe imen , in acco dance wi h good scien-
i ic p ac ice. Be o e aining, he en i e se o 65 ege a ion indices was e ained wi hou
applying au oma ic ea u e selec ion o dimensionali y educ ion echniques. This decision
was made o p ese e he ull spec al in o ma ion a ailable in he da ase , allowing he
machine-lea ning algo i hms o independen ly e alua e he ele ance o each index du ing
model i ing. Since he PyCa e lib a y in e nally handles algo i hm-speci ic egula iza ion
and weigh assignmen , models such as Lasso, Ridge, and ee-based ensembles inhe en ly
pe o m implici ea u e p io i iza ion du ing aining. The da a was di ided in o a aining
se and a es se , wi h 280 and 120 samples (0.7/0.3 a io), espec i ely. This pa i ioning
was implemen ed o allow o obus aining and e alua ion o machine-lea ning models.
The a iable a ge ed o eg ession was deno ed as ‘Yield’, which ep esen s he whea
yield ha he expe imen aims o p edic . Using machine-lea ning algo i hms, he so wa e
lea ns how o ecognize pa e ns and ela ionships be ween MS and RGB indices and yield
da a. Th ough an i e a i e p ocess, he so wa e is op imized o achie e as accu a e a yield
es ima ion as possible.
A 10- old c oss- alida ion app oach was implemen ed o e alua e he models’ pe o -
mance, using he KFold algo i hm exclusi ely on he aining se . In his p ocess, each old
was used once as a alida ion se while he k-1 emaining olds we e used o he aining.
This alida ion echnique p o ides a obus way o assess he model’s pe o mance wi hin
he aining se , minimizing he bias and a iance associa ed wi h a single andom pa i ion
o his subse . The buil -in ‘ une model’ unc ion o PyCa e used in ou s udy enables au o-
ma ed hype pa ame e uning on he aining olds, educing manual e o and expe ise
equi ed o op imize model pe o mance wi hin he aining da a. This p ocess ensu es
ha he model is no only op imized bu also alida ed in a igo ous manne be o e being
inally e alua ed on a sepa a e es se , which is c i ical in scien i ic s udies whe e op imum
model se ings a e essen ial and need o be alida ed e ec i ely [19].
The uning p ocess u ilizes g id sea ch and andom sea ch s a egies in e nally, de-
pending on he algo i hm, and selec s hype pa ame e s based on pe o mance me ics such
as R
2
and RMSE ac oss he c oss- alida ion olds. All op imiza ion s eps we e au oma ed
and ep oducible, con ibu ing o model s abili y.
A e comple ing he lea ning p ocess, PyCa e so wa e (Ve sion: 3.0, To on o, ON,
Canada) can apply he lea ned models o new MS and RGB indices da a o es ima e c op
yields on ag icul u al c op ields.
Ag icul u e 2025,15, 1534 16 o 32
6 June 2022 SVR Model Analysis:
•
Pe o mance Me ics: Fo his da e, he model p oduced a aining R
2
o 0.937 and a
es R
2
o 0.916. Al hough hese numbe s a e somewha lowe han hose om he
p e ious da es, hey s ill indica e s ong p edic i e pe o mance. Wi h an explana ion
o o e 93% o he da a a iance, he model emains aluable o ag icul u al planning
and op imiza ion based on i s o ecas s.
•
Residual Plo Analysis: The esiduals, al hough mos ly su ounding he ze o line,
showcase a mo e dispe sed pa e n as compa ed o he SVR model e alua ed on 9
May 2022. This indica es a sligh ly lesse p edic ion accu acy o his speci ic da ase .
•
Dis ibu ion Analysis: The dis ibu ion o esiduals on he igh displays a nea -no mal
pa e n, albei wi h a hin o igh skewness, poin ing owa ds mino p edic ion biases.
While indi idual model diagnos ics o each da e p o ide g anula insigh , compa ing
esidual plo s and dis ibu ion shapes e eals b oade ends. Fo example, he inc ease
in esidual sp ead om 9 May o 6 June e lec s g owing p edic ion unce ain y as he
whea ma u es. This could be linked o inc easing canopy closu e and spec al sa u a ion
in la e s ages, educing he dis inc i eness o ege a ion indices. Addi ionally, he shi
om nea ly no mal esidual dis ibu ions o sligh ly skewed o bimodal o ms sugges s
mo e complex e o s uc u es in la e measu emen s, possibly due o ield he e ogenei y
o wea he a iabili y. These insigh s imply ha while eg ession models pe o m well
h oughou he season, hei p ecision may be highes du ing he heading o lowe ing
phases, as cap u ed in he ea lie da es.
Conside ing he eg ession models’ pe o mance on h ee dis inc e alua ion da es,
he diag ams illus a ing hei capabili ies a e p esen ed in Figu e 3.
9 May 2022—SVR Model Analysis:
•
Pe o mance Me ics: The SVR model on his da e achie ed an R
2
alue o 0.947. In
he con ex o whea yield p edic ions, his high R
2
shows he model’s accu acy. I
indica es ha he model can e ec i ely cap u e mos o he da a a iance, making i
eliable o whea yield p edic ions.
•
Diag am Insigh : The plo po ays p edic ed alues agains ue alues. A close
alignmen o poin s wi h he iden i y line indica es be e p edic ions. While mos da a
poin s align wi h he “bes i ” line, sligh de ia ions highligh he model’s a eas o
po en ial imp o emen .
20 May 2022—MLP Reg esso Model Analysis:
•
Pe o mance Me ics: The MLP Reg esso on his da e eco ded an R
2
o 0.938.
E en hough ma ginally lowe han he SVR model on 9 May 2022, i emains high
in accu acy.
•
Diag am Insigh : The plo ed da a poin s la gely ollow he iden i y line, sugges ing
a good ma ch be ween p edic ed and ac ual alues. Howe e , a ew da a poin s
di e ge, sugges ing a eas whe e he model migh ha e aced challenges, possibly due
o in ica e pa e ns o ou lie s in he da ase .
6 June 2022—SVR Model Analysis:
•
Pe o mance Me ics: On his da e, he SVR model epo ed an R
2
o 0.916. While
sligh ly lowe han p e ious esul s, an R
2
abo e 0.9 in ag icul u e s ill highligh s a
s ong p edic i e capabili y.
•
Diag am Insigh : Mos da a poin s a e nea he iden i y line, showing he model’s
consis ency in p edic ions. The sca e , al hough sligh ly mo e p onounced com-
pa ed o he e alua ion o 9 May 2022, is s ill wi hin accep able bounds o whea
yield o ecas ing.

Ag icul u e 2025,15, 1534 17 o 32
(a) (b)
(c)
Figu e 3. Compa a i e isualiza ion o p edic ion e o s ac oss eg ession models: (a) da a o 9 May
2022; (b) da a o 20 May 2022; (c) da a o 6 June 2022.
In summa y, bo h he esidual analysis and p edic ed- s-ac ual plo s con i m he
s abili y o model pe o mance ac oss all da es, while also e ealing sub le a ia ions ha
a e ele an o p ac ical implemen a ion. The sligh ly declining accu acy and inc easing
esidual dispe sion o e ime unde sco e he impo ance o ea ly-season da a collec ion
o maximizing p edic ion p ecision. These indings suppo he in eg a ion o empo al
op imiza ion in UAV-based moni o ing wo k lows.
Fu he mo e, he obse ed luc ua ions in model ankings ac oss da es can also be
a ibu ed o he in insic sensi i i y o indi idual algo i hms o he unde lying da a dis i-
bu ion and noise pa e ns. Fo ins ance, Suppo Vec o Reg ession (SVR), which elies on
op imal ma gin bounda ies, may pe o m excep ionally well when he da a exhibi s linea
o quasi-linea ends wi h minimal noise, as obse ed on 9 May and 6 June. Howe e , on
20 May, whe e da a cha ac e is ics may ha e been mo e nonlinea o a ec ed by sub le
ou lie s, he MLP Reg esso , known o i s capabili y o cap u e complex pa e ns h ough
neu al laye s, ou pe o med SVR. These di e ences highligh he impo ance o aligning
Ag icul u e 2025,15, 1534 18 o 32
model selec ion wi h da a-speci ic ai s, ensu ing he obus ness o p edic i e analy ics in
ag icul u al scena ios.
The esul s om he speci ied e alua ion da es p o ide a nuanced unde s anding o
he di e en eg ession models’ capabili ies. While each model showed high p edic i e
powe , sub le di e ences in pe o mance me ics and isual insigh s unde line he im-
po ance o con inuous e alua ion. I is e iden ha , while all models o e high alue in
p edic ing whea yield, hei e ec i eness can a y depending on he da a’s cha ac e is ics
and complexi ies. This igo ous assessmen unde sco es he signi icance o selec ing he
igh model o speci ic da ase s and he need o ongoing alida ion o ensu e op imal
pe o mance in he ield o whea yield p edic ion.
4. Discussion
The indings om his s udy can o e no el insigh s in o he applica ion o machine
lea ning o p edic ing whea yields [
19
]. The ollowing sec ions b eak down he discussions
based on he de i ed esul s.
4.1. The Po en ial o Spec al Indices o Yield P edic ion
The esul s o he co ela ion coe icien un eil he ela ionship be ween a ious indices
and whea yield. The ocus he e is no only on he s eng h o he co ela ion bu also on
he ype (posi i e o nega i e) and he consis ency o e ime.
The MS indices show a consis en ly high co ela ion wi h whea yield ac oss he h ee
da es. NDVI, a widely ecognized index o ege a ion igo , shows consis en ly high
co ela ion, unde sco ing i s eliabili y in p edic ing whea yields [
20
]. Blue No malized
Di e ence Vege a ion Index (BNDVI) and S uc u e Insensi i e Pigmen Index (SIPI), pa -
icula ly o he 9 May 2022 measu emen , display s ikingly high posi i e co ela ions,
sugges ing hei po en ial u ili y in p edic ing whea yields. The almos iden ical co ela-
ion coe icien o hese indices sugges s hey cap u e simila a iabili y in he da a, which
migh be indica i e o chlo ophyll con en o gene al plan heal h [
21
]. Howe e , i is
c ucial o no e he changing na u e o hese co ela ions o e di e en da es. The indices
showed he highes a e age co ela ion on 9 May 2022 and 20 May 2022, indica ing a
possible ela ionship wi h a speci ic g ow h s age o whea . These high co ela ions migh
co espond o pe iods when he whea plan s a e a hei heading ege a i e s age, o when
he g ain- illing is aking place, emphasizing he signi icance o he iming in u ilizing hese
indices o yield p edic ion [22,23].
On he o he hand, he co ela ion coe icien s o he RGB indices seem o be mo e
a ied and gene ally weake compa ed o he MS indices. Modi ied G een–Red Vege a ion
Index (MGRVI) on 9 May 2022 and Colo In ensi y (INT) on 20 May 2022 s ood ou wi h
hei s ong posi i e and nega i e co ela ions, espec i ely. In iguingly, he e was a
ma ked dec ease in he absolu e a e age alue o he co ela ion coe icien om 0.83 o
0.78 du ing he ini ial wo da es, culmina ing in a me e 0.40 by 6 June 2022 [
24
]. This
decline can po en ially be asc ibed o he physiological shi s in pigmen composi ion as he
whea unde goes ma u a ion p ocesses [
25
]. The dynamism o hese pigmen al e a ions
h oughou he de elopmen al s ages is likely ins umen al in he obse ed diminishmen
o RGB index alues by 6 June 2022 [26].
D awing om hese esul s, he selec ion o ea u es o machine-lea ning models
dedica ed o whea yield p edic ion becomes pa amoun . Indices wi h consis en ly high
co ela ion coe icien s, such as BNDVI, SIPI, and Simple Ra io Red/NIR Ra io Vege a ion-
Index (ISR) om he MS indices, should be p io i ized in model aining [
27
]. Thei
eliabili y sugges s ha hey encapsula e i al in o ma ion ela ed o whea g ow h and, by
ex ension, yield [
28
]. Con e sely, while RGB indices o e aluable insigh s, hei inclusion
Ag icul u e 2025,15, 1534 19 o 32
should be app oached wi h cau ion, especially conside ing hei luc ua ing co ela ions
o e ime. None heless, hey should no be en i ely dismissed as hey migh enhance he
model’s p edic i e capabili y in conjunc ion wi h o he indices.
4.2. Implica ions o Machine-Lea ning Models
The analysis using PyCa e s ands ou o i s capabili y o au oma ically ine- une
hype pa ame e s o 25 di e en machine-lea ning models, simpli ying he p ocess o
iden i ying he mos sui able model o a gi en da ase , as s a ed by [
3
,
19
]. PyCa e
highligh ed ha he SVR model was especially p o icien in p edic ing whea yield o 9
May 2022 and 6 June 2022, wi h no able R
2
alues o 0.95 and 0.91, and RMSEs o 0.26
and 0.33 /ha, espec i ely. This high coe icien o de e mina ion sugges s ha he SVR
model can explain a signi ican p opo ion o he a iabili y in he whea yield o hese
speci ic da es. Meanwhile, o 20 May 2022, he MLP Reg esso (Neu al Ne wo k) s ood
ou wi h an R
2
o 0.94 and an RMSE o 0.28 /ha, indica ing i s capabili y o model he
da ase e ec i ely o ha da e.
The esul s o his s udy, wi h signi ican ly highe p ecision, likely s em om he
comp ehensi e na u e o he expe imen al se up. A di e se da ase comp ising 400 dis inc
expe imen al plo s was u ilized, p o iding b oad a ia ion and ichness o da a. This
ex ensi e da ase acili a ed he e ec i e applica ion o machine-lea ning models, ensu ing
a high deg ee o accu acy in yield p edic ions. The use o a la ge numbe o ege a ion
indices and he applica ion o 25 di e en machine-lea ning models helped in p ecisely
classi ying ma hema ical models by accu acy c i e ia.
The s udy [
28
] also ocused on p edic ing whea yield using UAV image y du ing
he same ege a i e pe iod as his esea ch. They epo ed ha , like hese indings, he
SVR model and he Deep Neu al Ne wo k (DNN) model we e among he mos e ec i e
o yield p edic ion. Howe e , hei app oach u ilized a smalle se o ege a i e indices
(10 RGB and 16 MS indices) compa ed o his s udy. This limi a ion in he ange o indices
may con ibu e o he gene ally lowe p ecision o hei models, wi h he SVR model
achie ing an R
2
anging om 0.502 o 0.666, and he DNN model anging om 0.489 o
0.670 in e ms o R
2
. Impo an ly, e . [
2
] emphasized ha he a ia ion in R
2
alues wi hin
hei models is di ec ly linked o he inco po a ion o a mo e ex ensi e a ay o ege a i e
indices, sugges ing ha a combina ion o bo h RGB and MS indices yields a mo e accu a e
model compa ed o using ei he RGB o MS indices in isola ion. Re . [
29
] no ed a signi ican
co ela ion be ween NDVI and ea ly yield p edic ion o win e whea , wi h R
2
anging
om 0.69 o 0.90 o di e en a ie ies, ein o cing he impo ance o ege a ion indices
in yield p edic ion. Re . [
2
] combined he Ag icul u al P oduc ion Sys ems Simula o
(APSIM)—simula ed biomass wi h ex eme clima ic condi ions and ege a ion indices
like NDVI and S anda dized P ecipi a ion E apo anspi a ion Index (SPEI) in a hyb id
app oach using Random Fo es (RF) and eg ession models. Thei indings unde line
he c i ical ole o adap ing models o di e en en i onmen al condi ions, pa icula ly
highligh ing d ough as a signi ican dis up o o yield p edic ions. Re . [
30
] demons a ed
ha deep-lea ning models like Con olu ional Neu al Ne wo k (CNN) and Long Sho -Te m
Memo y (LSTM) a e highly e ec i e in p edic ing c op yields, sugges ing he po en ial
o he me hodology applied in his s udy o inco po a e hese models o mo e obus
p edic ions. Compa a i ely, e . [
31
] showed ha machine-lea ning me hods, pa icula ly
when in eg a ing clima ic and sa elli e da a, ou pe o m adi ional eg ession echniques
in whea yield p edic ion. Thei use o Enhanced Vege a ion Index (EVI) p o ided be e
esul s compa ed o Sun-Induced Fluo escence (SIF) due o lowe inhe en noise, wi h
op imal p edic i e capabili y achie ed app oxima ely wo mon hs be o e whea ma u i y.
This aligns wi h he app oach used in his s udy o le e aging a wide ange o indices,
Ag icul u e 2025,15, 1534 20 o 32
including BNDVI, SIPI, and ISR, which ha e demons a ed s ong co ela ions wi h yield
and con ibu ed o he high accu acy o he models. Fu he mo e, e . [
1
] indica ed ha
Pa ial-Leas -Squa es Reg ession (PLSR) achie ed he mos p ecise esul s using bo h
spec al indices and plan heigh da a, highligh ing he ad an age o PLSR in in e p e ing
hype spec al da a o yield es ima ion. This insigh sugges s ha inco po a ing plan
s uc u al in o ma ion alongside spec al da a could enhance model accu acy. Re . [
32
],
who employed UAVs equipped wi h MS and he mal in a ed came as in a s udy on win e
whea , achie ed he bes esul s using a combina ion o LSTM neu al ne wo ks and RF
wi h an R
2
o 0.78 and RMSE o 0.68 /ha. Re . [
33
] demons a ed ha machine-lea ning
models like Suppo Vec o Machine (SVM), RF, AdaBoos , and DNN ou pe o med linea
eg ession echniques o whea yield p edic ion in he Uni ed S a es. Pa icula ly, AdaBoos
achie ed an R
2
o 0.86 and RMSE o 0.51 /ha, showcasing he e ec i eness o combining
a ious da a sou ces o yield o ecas ing up o 2.5 mon hs be o e ha es . Finally, e . [
34
]
highligh ed he e iciency o CNNs in p edic ing whea yield in Ge many wi h an R
2
o 0.78, unde sco ing he applicabili y o deep-lea ning models in di e se geog aphic
con ex s. While hei indings e lec he po en ial o ad anced machine-lea ning models
in yield p edic ion, he lowe R
2
alues compa ed o he esul s o his s udy highligh
he e ec i eness o using an ex ensi e da ase and a b oad ange o indices, as well as a
comp ehensi e expe imen al design.
Fu he mo e, when compa ed o p e ious s udies in he domain o UAV-based yield
p edic ion, he models de eloped in his esea ch demons a e no ably supe io p edic i e
pe o mance, pa icula ly in e ms o R
2
and RMSE alues. P io esea ch ypically epo ed
R2 alues anging om 0.50 o 0.90, depending on ac o s such as c op ype, phenological
s age, and he spec al da a sou ces u ilized.
The excep ionally high accu acy achie ed in his s udy—exceeding an R
2
o 0.94 and
RMSE below 0.30 /ha—can be p ima ily a ibu ed o se e al key me hodological s eng hs.
Fi s , he use o a la ge and di e se da ase encompassing 400 expe imen al plo s enabled a
b oad ep esen a ion o yield a iabili y. Second, he in eg a ion o a comp ehensi e se o
ege a ion indices, including bo h RGB and mul ispec al (MS) indices, allowed o a mo e
de ailed and nuanced modeling o c op biophysical cha ac e is ics. Thi d, he consis en
applica ion o 25 di e en machine-lea ning algo i hms, ollowed by pe o mance-based
model selec ion, ensu ed bo h obus op imiza ion and ai compa a i e e alua ion.
Unlike many ea lie s udies ha ocused on a na ow empo al window o speci ic
phenological phases, his esea ch assessed model pe o mance ac oss mul iple key g ow h
s ages. These me hodological ad an ages collec i ely p o ided a s ong amewo k o min-
imizing bias and o e i ing, he eby esul ing in mo e gene alizable and eliable models.
This s udy clea ly demons a es ha p ecision and ep oducibili y in yield p edic ion
can be signi ican ly enhanced when spec al di e si y, imely measu emen s, and au oma ed
modeling amewo ks a e sys ema ically in eg a ed. The b oade empo al assessmen
u he con ibu es o he obus ness o he esul s, ein o cing his esea ch’s con ibu ion
o he expanding ield o UAV-based yield p edic ion.
4.3. Limi a ions and Fu u e Scope
This s udy accen ua es he impo ance o unde s anding whea yield a iabili y and
ha nessing he powe o spec al indices o i s p edic ion. By le e aging he insigh s
de i ed, machine-lea ning models can be op imized o p edic ing whea yields wi h
enhanced p ecision [
27
]. While ce ain indices p o e mo e consis en and eliable, a holis ic
app oach ha conside s bo h he s eng hs and limi a ions o each index is pi o al o
ad ancing he ag icul u al domain h ough echnology. Such insigh s no only p opel he
Ag icul u e 2025,15, 1534 21 o 32
scien i ic unde s anding o wa d bu also p omise angible bene i s o he ag icul u al
communi y, ensu ing ood secu i y and sus ainabili y in he long e m [33].
While his s udy achie ed high accu acy in whea yield p edic ion using MS UAV
da a, he e is s ill a need o u he esea ch o enhance he obus ness and gene alizabili y
o hese models. Re s. [
9
,
10
] demons a ed in hei wo ks he e ec i eness o combining a
successi e p ojec ions algo i hm (SPA) wi h an LSTM o imp o ing he p ecision o abo e-
g ound biomass es ima ion. This app oach no only helped in iden i ying he mos ele an
spec al ea u es bu also in cap u ing he empo al dynamics o c op g ow h ac oss di e -
en phenological s ages. By in eg a ing hese ad anced me hodologies, u u e s udies could
add ess cu en limi a ions and imp o e he adap abili y o whea yield p edic ion models
o a ying en i onmen al condi ions and c op managemen p ac ices. Inco po a ing SPA
and LSTM echniques wi h hype spec al da a, as exempli ied by Liu e al., could po en ially
lead o e en mo e accu a e and eliable p edic ions, ensu ing be e esou ce alloca ion and
managemen in ag icul u al sys ems [
35
,
36
]. Ano he limi a ion o his s udy is i s eliance
solely on spec al a iables, which, while aluable, may no cap u e he ull complexi y
o ac o s a ec ing whea yield. Fu u e esea ch should conside in eg a ing addi ional
da a ypes, such as en i onmen al and ag onomic a iables, including p ecipi a ion le els,
cumula i e empe a u e sums, and soil composi ion, o imp o e he obus ness o yield
p edic ions. Addi ionally, his s udy ocuses on Eu opean whea a ie ies, limi ing he gen-
e alizabili y o indings o o he egions wi h di e en whea cul i a s and en i onmen al
condi ions. To push he bounda ies o cu en me hodologies, u u e esea ch could explo e
he in eg a ion o eal- ime UAV da a s eams wi h edge-compu ing sys ems o in- ield
yield o ecas ing. The inco po a ion o ede a ed lea ning app oaches may also enable col-
labo a i e model aining ac oss geog aphically dis ibu ed a ms wi hou comp omising
da a p i acy. Fu he mo e, he usion o spec al da a wi h eme ging echnologies such as
soil heal h senso s, au onomous g ound obo s, and high- esolu ion sa elli e cons ella ions
could unlock new on ie s in p ecision ag icul u e. Adop ing such o wa d-looking, mul-
idisciplina y s a egies would align u u e esea ch wi h global ends in sma a ming
and ag icul u al digi aliza ion. Inco po a ing di e se whea a ie ies, along wi h clima e
and soil da a, would help c ea e a mo e adap able model sui ed o a b oade ange o
condi ions and managemen p ac ices, he eby enhancing he applicabili y and p ecision o
yield p edic ions ac oss a ied ag icul u al se ings.
Fu he mo e, ce ain limi a ions s em om po en ial inconsis encies in UAV image
quali y due o a ying ligh condi ions, a mosphe ic in e e ence, o ligh pa h a ia ions,
which could in oduce noise in o he da a and a ec index accu acy. Al hough ca e was
aken o conduc ligh s du ing consis en midday condi ions, sligh a iabili ies emain a
possible sou ce o e o .
In e ms o model selec ion, despi e he use o 25 machine-lea ning algo i hms, he
s udy did no inco po a e deep-lea ning a chi ec u es such as CNNs o hyb id models,
which ha e shown p omise in ela ed s udies. The omission o hese models migh ha e
limi ed he ull explo a ion o pe o mance bounda ies.
Addi ionally, due o he high dimensionali y o he da ase , he e is a isk o o e -
i ing, especially when using complex algo i hms on ela i ely small samples om
speci ic measu emen da es. Al hough c oss- alida ion and uning we e pe o med o
mi iga e his, u u e s udies should alida e model pe o mance wi h ex e nal da ase s
o con i m gene alizabili y.
5. Conclusions
This s udy e alua ed 25 eg ession models o es ima ing whea yield using mul-
ispec al (MS) and RGB ege a ion indices de i ed om UAV image y, es ed ac oss

Ag icul u e 2025,15, 1534 22 o 32
h ee di e en measu emen da es. Among hese, Suppo Vec o Reg ession (SVR) and
Mul i-Laye Pe cep on (MLP) Reg esso consis en ly deli e ed he highes p edic i e
pe o mance, wi h SVR achie ing R
2
alues o 0.95 and 0.91 and RMSE alues o 0.26 and
0.33 /ha, while MLP Reg esso achie ed R
2
= 0.94 and RMSE = 0.28 /ha. These models
we e capable o explaining up o 95% o he a ia ion in whea yield.
The s udy also e ealed impo an di e ences among i e Eu opean whea cul i-
a s. NS Obala eco ded he highes a e age yield (5.03 /ha) and lowes a iabili y
(
CV = 21.63%
), while NS Rajna had he lowes a e age yield (4.69 /ha) and he highes
a iabili y (CV = 27.55%). These esul s unde sco e he obus ness o he models when
applied o gene ically di e se ma e ial.
Key MS indices such as BNDVI and SIPI exhibi ed s ong and consis en co ela ions
wi h yield, while RGB indices we e mo e a iable. These insigh s sugges he need o
cau ion when using RGB indices o yield p edic ion.
O e all, he indings ad ance ou unde s anding o in eg a ing UAV-de i ed da a
wi h machine-lea ning models o c op yield p edic ion. This wo k con ibu es o ill-
ing he knowledge gap in empo al model pe o mance, cul i a -speci ic a iabili y, and
he e ec i eness o MS s. RGB indices. The p ac ical implica ions suppo he de el-
opmen o adap able ools o p ecision ag icul u e and in o med decision-making in
whea p oduc ion.
Au ho Con ibu ions: Concep ualiza ion, K.K., Z.S., M.K. and V.A.; me hodology, K.K., Z.S., M.K.
and V.A.; so wa e, K.K., D.T. and T.N.; alida ion, Z.S., M.K. and N.M.; o mal analysis, K.K., D.T.,
T.N. and A.I.; in es iga ion, K.K. and Z.S.; esou ces, V.A.; da a cu a ion, K.K. and M.I.; w i ing—
o iginal d a p epa a ion, K.K. and Z.S.; w i ing— e iew and edi ing, M.K., M.I. and N.M.; isual-
iza ion, M.I. and A.I.; supe ision, N.M. and M.I.; p ojec adminis a ion, N.M.; unding acquisi ion,
N.M. All au ho s ha e ead and ag eed o he published e sion o he manusc ip .
Funding: This publica ion is pa o he TALLHEDA p ojec ha has ecei ed unding om he
Eu opean Union’s Ho izon Eu ope esea ch and inno a ion p og amme unde g an ag eemen
No. 101136578. Funded by he Eu opean Union. Views and opinions exp essed a e howe e hose
o he au ho (s) only and do no necessa ily e lec hose o he Eu opean Union o he Eu opean
Resea ch Execu i e Agency (REA). Nei he he Eu opean Union no he g an ing au ho i y can be
held esponsible o hem.
Da a A ailabili y S a emen : Da a a e con ained wi hin he a icle.
Acknowledgmen s: The inancial suppo men ioned in he Funding pa is g a e ully acknowledged.
Con lic s o In e es : The au ho s decla e no con lic o in e es .
Ag icul u e 2025,15, 1534 23 o 32
Appendix A
Figu e A1. Wo k low Diag am o Whea Yield P edic ion Using UAV-Based Da a and Machine-
Lea ning Models.
Table A1. Vege a ion indices, accompanied by hei compu a ional equa ions, de i ed om he
nume ical in ensi ies o RGB bands [3].
Index Type Fo mula
Red (R), G een (G), Blue (B) Nume ical alues
No malized Red =Red
Red+G een+Blue
No malized G een g=G een
Red+G een+Blue
No malized Blue b=Blue
Red+G een+Blue
G een–Red Ra io Index GRRI =G een
Red
Ag icul u e 2025,15, 1534 24 o 32
Table A1. Con .
Index Type Fo mula
G een–Blue Ra io Index GBRI =G een
Blue
Red–Blue Ra io Index RBRI =Red
Blue
Excess Red Vege a ion Index ExR =1.4· −g
Excess G een Vege a ion Index ExG =2·g− −b
Excess Blue Vege a ion Index ExB =1.4·b−g
Excess G een Minus Excess Red Index ExGR =ExG −ExR
Woebbecke Index WI =G een−Blue
G een+Red
No malized Di e ence Index NDI = −g
+g+0.01
Colo In ensi y INT =Red+Blue+G een
3
G een Lea Index 1 GLI1=2·G een−Red−Blue
2·G een+Red+Blue
G een Lea Index 2 GLI2=2·G een−Red+Blue
2·G een+Red+Blue
Vege a i e Index VEG =Red(2/3)·b(1/3)
Red
Colo Index o Vege a ion CIVE =0.441· −0.811·g+0.3856·b+18.79
Combina ion COM =0.25·ExG +0.3·ExGR +0.33·CIVE +0.12·VEG
No malized G een–Red Vege a ion Index NGRVI =G een−Red
G een+Red
Kawashima Index IKAW =Red−Blue
Red+Blue
Visible-band di e ence ege a ion Index VDVI =2·g− −b
2·g+ +b
Visible A mosphe ically Resis ance Index VARI =g−
g+ −b
P incipal Componen Analysis Index IPCA =
0.994·|Red −Blue|+0.961·|G een −Blue|+0.914·|G een −Red|
Modi ied G een–Red Vege a ion Index MGRVI =G een2−Red2
G een2+Red2
Red–G een–Blue Vege a ion Index RGBVI =G een2−Blue·Red
G een2+Blue·Red
Table A2. Vege a ion indices, along wi h hei associa ed equa ions, ound on he nume ical in ensi ies
o MS bands.
Index Type Fo mula Re e ence
No malized Di e ence Vege a ion Index NDVI =NIR−Red
NIR+Red [6]
Reno malized Di e ence Vege a ion Index RDVI =NIR−Red
(NIR+Red)1/2 [7]
Di e ence ege a ion index DVI =NIR −Red [4]
Blue no malized di e ence ege a ion index BNDVI =NIR−Blue
NIR+Blue [6]
G een no malized di e ence ege a ion index GNDVI =NIR−G een
NIR+G een [37]
Modi ied Soil Adjus ed Vege a ion Index MSAVI =2NIR+1−√(2NIR+1)2−8(NIR−Red)
2[38]
Red-Edge Chlo ophyll Vege a ion Index ReCI =NIR
Red−1[39]
No malized Di e ence Red
Edge Index NDRE =NIR−Red Edge
NIR+Red Edge [37]
No malized Di e ence Wa e Index NDWI =G een−NIR
G een+NIR [40]
Ag icul u e 2025,15, 1534 25 o 32
Table A2. Con .
Index Type Fo mula Re e ence
Op imized Soil-Adjus ed
Vege a ion Index OSAVI =(1+0.16)·(NIR−Red)
(NIR+Red+0.16)[37]
The Simple Ra io SR =NIR
Red [37]
Modi ied Simple Radio MSR =NIR
Red −1
(NIR
Red )1/2+1
[41]
In a ed pe cen age ege a ion index IPVI =NIR
NIR+Red [38]
Enhanced Vege a ion Index EVI =2.5·(NIR−Red)
(NIR+6·Red−7.5·Blue+1)[42]
G een a mosphe ically esis an ege a ion index GARI =(NIR−(G een−(Blue−Red)))
(NIR−(G een+(Blue−Red))) [43]
Soil-Adjus ed Vege a ion Index SAVI =(NIR−Red)
(NIR+Red+0.5)·(1+0.5)[38]
G een Soil Adjus ed Vege a ion Index GSAVI =(NIR−G een)
(NIR+G een+0.5)·(1+0.5)[44]
G een Op imized Soil Adjus ed Vege a ion Index GOSAVI =NIR−G een
NIR+G een+0.16 [44]
G een Chlo ophyll Vege a ion Index GCI =NIR
G een −1[45]
Plan Senescence Re lec ance Index PSRI =Red−G een
NIR [46]
Nonlinea ege a ion index NLI =NIR2−Red
NIR2+Red [47]
T ans o med di e ence ege a ion index TDVI =1.5·(NIR−Red)
q(NIR2+Red+0.5)[48]
Visible A mosphe ically Resis an Index VARI =G een−Red
G een+Red−Blue [49]
Wide Dynamic Range Vege a ion Index WDRVI =0.1NIR−Red
0.1NIR+Red [43]
G een-Red NDVI GRNDVI =NIR−(G een+Red)
NIR+(G een+Red)[41]
G een-Blue NDVI GBNDVI =NIR−(G een+Blue)
NIR+(G een+Blue)[50]
Red-Blue NDVI GRNDVI =NIR−(Red+Blue)
NIR+(Red+Blue)[50]
Pan NDVI PNDVI =NIR−(G een+Red+Blue)
NIR+(G een+Red+Blue)[50]
Simple Ra io Red/NIR Ra io Vege a ion-Index ISR =Red
NIR [51]
Lea Chlo ophyll Index LCI =NIR−Red Edge
NIR+Red [4]
Ra io Be ween NIR and
G een Bands VI(NIR
G een )=NIR
G een [52]
Ra io Be ween NIR and Red
Edge Bands VI(NIR
Red Edge )=NIR
Red Edge [53]
Simpli ied Canopy Chlo ophyll
Con en Index SCCCI =NDRE
NDVI [3]
Modi ied Chlo ophyll
Abso p ion Re lec ance Index
MCARI =
(Red Edge −Red −0.2·(Red Edge −G een))·Red Edge
Red
[4]
T ans o med Chlo ophyll
Abso p ion Re lec ance Index
TCARI =
3·(Red Edge −Red)−0.2·(Red Edge −G een)·Red Edge
Red [37]
S uc u e Insensi i e Pigmen Index SIPI =NIR−Blue
NIR−Red [41]
TCARI/OSAVI TCARI
OSAVI [41]
MCARI/OSAVI MCARI
OSAVI [41]
Red-Edge Chlo ophyll Index 1 CI1=NIR
Red Edge −1[54]
Red-Edge Chlo ophyll Index 2 CI2=Red Edge
G een −1[55]
Table A3. Lis o Reg ession Models wi h Co esponding Abb e ia ions.
Model Type Model Abb e ia ion
Linea Reg ession l
Lasso Reg ession lasso
Ag icul u e 2025,15, 1534 32 o 32
54.
Zhang, H.; Li, J.; Liu, Q.; Lin, S.; Hue e, A.; Liu, L.; C o , H.; Cle e s, J.G.P.W.; Zeng, Y.; Wang, X.; e al. A no el ed-edge spec al
index o e ie ing he lea chlo ophyll con en . Me hods Ecol. E ol. 2022,13, 2771–2787. [C ossRe ]
55.
Cle e s, J.G.P.W.; Gi elson, A.A. Remo e es ima ion o c op and g ass chlo ophyll and ni ogen con en using ed-edge bands on
Sen inel-2 and -3. In . J. Appl. Ea h Obs. Geoin . 2013,23, 344–351. [C ossRe ]
Disclaime /Publishe ’s No e: The s a emen s, opinions and da a con ained in all publica ions a e solely hose o he indi idual
au ho (s) and con ibu o (s) and no o MDPI and/o he edi o (s). MDPI and/o he edi o (s) disclaim esponsibili y o any inju y o
people o p ope y esul ing om any ideas, me hods, ins uc ions o p oduc s e e ed o in he con en .