Ci a ion: Janoušek, J.; Ma coˇn, P.;
Dohnal, P.; Jambo , V.; Synko á, H.;
Raichl, P. P edic ing he Op imum
Co n Ha es Time ia he Quan i y
o D y Ma e De e mined wi h
Vege a ion Indices Ob ained om
Mul ispec al Field Imaging. Remo e
Sens. 2023,15, 3152. h ps://doi.o g/
10.3390/ s15123152
Academic Edi o : Guido D’U so
Recei ed: 24 Ap il 2023
Re ised: 7 June 2023
Accep ed: 14 June 2023
Published: 16 June 2023
Copy igh : © 2023 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/).
emo e sensing
A icle
P edic ing he Op imum Co n Ha es Time ia he Quan i y o
D y Ma e De e mined wi h Vege a ion Indices Ob ained om
Mul ispec al Field Imaging
Jiˇ íJanoušek 1, Pe Ma coˇn 1,* , Pˇ emysl Dohnal 1, Václa Jambo 2, Hana Synko á2and Pe Raichl 1
1Facul y o Elec ical Enginee ing and Communica ion, B no Uni e si y o Technology,
61600 B no, Czech Republic; xjanou09@ u b .cz (J.J.); [email p o ec ed] (P.D.); [email p o ec ed] (P.R.)
2Nu iVe s. .o., Vídeˇnská1023, 69123 Pohoˇ elice, Czech Republic; jambo [email p o ec ed] (V.J.);
[email p o ec ed] (H.S.)
*Co espondence: ma [email p o ec ed]
Abs ac :
Es ima ing he op imum ha es ime and yield embodies an essen ial ood secu i y
ac o . Vege a ion indices ha e p o en o be an e ec i e ool o widescale in- ield plan heal h
mapping. A d one-based mul ispec al came a hen con enien ly allows acqui ing da a on he
condi ion o he plan . This a icle examines and discusses he ela ionships be ween ege a ion
indices and nu i iolnal alues ha ha e been de e mined ia chemical analysis o plan samples
collec ed in he ield. In his con ex , emphasis is placed on he no malized di e ence ed edge index
(NDRE), no malized di e ence ege a ion index (NDVI), g een no malized di e ence ege a ion
index (GNDVI), and nu i ional alues, such as hose o d y ma e . The ela ionships be ween he
a iables we e co ela ed and desc ibed by means o eg ession models. This p oduced equa ions
ha a e applicable o es ima ing he quan i y o d y ma e and hus de e mining he op imum co n
ha es ime. The ob ained equa ions we e alida ed on i e di e en ypes o co n hyb ids in ields
wi hin he Sou h Mo a ian Region, Mo a ia, he Czech Republic.
Keywo ds:
co n; mul ispec al imaging; ege a ion indices; nu i ional analysis; co ela ion; pho-
og amme y; op imal ha es ime; UAV
1. In oduc ion
1.1. Remo e Sensing
The emo e sensing o he Ea h’s su ace has assumed a signi ican ole in p ecision
ag icul u e, and has main ained his posi ion on a long- e m basis. Imaging ag icul u al
a eas is enabled h ough sa elli es and hype spec al o mul ispec al came as [
1
]. These
a e employed no only in emo e sensing, bu also, o example, in de ec ing dying ees in-
es ed wi h pes s [
2
], o en o mechanically damaged ui and ege ables [
3
], ecognizing
ecal pollu ion [
4
], es ablishing cold-induced de e io a ion o cucumbe s [
5
], measu ing
ui ipening [
6
], classi ying whea ke nels in ec ed wi h ungi [
7
], and many o he ap-
plica ions [
8
,
9
]. Recen ly, he ac ual app oach and associa ed me hodologies ha e been
de eloping subs an ially.
The esea ch ou lined he ein exploi s a p e iously published case s udy [
1
], hus
building on, e i ying, and ma kedly enhancing an al eady es ablished co ela ion be ween
plan nu i ional alues and ege a ion indices. Impo an ly, ou la es conclusions we e
o mula ed om da a measu ed o e h ee yea s, i.e., h ee ha es seasons, while he
e e enced a icle [1] p esen s and analyzes esul s ob ained du ing one season only.
The o al ha es ed c op biomass consis s o whole co n plan s. The basic indica o o
plan phenophase is based on speci ying he d y ma e con en s; hese inc ease signi ican ly
as he c op ma u es. In co n, he d y ma e cha ac e izes he g ow h ma u i y le el, and
i s olume in luences he silage quali y ma e ially and p ocedu ally [
10
]. The chemical
Remo e Sens. 2023,15, 3152. h ps://doi.o g/10.3390/ s15123152 h ps://www.mdpi.com/jou nal/ emo esensing
Remo e Sens. 2023,15, 3152 2 o 19
composi ion o co n plan s changes o e he cou se o he g owing pe iod. Be o e he
plan de elops ea s, i s ene gy is concen a ed mainly in he ibe , whose p opo ion a ies
be ween plan s, depending on he ac ual ha es ime. To ensu e ha he inal co n silage
p oduc comp ises no only ibe bu also s a ch, he ha es ing has o be pe o med a he
wax ma u i y s age, namely, when he d y ma e p opo ion alues in he whole plan
each be ween 280 and 330 g/kg. In such cases, he milk line s age a ains 2/3 o he co n
g ain. Ano he indica o o g ow h ma u i y is he abili y o be ensiled, o , in o he wo ds,
o gene a e e men a ion acids ha p ese e he silage.
The ha es ing ime and he o al amoun o biomass ha e an essen ial impac on he
cha ac e o he silage e men a ion. The quali y o he co n cul i a ion p ocesses and he
subsequen ensiling ollows om he wea he condi ions in a pa icula yea , he choice o
a sui able hyb id wi h an app op ia e FAO numbe o speci y he ea liness le el, ea men ,
and cha ac e o sowing.
Co n samples a e ou inely collec ed a di e se loca ions in he ield o allow he
assessing o he condi ion and phenophase. When he milk line s age has been eached, he
samples a e submi ed o a labo a o y o chemical analysis o de e mine he d y ma e
con en in bo h he g ain and he whole plan . Depending on he deg ee o which he
plan and he d y ma e ha e de eloped, he ha es ing ime is se p elimina ily, a ying
acco ding o he planned a ge use o he co n, namely, milk p oduc ion o me hane
gene a ion a biogas acili ies.
As he d y ma e con en embodies a majo pa ame e o de ining he op imum
ha es ime, i is impo an o es ablish whe he mo e accu a e da a can be ob ained on he
a e age d y ma e alue wi hin an en i e, non-homogeneous ield. This a icle p oposes
o sol e he p oblem using an e ec i e in eg a ion o di e en me hods and echnologies,
in ol ing a d one wi h a mul ispec al came a, image da a analysis o acqui e ege a ion
indices, and a chemical analysis o all samples collec ed in he ield.
1.2. Field-Wide Image Da a Cap u ing
Comp ehensi e da a ela ing o he condi ion o a ield and hus also he a e age
con en o d y ma e a e ob ainable ia one o wo undamen al echnologies, namely,
sa elli e image y o pho og amme y pe o med by using a mul ispec al o hype spec al
came a moun ed on an ae ial ehicle. Bo h o hese app oaches can be applied o p edic
he yield o ag icul u al c ops.
Pho og amme ic imaging wi h unmanned ae ial ehicles (UAVs) u ilizes di e en
ypes o mul ispec al o hype spec al came as [
11
–
16
]. The p oblem o c op yield p edic-
ion om pho og amme ic da a acqui ed by UAVs has been add essed in he li e a u e [
11
].
Ou a icle expands on he p e ious esea ch, p esen ing no el indings ega ding he co -
ela ion be ween d y ma e yield and ege a ion indices.
The o he o he wo imaging op ions elies on sa elli es. Sa elli e image y di e s om
he UAV-based me hod in he dis ance o he senso om he a ea o in e es . Sa elli es mo e
a a cons an al i ude o no less han 400 km along o bi s—ei he geos a iona y ones, which
ci cle he Ea h abo e he equa o , o o he s. Impo an ly, he sa elli es wi h he la e ype
e ol e a ound he Ea h p og essi ely o e i s en i e su ace, in a no h–sou h di ec ion.
A i icial sa elli es ensu e egula imaging wi h long s abili y and epea abili y o e
ime, and hese aspec s embody he mos signi ican ad an age o he echnique. By
con as , he main d awback es s in a lowe image esolu ion, an issue ha subs an ia es
he use o d ones in compiling high esolu ion maps. The sa elli es allow us o easily
de e mine hei ime o passage o e he a ea being moni o ed; such ime, howe e , canno
be adjus ed acco ding o need o o sui he posi ion o he a ea o in e es , as he o bi ing
speed emains cons an . Fu he mo e, ob aining high quali y images depends on a o able
wea he incompa ably mo e han in UAV econnaissance; he p ocess is ulne able o
cons aining e ec s ha include, o ins ance, cloud bands.
Remo e Sens. 2023,15, 3152 3 o 19
Sa elli es ca y key senso s, such as mul ispec al and hype spec al senso s, lida s,
and RGB came as. Access o he images is ne e heless o en limi ed, equi ing p e-paid
se ices ha p o ide an image da abase.
The la ges numbe o sa elli es a e ope a ed by he US-based company Plane Labs
wi hin he Plane Scope, a sys em comp ising 175 sa elli es ha supply mul ispec al images
wi h a spa ial esolu ion o up o 3 m; he imaging is pe o med daily and co e s he en i e
su ace o he Ea h. The p ocessing u ilizes aw da a, applying a mosphe ic co ec ions
and o he ele an p ocedu es, such as single-pixel classi ica ion [17,18].
1.3. P edic ing C op Yield
The p edic ion o c op yield ia sa elli e image y has been discussed in mul iple
esea ch a icles. In his con ex , o ins ance, he au ho s o s udy [
19
] ocus on he op imum
ime o apply ni ogen chemicals o c ops a a e y ea ly g ow h s age, in es iga ing he
ac ual iming oge he wi h measu emen o he ege a ion index NDVI and plan heigh
as an indica o o d y ma e ou pu ; howe e , despi e his comp ehensi e app oach, only
ela i e alues o e wo yea s a e p o ided.
A icle [
20
] examines eg ession models o c op yield es ima ion ia he NDVI index
and measu emen o he ela i e c op ou pu (paddy ice, win e whea , and co n). The
au ho s iden i y he bes pe iod o es ima ing he c op yield eliably, cha ac e izing he
model ha showed a oo mean squa e e o o 206.59 kg/ha in co n as he bes i . The
models pe o m easonably well in small egions, especially in a eas whe e he c op ypes
a e no exac ly known.
In s udy [
21
], he NDVI was ound o deli e an excellen a e o co ela ion wi h yield
alues, albei wi h a delay o 4–6 weeks, in g ass used o biomass. In co n, he yield alue
co ela es wi h he NDVI wi h a delay o wo weeks.
Measu emen s ha ely on spec o adiome ic equipmen , whe e he ac i e adia ion
sou ce o an NDVI measu emen is ac i e, show s ong co ela ions be ween he NDVI and
du um whea geno ypes. A ela ed a icle [
22
] ne e heless also sugges s ha he measu ing
p ocedu es may ma kedly depend on he spec ome e used, mainly as ega ds hei o e all
sui abili y o he pu pose and he ope a ing ime equi ed. Th ough he ou comes o o he
esea ch p ojec s [
23
–
25
], he Mode a e Resol ed Imaging Spec o adiome e (MODIS)
appea s o p oduce good esul s when p edic ing ha es olumes. Co n yield p edic ion
and unce ain y analysis based on emo ely sensed a iables using a Bayesian neu al
ne wo k is add essed in s udy [
26
]. O he a i icial in elligence me hods o es ima ing c op
yield quan i a i ely a e p esen ed wi hin sou ces [27–33].
In e es ingly, a signi ican co ela ion has been e ealed be ween s ess-exposed co n
plan s and wa e s ess in ela ion o he amoun o usable pixels ha ing an in o ma i e
alue [
34
]. By ex ension, some expe s ha e [
35
] a gued ha using (NDVI) da a acqui ed
wi h an NOAA–Ad anced Ve y High Resolu ion Radiome e (AVHRR) enables co n p o-
duc ion o be p edic able a leas 2 mon hs be o e he ac ual ha es and a an accu acy
mul iple imes highe han ha o he wa e s ess p ocedu e. The e e enced a icle [
36
]
also emphasizes ha combining clima ological NDVI da a embodies a bene icial s ep o
inc ease he accu acy o he models; his assump ion is con i med wi hin s udy [
36
]. A
combina ion o me eo ological da a and sa elli e images o p edic abo eg ound biomass
and d y ma e con en s in B achia ia pas u es is ou lined in [37].
The accu acy o NDVI-de i ed co n yield p edic ions appa en ly depends on he scan
ime [
38
] and he olume o wa e in he plan du ing a ious pe iods o he day, ega dless
o he senso used [39,40].
A p edic ing app oach ha u ilizes he Lea a ea index (LAI) and es ima es he d y
ma e ia ield e lec ance measu emen s execu ed wi h mul ispec al sys ems (Landsa 8,
RapidEye) is desc ibed in s udy [41].
Fu he mo e, ega ding he p oblems ele an o he opic in gene al, se e al esea ch
epo s, a icles, and pape s discuss he ela ionship be ween he ege a ion indices and
nu i ional alues, [
42
,
43
]; he la e sou ce examines da a co ela ion be ween ege a ion
Remo e Sens. 2023,15, 3152 4 o 19
indices and he ni ogen nu i ion index (NNI), he in es iga ion being ocused solely on
peppe plan s. The ege a ion indices and he ag onomic pe o mance o co n a ie ies
unde di e en ni ogen a es a e compa ed in a icle [
44
]. Ou e o s concep ually ela e
especially o hose ou lined in epo [
45
], which p oposes an insigh in o he co ela ion
be ween canopy ege a ion and he g ow h indices o co n a ie ies wi h di e en ni ogen
e iciencies; he au ho s o [
45
], howe e , do no show conc e e ma hema ical exp essions
o inspec he ege a ion- o-nu i ional index ela ionships ha allow o he es ablishing
o he op imum co n ha es ime.
Ou a icle b oadly expands on he knowledge, esea ch, and applica ions a ailable
o da e. The ac ual no el y lies in he design o a new and mo e accu a e me hodology
(compa ed o, o ins ance, he solu ion adop ed in [
1
]) o de e mining he op imum
ha es ime by exploi ing he co ela ion be ween di e se ege a ion indices and he d y
ma e con en in a ious co n phenophases. Wi h such an inno a i e app oach, he a me
is no equi ed o sample he c op di ec ly in he ield and ha e i analyzed chemically, hus
sa ing a subs an ial amoun o ime and wo k. The de ini ion o he app op ia e ha es
ime leads o a scena io whe e he en i e p ocedu al chain is op imized, s a ing om he
seed plan ing and p oceeding h ough he ideal silage nu i ional alues o e en ually
secu e he maximum achie able yield in cow milk o biogas.
2. Ma e ials and Me hods
The da a collec ion and he ele an ma hema ical p ocessing a e cha ac e ized h ough
he block diag am and p esen a ion below. The le -hand po ion o Figu e 1A exposes
how a new equa ion is acqui ed ia u ilizing a eg ession model o he ege a ion indices
and a chemical analysis o he co n plan s; he igh -hand segmen (Figu e 1B), by con as ,
displays he use o an expe imen ally gene a ed equa ion o compu ing he d y ma e
wi hou ha ing o pe o m a chemical analysis. The d y ma e alue hen enables us o
es ablish he op imum ha es ime in he c op being in es iga ed.
Remo e Sens. 2023, 14, x FOR PEER REVIEW 4 o 20
Fu he mo e, ega ding he p oblems ele an o he opic in gene al, se e al esea ch
epo s, a icles, and pape s discuss he ela ionship be ween he ege a ion indices and
nu i ional alues, [42,43]; he la e sou ce examines da a co ela ion be ween ege a ion
indices and he ni ogen nu i ion index (NNI), he in es iga ion being ocused solely on
peppe plan s. The ege a ion indices and he ag onomic pe o mance o co n a ie ies
unde diffe en ni ogen a es a e compa ed in a icle [44]. Ou effo s concep ually ela e
especially o hose ou lined in epo [45], which p oposes an insigh in o he co ela ion
be ween canopy ege a ion and he g ow h indices o co n a ie ies wi h diffe en
ni ogen efficiencies; he au ho s o [45], howe e , do no show conc e e ma hema ical
exp essions o inspec he ege a ion- o-nu i ional index ela ionships ha allow o he
es ablishing o he op imum co n ha es ime.
Ou a icle b oadly expands on he knowledge, esea ch, and applica ions a ailable
o da e. The ac ual no el y lies in he design o a new and mo e accu a e me hodology
(compa ed o, o ins ance, he solu ion adop ed in [1]) o de e mining he op imum
ha es ime by exploi ing he co ela ion be ween di e se ege a ion indices and he d y
ma e con en in a ious co n phenophases. Wi h such an inno a i e app oach, he
a me is no equi ed o sample he c op di ec ly in he ield and ha e i analyzed
chemically, hus sa ing a subs an ial amoun o ime and wo k. The de ini ion o he
app op ia e ha es ime leads o a scena io whe e he en i e p ocedu al chain is
op imized, s a ing om he seed plan ing and p oceeding h ough he ideal silage
nu i ional alues o e en ually secu e he maximum achie able yield in cow milk o
biogas.
2. Ma e ials and Me hods
The da a collec ion and he ele an ma hema ical p ocessing a e cha ac e ized
h ough he block diag am and p esen a ion below. The le -hand po ion o Figu e 1A
exposes how a new equa ion is acqui ed ia u ilizing a eg ession model o he ege a ion
indices and a chemical analysis o he co n plan s; he igh -hand segmen (Figu e 1B), by
con as , displays he use o an expe imen ally gene a ed equa ion o compu ing he d y
ma e wi hou ha ing o pe o m a chemical analysis. The d y ma e alue hen enables
us o es ablish he op imum ha es ime in he c op being in es iga ed.
Figu e 1. A block diag am ou lining he ac ual speci ica ion, (A), and e i ica ion, (B), o he
ela ionships be ween he ege a ion indices and nu i ional alues in a ious ypes o co n hyb ids.
Figu e 1.
A block diag am ou lining he ac ual speci ica ion, (
A
), and e i ica ion, (
B
), o he ela ion-
ships be ween he ege a ion indices and nu i ional alues in a ious ypes o co n hyb ids.
2.1. Sensing Pe iods and Locali ies
The mul ispec al came a pho og amme ic imaging and he manual sampling we e
execu ed in co n ields a a ious spo s o he Sou h Mo a ian Region, Mo a ia, he Czech
Republic. The sampling ope a ions we e coo dina ed, e en hough he in e als sepa a ing
Remo e Sens. 2023,15, 3152 5 o 19
he indi idual s eps di e ed. The loca ions whe e samples we e collec ed o chemical
analysis we e eco ded in mul ispec al images (Figu e 2), and he p ese locali y selec ion
c i e ia had included ac o s such as su icien ege a ion he e ogenei y, soil composi ion,
and clima ic condi ions [
1
]. In esea ch yea 1, he sampling was ca ied ou nea he illage
o T oubsko om 23 July 2019 o 4 Sep embe 2019, a ou and i e di e se ime in e als
o plan phenophase in he silage and he g ain hyb ids, espec i ely.
Remo e Sens. 2023, 14, x FOR PEER REVIEW 5 o 20
2.1. Sensing Pe iods and Locali ies
The mul ispec al came a pho og amme ic imaging and he manual sampling we e
execu ed in co n ields a a ious spo s o he Sou h Mo a ian Region, Mo a ia, he Czech
Republic. The sampling ope a ions we e coo dina ed, e en hough he in e als
sepa a ing he indi idual s eps diffe ed. The loca ions whe e samples we e collec ed o
chemical analysis we e eco ded in mul ispec al images (Figu e 2), and he p ese locali y
selec ion c i e ia had included ac o s such as sufficien ege a ion he e ogenei y, soil
composi ion, and clima ic condi ions [1]. In esea ch yea 1, he sampling was ca ied ou
nea he illage o T oubsko om 23 July 2019 o 4 Sep embe 2019, a ou and i e di e se
ime in e als o plan phenophase in he silage and he g ain hyb ids, espec i ely.
(a) (b)
Figu e 2. (a) Visualizing he o e all a ea o he expe imen ; (b) posi ioning he co n ields ha we e
subjec ed o he pho og amme ic imaging in he ele an subsec o o he Sou h Mo a ian Region,
Mo a ia, Czech Republic.
In he pe iod om 12 Augus 2020 o 7 Oc obe 2020, he sampling was ca ied ou
be ween he municipali ies o Šlapanice and P ace (bo h in he B no coun y dis ic ). To
op imize and compa e he samples om he i s esea ch yea , we chose a highe
sampling equency, collec ing he i ems on 8 diffe en days. The same amoun o
sampling was alloca ed o he nex yea , when he expe imen s ook place in a ield nea
he own o Velké Pa lo ice (Břecla dis ic ). The samples comp ised wo co n hyb ids
and we e ga he ed om 2 Augus 2021 o 21 Sep embe 2021.
To es he alidi y o he co ela i e ela ionships and o con i m he hypo hesis ha
changes in he compu ed ege a ion indices a e p opo ional o a ia ions in he
nu i ional analysis, we conduc ed a sepa a e expe imen nea he illage o Knínice
(Blansko dis ic ), in ol ing 5 co n hyb ids on he day o hei ac ual ha es .
2.2. UAV Da a Collec ion and Analysis
The pho og amme ic da a o igina ed om a Micasence RedEdge-3 mul ispec al
came a moun ed on a DJI Ma ice 600 P o unmanned ae ial ehicle (Figu e 3). The
RedEdge de ice cap u es 5 diffe en bands (Table 1) and is i ed wi h a 3DR GPS module,
a downwelling ligh senso , E he ne , and o he in e aces.
Figu e 2.
(
a
) Visualizing he o e all a ea o he expe imen ; (
b
) posi ioning he co n ields ha we e
subjec ed o he pho og amme ic imaging in he ele an subsec o o he Sou h Mo a ian Region,
Mo a ia, Czech Republic.
In he pe iod om 12 Augus 2020 o 7 Oc obe 2020, he sampling was ca ied ou
be ween he municipali ies o Šlapanice and P ace (bo h in he B no coun y dis ic ). To
op imize and compa e he samples om he i s esea ch yea , we chose a highe sampling
equency, collec ing he i ems on 8 di e en days. The same amoun o sampling was
alloca ed o he nex yea , when he expe imen s ook place in a ield nea he own o Velké
Pa lo ice (Bˇ ecla dis ic ). The samples comp ised wo co n hyb ids and we e ga he ed
om 2 Augus 2021 o 21 Sep embe 2021.
To es he alidi y o he co ela i e ela ionships and o con i m he hypo hesis ha
changes in he compu ed ege a ion indices a e p opo ional o a ia ions in he nu i ional
analysis, we conduc ed a sepa a e expe imen nea he illage o Knínice (Blansko dis ic ),
in ol ing 5 co n hyb ids on he day o hei ac ual ha es .
2.2. UAV Da a Collec ion and Analysis
The pho og amme ic da a o igina ed om a Micasence RedEdge-3 mul ispec al
came a moun ed on a DJI Ma ice 600 P o unmanned ae ial ehicle (Figu e 3). The Red-
Edge de ice cap u es 5 di e en bands (Table 1) and is i ed wi h a 3DR GPS module, a
downwelling ligh senso , E he ne , and o he in e aces.
Be o e e alua ing he images, a su icien olume o he e ogeneous da a has o be
ob ained o allow me hods o be compa ed ha a e sui able o achie ing he bes possible
co ela ion wi h he nu i ional alues o he plan samples.
The imaging was pe o med along p e-p og ammed au oma ic ligh pa hs, each pa h
ha ing a p ecisely de ined, polygon-shaped scanning a ea wi hin he egion o in e es .
In he expe imen , we used he DJI au opilo and he Pix4D cap u e so wa e o plane he

Remo e Sens. 2023,15, 3152 6 o 19
pa h. The image p ocessing elied on S uc u e- om-Mo ion (SFM), a key pho og amme ic
echnique used o handle mul ispec al images ob ained om UAVs.
Remo e Sens. 2023, 14, x FOR PEER REVIEW 6 o 20
Figu e 3. Cap u ing he image da a wi h a d one-moun ed RedEdge came a.
Table 1. The pa ame e s o he RedEdge Micasense came a bands.
Band Numbe Band Colo Wa eleng h
[nm]
Bandwid h
[nm]
Calib a ion Panel
Re lec ance
1 Blue (B) 475 20 0.56
2 G een (G) 560 20 0.56
3 Red (R) 668 10 0.55
4 Nea in a ed
(NIR) 840 40 0.54
5 Red Edge (RE) 717 10 0.50
Be o e e alua ing he images, a sufficien olume o he e ogeneous da a has o be
ob ained o allow me hods o be compa ed ha a e sui able o achie ing he bes possible
co ela ion wi h he nu i ional alues o he plan samples.
The imaging was pe o med along p e-p og ammed au oma ic ligh pa hs, each
pa h ha ing a p ecisely de ined, polygon-shaped scanning a ea wi hin he egion o
in e es . In he expe imen , we used he DJI au opilo and he Pix4D cap u e so wa e o
plane he pa h. The image p ocessing elied on S uc u e- om-Mo ion (SFM), a key
pho og amme ic echnique used o handle mul ispec al images ob ained om UAVs.
The a ea co e ed o he es ing was small, meaning ha we assumed a ixed heigh ;
his heigh hen also cons i u ed he basis o he image compu a ion. In all o he h ee
esea ch yea s, he mapping co e ed a ec angula zone o 361 m × 362 m, i.e., an a ea o
app oxima ely 13.1 ha. The o al ligh pa h leng h eached 4.477 m. To scan he ull ange
o he in es iga ed sec o , a ligh las ed 31 min, wi h an o e lap o 70% be ween he
images. The UAV lew a a speed o 8.6 km/h and an al i ude o 40 m abo e he g ound.
In each o he spec al bands, we ook in a iably mo e han 330 images wi h a esolu ion
o 2.78 cm/pixel. The measu ed da a we e p ocessed wi h he Pix4D mappe a he use
Figu e 3. Cap u ing he image da a wi h a d one-moun ed RedEdge came a.
Table 1. The pa ame e s o he RedEdge Micasense came a bands.
Band Numbe Band Colo Wa eleng h [nm] Bandwid h [nm] Calib a ion Panel Re lec ance
1 Blue (B) 475 20 0.56
2 G een (G) 560 20 0.56
3 Red (R) 668 10 0.55
4
Nea in a ed(NIR)
840 40 0.54
5 Red Edge (RE) 717 10 0.50
The a ea co e ed o he es ing was small, meaning ha we assumed a ixed heigh ;
his heigh hen also cons i u ed he basis o he image compu a ion. In all o he h ee
esea ch yea s, he mapping co e ed a ec angula zone o 361 m
×
362 m, i.e., an a ea
o app oxima ely 13.1 ha. The o al ligh pa h leng h eached 4.477 m. To scan he ull
ange o he in es iga ed sec o , a ligh las ed 31 min, wi h an o e lap o 70% be ween he
images. The UAV lew a a speed o 8.6 km/h and an al i ude o 40 m abo e he g ound. In
each o he spec al bands, we ook in a iably mo e han 330 images wi h a esolu ion o
2.78 cm/pixel. The measu ed da a we e p ocessed wi h he Pix4D mappe a he use le el;
we did no es he image esolu ion changes o p ocessing ia a ious o he me hods.
The mul ispec al imaging deli e s ege a ion indices, which con ain in o ma ion
on di e en e lec ance alues o he elec omagne ic spec um ela ing o he biological
p ope ies o plan s. The mos widely used ege a ion indices a e hose whe e quan i a i e
indica o s, such as he olume o biomass wi hin an a ea, can be de e mined. A la ge
amoun o algo i hms o calcula e ege a ion indices a e a ailable, a ising om compu a ion
om a leas wo spec al images; he images a e selec ed in such a manne as o expose
ege a ion e lec ance changes, and in mos cases hey a e unc ionally equi alen . Mo e
han 150 ege a ion indices ha e been published in he li e a u e, bu only a small subse
ha e a s ong biophysical basis o ha e been sys ema ically es ed [46–48].
Remo e Sens. 2023,15, 3152 7 o 19
Each ege a ion index acks speci ic ege a ion cha ac e is ics and is con enien o
pa icula applica ions. Indices ha do no u ilize he nea -in a ed spec al band exhibi
limi ed (and limi ing) p ope ies and a e he e o e unsui able in p ac ical moni o ing o
ege a ion changes. To acili a e he analysis, we chose he a io indices NDVI,NDRE,
and GNDVI, all o which a e compu ed simila ly; hese ools, howe e , also con ain di -
e en spec al bands, and hus hey collec i ely o e a c oss-sec ion h ough impo an
wa eleng hs. Combining he indices hen yields applicable modi ica ions, whose da a a e
dissimila o hose deli e ed by he o iginally selec ed basic e sions [49].
Vege a ion indices a e no cons an , bu depend on sho - e m wea he changes and
he o e all amoun o sunligh . To e ine he esul s o he mul ispec al sensing, we need
o un calib a ion; his s ep is execu ed in a ious g owing seasons, unde di e se wea he
condi ions, and a he same phase o he day. Impo an ly, a da abase had o be o med
con aining he ou comes o se e al measu emen s, allowing us o choose he alues ha a e
achie able in op imum ci cums ances. Calib a ing he came a elimina es he inaccu acies
which s em om he use o one-o , single samples o he c ops, and c ea ing addi ional
images will acili a e compa ison o he indices.
2.2.1. NDVI (No malized Di e ence Vege a ion Index)
The NDVI is a nume ical indica o o plan heal h ha supplies da a on ege a ion
changes and, in a mo e de ailed sense, he amoun s o wa e s ess and chlo ophyll con-
ained in a plan . The index e alua es he moni o ed ege a ion su ace by using he a io
o he e lec ance o he ed and nea -in a ed pa s o he spec um [50].
The NDVI u ilizes he ed isible band, which is s ongly abso bed by he uppe
po ion o a plan ’s su ace, meaning ha he lowe le els do no signi ican ly con ibu e
o he NDVI measu emen . The co ela ion be ween he index and he plan ’s olume ic
p ope ies hus de e io a es; his is mo e p ominen in alle plan s wi h mul iple lea laye s
(such as co n a la e g ow h s ages) [51,52].
The e lec ance o he nea -in a ed spec um enables he index o easily dis inguish
sub le di e ences in ege a ion. In he ac ual sensing, he ac o s o majo impo ance
include shadows and he a mosphe e, whose impac leads o e lec ance changes wi hin
he di e en bands; he a mosphe ic e ec is eliminable ia co ec ion based on compa ing
images aken a a ious imes [49]. We ha e
NDVI =ρNIR −ρRed
ρNIR +ρRed
(1)
whe e
ρNIR
and
ρRed
deno e he e lec i i ies o he nea -in a ed and he ed wa eleng h
bands, espec i ely.
2.2.2. NDRE (No malized Di e ence Red Edge Index)
Simila o he abo e-cha ac e ized ool, he NDRE exploi s he nea -in a ed spec um
and he equency band ha lies in he ansi ion egion sepa a ing he isible and he
in a ed spec a, i.e., he ed edge; we ha e
NDRE =ρNIR −ρRedEdge
ρNIR +ρRedEdge
. (2)
2.2.3. GNDVI (G een No malized Di e ence Vege a ion Index)
This me hod employs he g een spec um wa eleng hs a he han he ed ones; hese
a e
ρNIR
and
ρG een
, deno ing he e lec ance alues in he nea -in a ed and he g een bands,
espec i ely [53,54]. We ha e
GNDVI =ρNIR −ρG een
ρNIR +ρG een
. (3)
Remo e Sens. 2023,15, 3152 8 o 19
2.3. Chemical Analysis o he Samples Ob ained om Field-Ga he ed Co n Plan s
To ob ain he nu i ional pa ame e s o he ield samples o co n, we ca ied ou a
dedica ed labo a o y chemical analysis. The ege a ion indices and he ou comes o he
analysis we e hen co ela ed a a ious phenological g ow h s ages o he moni o ed c ops
o es ablish he ideal ha es ime as ega ds he co n yield o silage making and animal
eed on he one hand, and me hane p oduc ion in biogas plan s on he o he .
The sampling was in a iably pe o med a iden ical ime in e als, oge he wi h he
mul ispec al imaging. To su ey he quali y o he co n hyb id, we op ed o sampling
acco ding o he me hodology ecommended by he Cen al Ins i u e o Supe ising and
Tes ing in Ag icul u e, B no, Mo a ia, he Czech Republic [
55
]. The samples we e acqui ed
om h ee di e en sec o s o expose he local ield g ow h homogenei y; in each o he
cases, we ook a ow o 10 whole co n plan s and ma ked hei posi ions on he mul ispec al
maps acqui ed o e he a eas speci ied in Figu e 2.
Subsequen ly, we modi ied and analyzed he plan s o de e mine he majo quan i ies,
namely, he FM—F esh ma e ( esh weigh )—and EW—Ea weigh . In gene al e ms,
he analysis also enables he ollowing nu i ional alues o be es ablished: he DM–d y
ma e , meaning he d y ma e olume– om which we hen de ine he alues o CP–c ude
p o ein (ni ogenous compounds); CF—c ude ibe (c ude ibe ); s a ch (s a ch con en ); ash
(ash p esence); NDF—neu al de e gen ibe (neu al de e gen ibe ); DNDF—diges ibili y
NDF (neu al de e gen ibe diges ibili y a e); and DOM—diges ibili y o ganic ma e
(o ganic ma e diges ibili y a e). The analyzed da a e en ually allow us o calcula e he
yield pe hec a e, comp ising he YFM—yield o esh ma e ( esh ma e sha e indica o )
and YDM—yield o d y ma e (d y ma e sha e indica o ); in o al, a hec a e is assumed
o p oduce 80,000 co n plan s.
2.4. Da a Co ela ion
To de ine he ela ionships be ween he esul s acqui ed wi h he nu i ional analysis on
he one hand (Nu ) and he alues o he ege a ion indices (Veg) on he o he , we calcula ed
he ege a ion index alues
Nu ,Veg
acco ding o Pea son’s co ela ion coe icien . The
deg ee o co ela ion is speci ied by he compu ed co ela ion coe icien , which can ake
alues om
−
1 o +1. The e minal alues o he coe icien +1 ep esen a comple ely di ec
ela ionship, and he i s a iable ends o inc ease; by con as , he alues o he coe icien
−
1 ep esen a ully in e se ela ionship, and he i s a iable ends o dec ease. I he
co ela ion coe icien equals ze o, he e is no linea ela ionship be ween he pa ame e
being moni o ed and he e lec ance o ege a ion index. We ha e
Nu ,Veg =
1
n∑n
i=1Nu i−VegVegi−Nu 
SNu ·SVeg
(4)
SNu =s1
n
n
∑
i=1Nu i2−Nu 2, (5)
SVeg =s1
n
n
∑
i=1Vegi2−Veg2, (6)
whe e
Nu
ep esen s he nu i ion analysis alue,
Veg
deno es he ege a ion index alue,
Veg and Nu s and o he sample means, and SVeg and SNu a e he s anda d de ia ions.
The quan i y
R2
indica es he coe icien o de e mina ion. I akes alues om 0 o 1,
was compu ed o exp ess he join a iabili y o he a iables, and speci ies he quali y o
he eg ession model. A alue o 1 means pe ec p edic ion o he alues o he dependen
a iable, while a alue o 0 signi ies minimum in o ma ion ela ing o he knowledge o he
dependen a iable. The coe icien was compu ed by using he ela ionships below.
Remo e Sens. 2023,15, 3152 9 o 19
A da ase has n alues ma ked as y
1
,
. . .
,y
n
(collec i ely known as y
i
o a ec o
y
= [y
1
,
. . .
,y]
nT
), each associa ed wi h a i ed (o modeled, p edic ed) alue
1
,
. . .
,
n
(deno ed by i).
I yis he mean o he obse ed da a,
y=1
n
n
∑
i=1
yi, (7)
hen he da ase a iabili y can be measu ed wi h wo sums-o -squa es o mulas. Fi s , le
us no e he sum o he squa es o esiduals, also called he esidual sum o squa es:
SS es =∑
i
(yi− i)2. (8)
The la e equa ion embodies he o al sum o squa es (p opo ional o he da a a i-
ance), eading
SS o =∑
i
(yi−y)2. (9)
The mos gene al de ini ion o he coe icien o de e mina ion is
R2=1−SS es
SS o . (10)
In he bes case, he modeled alues exac ly ma ch he obse ed ones, esul ing in
SS es =
0 and
R2=
1. A baseline model, which always p edic s
y
, will ha e
R2=
0; models
ha deli e p edic ions wo se han he baseline will assume a nega i e R2[56].
To ob ain ano he pa ame e o de e mining whe he he co ela ion coe icien s
ake a alue ha e ec i ely implies an in e -coe icien ela ionship, we compu ed hei
s a is ical signi icance.
The s a is ically signi ican a e was es ablished by using a con inuous p obabili y
dis ibu ion based on S uden ’s concep ( -dis ibu ion); we ha e
sco e = ( Nu ,Veg·pn−2)
q1− Nu ,Veg2), (11)
whe e nis he amoun o he obse ed co ela ion phases.
When seeking a s a is ically ele an alue, we selec ed a signi icance le el o 2%,
co esponding o a qua ile o 99%. The -dis ibu ion alues o se en, ou , and h ee
deg ees o eedom equal 2.998, 3.747, and 4.541, espec i ely. I he co ela ion coe icien
exceeds he c i ical alue, he co ela ion can be conside ed s a is ically ele an .
2.5. Me hod o Ve i y he Resul ing Equa ions: A Sepa a e Co n Field
The equa ions de ining he linea ela ionship o he d y ma e alues o he co ela ed
ege a ion indices NDVI,NDRE, and GNDVI we e alida ed agains he ou comes o a
single-sho expe imen o 5 hyb ids ( he ES Joke , ES Welling on, KTG Ka laxx, Absolu is-
simo, and Rudol inio) on he day o hei ac ual ha es . The d y ma e con en p edic ions
co e ed hyb ids g own o g ain, wi h he ideal ha es window shi ed o alues be ween
380 g/kg and 420 g/kg.
In each o hese hyb ids, he in e ac ion o he acqui ed ela ionships (14)–(16) was
se down and e i ied. Using nu i ional analysis, we de e mined he d y ma e olume
in he whole plan s, and his quan i y was deno ed as he d y ma e con en ional ue
alue,
DMCTV
. Subsequen ly, we applied he ege a ion indices o compu e he p edic ed
d y ma e alue,
DMPV
, and es ablished he absolu e and ela i e de ia ions,
∆DM
and
Remo e Sens. 2023,15, 3152 16 o 19
4.5. Compa ing he Resul s
This a icle de elops he ou comes o s udy [
1
], connec ing hem wi h no el esea ch
and ou lining a mo e comp ehensi e app oach o he p oblem. While he e e enced
sou ce [
1
] e alua es one co n hyb id in one season, he p esen a icle discusses he ela ion-
ship be ween he d y ma e and he ege a ion indices o e da a collec ed du ing h ee
yea s, con i ming ha he esul s a e alid o no me ely a single hyb id, bu gene ally. In
con as , no s a is ically signi ican ela ionship o he CF has been shown, and he s a ch
alue appea ed o be ele an only in he NDVI.
A icle [
20
] examines eg ession models o es ima ing c op yield ia he NDVI and
measu emen s o ela i e c op yields (paddy ice, win e whea , and co n); he au ho s ec-
ommend using he models especially in a eas whe e he c op ypes a e no exac ly known.
In epo [
41
], he d y ma e alue was con i med ia ield e lec ance measu emen s
execu ed wi h mul ispec al sys ems (Landsa 8, RapidEye). By compa ison, ou app oach,
when con on ed wi h he sa elli e image-based da a acquisi ion, o e s he ad an age o a
highe esolu ion in he imaging and map o ming, and his capabili y hen ensu es be e
da a accu acy.
The esul s o he expe imen he ein con i m he ege a ion- o-nu i ional index da a
co ela ion de ailed elsewhe e, especially in he e e enced sou ce [
45
]. The cen al asse
o ou a icle ne e heless lies in he speci ied ma hema ical ela ionships be ween he
ege a ion and he nu i ional indices; hese ins umen s, impo an ly, acili a e de e mining
he d y ma e alue om an en i e ield and hus op imizing he ha es ime.
4.6. Limi a ions o he App oach
The p oposed me hod o UAV mul ispec al came a ield scanning and ege a ion-index-
based d y ma e compu a ion includes unce ain ies; hese unce ain ies es in he quali y
o he mul ispec al senso and also i s calib a ion o sui he season and en i onmen .
The epea abili y o he p ocedu e depends on he wea he condi ions, as he ope a ion
o an unmanned ae ial ehicle is a ec ed by ain, wind, and loca ion o he c ops o be
moni o ed ( o example, in a d one ligh es ic ion zone). A majo disad an age is he
limi ed ange o an UAV: O e a eas la ge han 200 ha, imaging wi h his me hod becomes
challenging due o he ba e y capaci y. Al e na i ely, ixed-wing UAVs may be employed
because hey p o ide a longe ange pe ba e y (~50 min); he eBee X, howe e , deli e s
up o 90 min. Using a d one is e ec i e only o la ge ege a ion uni s.
5. Conclusions
Analyzing mul ispec al images by using p ecise knowledge o c op heal h is one o
he p ocesses ha suppo s he ansi ion om adi ional a ming o p ecision ag icul u e.
Inc easing he quali y o ha es ed co n and educing he eed c op consump ion by
de e mining he co ec ha es ime will p oduce an inno a i e app oach, namely, non-
con ac analysis o he plan a di e en s ages o g ow h; his echnique will o e a po en ial
o au oma ed and apidly scalable applica ion in mos ypes o cul i a ed ege a ion. In
co n, he app op ia e ha es ime is es ablished om he amoun o d y ma e , depending
on whe he he chopped plan s a e o be ensiled o odde o used as me hane p oduc ion
ma e ial in a biogas plan . Thus, up- o-da e, accu a e knowledge o he nu i ional alues,
ideally collec ed ac oss he c op ield, embodies an essen ial ac o in selec ing he igh
ime window.
Such goals and asks can be e ec i ely pe o med by means o emo e sensing wi h a
UAV-moun ed mul ispec al came a and ia he equa ions se ou in Figu e 4. The discussed
me hod elimina es he need o chemical analysis o samples collec ed om only a ew
loca ions in a la ge ield ha suppo s he e ogeneous ege a ion. Speci ying he op imum
ha es pe iod is assigned conside able ecological and economic impo ance, especially i
ela ed o he en i e p ocessing chain; The au ho s p oceed om op imum co n ha es ing
based on he p e-de e mined olume o d y ma e o me hane p oduc ion in biogas plan s,
espec ing also he links be ween eed c op and cow milk.

Remo e Sens. 2023,15, 3152 17 o 19
The ege a ion ela ionship g aphs in Figu e 4lead o equa ions ha ind use in p e-
dic ing he op imum ha es ime ia d y ma e alues. E alua ing he in o ma ion om
he abo e chap e s, we can conclude ha he g ea es p edic ion ele ance is embedded in
Equa ion (16), which de ines he ela ionship be ween he GNDVI and d y ma e . Resul s
cha ac e izable as e y good bu somewha in e io o hose ob ained o he GNDVI we e
ound in he NDVI–d y ma e ela ionship (15). The GNDVI and NDVI alues also allow
o es ima ing he yield cha ac e is ics, such as he YFM and YDM.
In iew o he e y s ong co ela ion be ween he GNDVI and d y ma e con en
alues, he GNDVI can be desc ibed as ha ing he bes p edic ion esul s in he linea model.
The main bene i s o he me hod include he gene al alidi y o he ela ionships
be ween he ege a ion indices and he d y ma e o di e en co n hyb ids. Con e sely, a
cen al disad an age lies in he sensi i i y o clima ic condi ions; The sensing is no easible
du ing ain o hea y winds.
Au ho Con ibu ions:
Concep ualiza ion, J.J. and V.J.; me hodology, J.J. V.J. and P.M.; da a cu a ion,
J.J., V.J. and H.S.; w i ing—o iginal d a p epa a ion, J.J., V.J., P.M., H.S. and P.D.; unding acquisi ion,
P.R. All au ho s ha e ead and ag eed o he published e sion o he manusc ip .
Funding:
This pape was unded om he gene al s uden de elopmen p ojec a B no Uni e si y
o Technology.
Da a A ailabili y S a emen :
The da a p esen ed in his s udy a e a ailable on eques om he
co esponding au ho .
Con lic s o In e es : The au ho s decla e no con lic o in e es .
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