Remo e Sens. 2010, 2, 432-445; doi:10.3390/ s2020432
Remo e Sensing
ISSN 2072-4292
www.mdpi.com/jou nal/ emo esensing
A icle
Compa ing Accu acy o Ai bo ne Lase Scanning and
Te aSAR-X Rada Images in he Es ima ion o Plo -Le el
Fo es Va iables
Ma kus Holopainen 1,*, Reija Haapanen 2, Mika Ka jalainen 3, Mikko Vas a an a 1,
Juha Hyyppä 3, Xiaowei Yu 3, Saka i Tuominen 4 and Hannu Hyyppä 5
1 Depa men o Fo es Resou ce Managemen , Uni e si y o Helsinki, P.O.Box 27
(La oka anonkaa i 7), 00014 Finland; E-Mail: [email p o ec ed]
2 Haapanen Fo es Consul ing, Kä jenkosken ie 38, 64810 Vanhakylä, Finland;
E-Mail: [email p o ec ed]
3 Finnish Geode ic Ins i u e, P.O.Box 15, 02431 Masala, Finland; E-Mails: [email p o ec ed]
(M.K.); [email p o ec ed] (X.Y.); [email p o ec ed] (J.H.)
4 Finnish Fo es Resea ch Ins i u e, Me la, P.O.Box 18, 01301 Van aa, Finland;
E-Mail: saka i. uominen@me la. i
5 Resea ch Ins i u e o Modelling and Measu ing o he Buil En i onmen , Uni e si y o
Technology, Finland; E-Mail: [email p o ec ed]
* Au ho o whom co espondence should be add essed; E-Mail: m[email p o ec ed];
Tel.: +358-50-380-4984.
Recei ed: 7 Decembe 2009; in e ised o m: 13 Janua y 2010 / Accep ed: 22 Janua y 2010 /
Published: 28 Janua y 2010
Abs ac : In his s udy we compa ed he accu acy o low-pulse ai bo ne lase scanning
(ALS) da a, mul i- empo al high- esolu ion nonin e e ome ic Te aSAR-X ada da a and
a combined ea u e se de i ed om hese da a in he es ima ion o o es a iables a plo
le el. The Te aSAR-X da a se consis ed o se en dual-pola ized (HH/HV o VH/VV)
S ipmap mode images om all seasons o he yea . We we e especially in e es ed in
dis inguishing be ween he ee species. The dependen a iables es ima ed included mean
olume, basal a ea, mean heigh , mean diame e and ee species-speci ic mean olumes.
Selec ion o bes possible ea u e se was based on a gene ic algo i hm (GA). The
nonpa ame ic k-nea es neighbou (k-NN) algo i hm was applied o he es ima ion. The
esea ch ma e ial consis ed o 124 ci cula plo s measu ed a ee le el and loca ed in he
icini y o Espoo, Finland. The e a e la ge a ia ions in he ele a ion and o es s uc u e in
he s udy a ea, making i demanding o image in e p e a ion. The bes ea u e se con ained
OPEN ACCESS
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12 ea u es, nine o hem o igina ing om he ALS da a and h ee om he Te aSAR-X
da a. The ela i e RMSEs o he bes pe o ming ea u e se we e 34.7% (mean olume),
28.1% (basal a ea), 14.3% (mean heigh ), 21.4% (mean diame e ), 99.9% (mean olume o
Sco s pine), 61.6% (mean olume o No way sp uce) and 91.6% (mean olume o
deciduous ee species). The combined ea u e se ou pe o med an ALS-based ea u e se
ma ginally; in ac , he la e was be e in he case o species-speci ic olumes. Fea u es
om Te aSAR-X alone pe o med poo ly. Howe e , due o a o able empo al esolu ion,
sa elli e-bo ne ada imaging is a p omising da a sou ce o upda ing la ge-a ea o es
in en o ies based on low-pulse ALS.
Keywo ds: o es in en o y; o es planning; lase scanning; ada imaging; Te aSAR-X;
k-NN; ea u e selec ion; gene ic algo i hm
1. In oduc ion
The bigges ad ances in o es in en o y echnology in ecen yea s ha e been in applica ions based
on ai bo ne lase scanning (ALS). The wo main app oaches in de i ing o es in o ma ion om
small- oo p in ALS da a ha e been hose based on lase canopy heigh dis ibu ion (a ea-based
me hod, [1]) and indi idual ee de ec ion [2]. ALS is as accu a e as adi ional ocula ield
measu emen s in es ima ing he s and mean olume (V) a plo le el wi h a ea-based in en o y
me hods (e.g., [3,4]) o ia single- ee cha ac e is ics (e.g., [5-7]). A ea-based lase scanning is mo e
cos -e icien , due o i s spa se pulse densi y equi emen s. Fu he mo e, ee-le el es ima ion is
compu a ionally hea ie ; hus in la ge-a ea in en o ies he a ea-based app oach can, a leas cu en ly,
be conside ed mo e easible. ALS is ca ied ou a ela i ely low al i udes, which consequen ly makes
i ela i ely expensi e pe a ea uni . O he emo ely sensed da a will s ill be needed, especially when
upda ed in o ma ion is equi ed e.g.,se e al imes pe yea . O special in e es a e inexpensi e images
wi h a ou able empo al esolu ion ha can be u ilized in mul iphase sampling and change de ec ion
in addi ion o he ALS measu emen s.
A majo ad an age o ada images, compa ed wi h op ical egion sa elli e images, has been hei
eady a ailabili y ( empo al esolu ion) unde all imaging condi ions. This makes ada imaging,
especially he Syn he ic Ape u e Rada (SAR) ca ied by sa elli es, an in iguing op ion in de eloping
me hods o ope a ional in en o y o o es esou ces.
Mos commonly, he ampli ude in o ma ion o SAR backsca e ing is exploi ed in he es ima ion o
o es pa ame e s. Fo example, Le Toan e al. [8] used an ai bo ne mul i equency SAR sys em o
demons a ing he capabili y o SAR images in o es biomass e ie al and concluded ha he
c oss-pola iza ion channel o he long wa eleng hs (L and P bands) yielded he bes sensi i i ies.
La e , p omising esul s (wi h p esumably enhanced es ima ion accu acies) we e achie ed, using
SRTM (Shu le Rada Topog aphic Mission) SAR in e e ome y [9], in e e ome ic cohe ence [10],
pola ime ic SAR in e e ome y [11], and usion o SAR wi h ai bo ne lase scanning (ALS) [12]. The
ange measu emen s o ALS p o ide e y accu a e geome ic in o ma ion on o es s. The main
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ad an age o SAR, especially in he sa elli e-bo ne sys em, is he e y equen imaging capabili y in
compa ison o op ical sa elli e images, ae ial image y and ALS.
SAR measu emen s expe ienced a b eak h ough simila o ha in he ALS me hod, when in he
ea ly 2000s sa elli e ada image y wi h spa ial esolu ions as high as 1–3 m (single-pola iza ion
imaging) we e de eloped. In addi ion o he imp o ed spa ial esolu ion, he cen al imp o emen s in
he new SAR sa elli e images ha e been hei abili y o u ilize in e e ome y and pola ime y. In
combining da a om se e al sa elli e ypes, in o ma ion om di e en wa eleng h a eas can be
ob ained. These ac o s should imp o e he es ima ion accu acies in o es applica ions, compa ed wi h
p e ious ins umen gene a ions.
Raus e e al. [13] epo ed ha he es ima ion o g owing s ock olume is sligh ly mo e accu a e wi h
he ull-pola ime ic, high- esolu ion Ad anced Land Obse ing Sa elli e (ALOS) ada images han wi h
he ea lie Japanese Ea h Resou ces Sa elli e 1 (JERS-1), bu he es ima es s ill sa u a e a 150 m3/ha. An
ai bo ne senso , he Expe imen al Syn he ic Ape u e Rada (E-SAR), owned by he Ge man Ae ospace
Cen e (DLR), has been used o simula e he esul s ob ainable wi h he Te aSAR-X. Holopainen e al. [14]
compa ed E-SAR, Landsa Enhanced Thema ic Mappe (ETM) and ae ial pho og aphs in es ima ion o
plo -le el o es a iables and epo ed ela i e oo -mean-squa ed-e o s (RMSEs) o E-SAR
o 45%, 29%, 28% and 38% o Vol (m3/ha), mean diame e (Dg; cm) , mean heigh (Hg; m) and basal
a ea (BA; m2/ha), espec i ely. In combining E-SAR wi h ae ial pho og aphs, he ela i e RMSEs o he
same a iables we e 38%, 26%, 23% and 33%. Raus e e al. [15], s udied ALOS and Te aSAR-X da a
o mapping biomass in bo eal o es zone, Finland. Acco ding o hei esul s ALOS da a pe o med
be e han Te aSAR-X da a in biomass es ima ion. The phase o he HH-VV c oss-cohe ence p oduced
he highes biomass co ela ions among he Te aSAR-X ea u es.
Holopainen e al. [16] in es iga ed he heo e ical bene i o using ee species-speci ic in en o y
da a ins ead o s and-le el mean da a in o es -planning simula ions. The esul s showed ha he use o
ee species s a um da a in o es -planning simula ions is highly ele an om he iewpoin o bo h
he de elopmen o s and cha ac e is ics and he iming o logging ope a ions. The signi icance o he
s a umwise inpu da a culmina ed in he unc ioning o he specieswise g ow h models a di e en
s ages o s and de elopmen .
While ALS da a wi h e y accu a e heigh eadings and consequen h ee-dimensional (3D) p o iles
o he s and a e a g ea imp o emen o e he adi ional op ical a ea senso s used in o es
emo e-sensing applica ions, he e ha e been p oblems in ee species ecogni ion and hus also
species-speci ic es ima es. In espec o a ea-based ALS in e p e a ion, species s a um le el
cha ac e is ics a e es ima ed a a conside ably lowe accu acy le el han s and le el mean
cha ac e is ics. The ela i e RMSE o s a um le el cha ac e is ic in e p e a ion has been epo ed o
ange om 25% o 80% [17-19]. Es ima ion accu acies can ypically be imp o ed wi h a combina ion
o da a sou ces wi h complemen a y p ope ies. In he case o ALS da a, combina ion wi h ae ial
pho og aph-based ea u es has imp o ed he species-speci ic esul s [e.g., 20].
The objec i e o he s udy was o compa e he accu acy o low-pulse ALS, high- esolu ion
nonin e e ome ic Te aSAR-X ada da a and hei combined ea u e se in he es ima ion o o es
a iables a he plo le el. Gene ic algo i hms (GAs) we e used o educe he dimensions o he la ge
ea u e se s; howe e , he o iginal ea u e se s we e also used o benchma king esul s. The es ima ion
was ca ied ou wi h he nonpa ame ic k-nea es neigbou (k-NN) algo i hm. The o es a iables
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es ima ed included mean olume (Vol), basal a ea (BA), mean heigh (Hg), mean diame e (Dg) and
ee species-speci ic mean olumes o Sco s pine (VolP), No way sp uce (VolS) and deciduous ee
species (VolD).
2. Me hods
2.1. S udy A ea and Field Da a
The s udy a ea is loca ed in he icini y o Espoo, Finland (24°30’E and 60°18’N). The esea ch
ma e ial consis ed o 124 ee le el measu ed ixed- adius (7.98 m) plo s. Field measu emen da a om
hese plo s we e collec ed in 2007 and 2008. The plo s we e loca ed wi h ALS-based ee maps and he
Global Posi ioning Sys em (GPS). The ollowing a iables we e measu ed o ees ha ing a
diame e -a -b eas heigh (dbh) o o e 5 cm: loca ion, ee species and dbh. T ee heigh s we e
measu ed om 46 plo s and he heigh model was hen o mula ed. The olumes we e calcula ed wi h
s anda d Finnish models [21]. Plo -le el da a we e ob ained by summing he ee da a. S and
cha ac e is ics acco ding o he ield measu emen s a e p esen ed in Table 1.
Table 1. Mean, ange and s anda d de ia ion o he s and cha ac e is ics (n = 124).
Mean Min Max S d
Volume (Vol) 196.3 9.1 541.3 113.6
Basal a ea (Ba) 24.5 1.6 59.5 11.2
Heigh (Hg) 17.2 6.1 24.2 3.5
Diame e (Dg) 26.6 8.4 41.0 6.7
Volume, pine (VolP) 58.7 0.0 287.5 75.1
Volume, sp uce (VolS) 83.5 0.0 450.1 106.5
Volume, deciduous (VolD) 54.1 0.0 488.4 76.5
2.2. Acquisi ion and P ocessing o ALS Da a
The ALS da a we e acqui ed on 14 May 2006 wi h an Op ech3100 lase scanne . The lying al i ude
was 1,000 m. The densi y o he e u ned pulses wi hin he ield plo s was app oxima ely 4 poin s/m2.
The ALS da a we e i s classi ied in o g ound and nong ound poin s. A digi al e ain model (DTM)
was hen de eloped, using classi ied g ound poin s and lase heigh s abo e g ound (no malized heigh
o canopy heigh ) we e calcula ed by sub ac ing he g ound ele a ion om he lase measu emen s.
Canopy heigh s close o ze o we e conside ed as g ound e u ns and hose g ea e han 2 m as
ege a ion e u ns. The da a in e media e be ween hem we e conside ed as e u ns om g ound
ege a ion o bushes. Only ege a ion e u ns we e used o ALS ea u e ex ac ion. Se e al ea u es
we e ex ac ed om ege a ion e u ns o sample plo s. They included he maximum lase hi o he
plo , mean, s anda d de ia ion and coe icien o a ia ion o he canopy heigh s, pene a ion as
ege a ion e u ns e sus o al e u ns, heigh pe cen iles o he dis ibu ion o canopy heigh s om
10% o 100% wi h in e als o 10%, canopy co e pe cen ile as p opo ion o lase e u ns below a
gi en pe cen age ( om 10% o 100% wi h 10% in e als) o o al heigh . The ea u es we e calcula ed
om i s and las e u ns sepa a ely.
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2.3. Acquisi ion and P ocessing o Te aSAR-X Images
Te aSAR-X is a Ge man pola -o bi ing sa elli e equipped wi h a mode n SAR sys em using he X
band mic owa e adia ion ca ie equency (wa eleng h o 3.1 cm). The sa elli e was launched on 15
June 2007 and is capable o acqui ing e y-high- esolu ion SAR images, a i s bes wi h a spa ial
esolu ion o abou 1 m in he Spo ligh imaging mode.
In his s udy, he S ipmap imaging mode was used. S ipmap images ha e an azimu h esolu ion o
6.6 me e s and a g ound ange esolu ion o 2.0 and 2.7 me e s o he incidence angles o 36° and 26°,
espec i ely. S ipmap images ha e a coa se spa ial esolu ion han Spo ligh images, bu on he
con a y hey allow imaging o la ge a eas. Al oge he 8 dual-pola iza ion S ipmap images we e
o de ed om he es a ea. A lis o images is p esen ed in Table 2. The image acquisi ion on 5
Sep embe 2008 was cancelled o an unknown eason. The wea he condi ions p esen ed in Table 2
a e ough es ima es based on isual obse a ions and a he mome e loca ed some 20 kilome e s om
he es a ea.
Table 2. Te aSAR-X S ipmap images acqui ed om he es a ea.
Da e O bi
Incidence
angle
(mid- ange)
Pola iza ion P oduc Wea he
4 Sep embe 2008 Descending 26° VH+VV Single-look complex +13 °C, no snow, ai
5 Sep embe 2008 - - - Acquisi ion cancelled
3 Janua y 2009 Descending 26° VH+VV Mul ilook G ound Range −12 °C, os , ai
8 Janua y 2009 Ascending 36° HH+HV Mul ilook G ound Range −13 °C, os , ai
12 Ap il 2009 Descending 26° VH+VV Mul ilook G ound Range −1 °C, cloudy
17 Ap il 2009 Ascending 36° VH+VV Mul ilook G ound Range +0 °C, cloudy
9 June 2009 Descending 26° VH+VV Mul ilook G ound Range +15 °C, ain
14 June 2009 Ascending 36° VH+VV
Mul ilook G ound Range +10 °C, ai
P ocessing o he Te aSAR-X images was ca ied ou a he Finnish Geode ic Ins i u e (FGI). Fi s ,
all images we e con e ed o in ensi y images (squa ed ampli ude), because in his s udy only he
ampli ude in o ma ion o he backsca e ing was used (in e e ome ic p ocessing can be applied only
o images wi h same imaging geome ies). In o de o ex ac plo -le el speci ic o es in o ma ion, he
images should be accu a ely egis e ed wi h each o he and wi h exis ing opog aphic maps. Because
he side-looking imaging geome y o SAR causes image dis o ions, a Digi al Ele a ion Model
(DEM) and a p ope geocoding model was used in he o ho ec i ica ion p ocess. In his s udy, he PCI
Geoma ica so wa e (PCI Geoma ics, Richmond Hill, On a io, Canada) and he DEM o he Na ional
Land Su ey o Finland wi h a g ound sampling dis ance o 25 m we e used. The esul ing RMS e o s
using 26 g ound con ol poin s we e 4.5 me e s in he eas ing di ec ion and 3.8 me e s in he no hing
di ec ion. The g ound con ol poin s we e acqui ed om he digi al maps o he Na ional Land Su ey
o Finland. Finally, he o ho ec i ied images we e isually compa ed o he digi al maps and a e y
good ag eemen was obse ed. The e o e, we can sa ely assume ha he geome ic accu acy should be
good enough o ex ac plo le el in o ma ion. A alse colo usion o all se en images is p esen ed in
Figu e 1. In his case, black and da k blue a eas co espond o wa e bodies whe eas b igh whi e a eas

Remo e Sens. 2010, 2
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co espond o build-up en i onmen , bu also o a eas o s eep slopes, which a e acing o he sa elli e.
G een a eas a e co e ed by o es . The ield plo s a e loca ed in he no h-wes co ne in Figu e 1.
Figu e 1. False colo usion o all used Te aSAR-X images (Red: a e age ampli ude o
co-pola ized image channels, G een: a e age ampli ude o c oss-pola ized image channels,
and Blue: s anda d de ia ion o ampli ude o all image channels). Map p ojec ion: Finnish
Uni o m Coo dina e Sys em. O iginal Da a © 2008–2009, Ge man Ae ospace Cen e .
To collec SAR ea u es, ci cles wi h adii o 20 m we e o med using he cen e poin s o he ield
plo s. The SAR ea u e ex ac ion uni was la ge han he ield plo ( adius 7.98 m). Howe e , he
ield plo s and cha ac e is ics we e assumed o ep esen s and cha ac e is ics in he SAR ea u e
ex ac ion uni . The use o he 20-m adii ensu ed ha enough Te aSAR-X pixels could be used o
calcula e he a e age backsca e ing in ensi y and i s s anda d de ia ion o he es plo s. A e
calcula ion o he a e age in ensi y, adiome ic no maliza ion was applied o he in ensi y alues. In
he adiome ic no maliza ion, he me hod based on he p ojec ion angle was used [22]. The p ojec ion
angle based me hod uses he local slope and aspec angles o he su ace calcula ed om a DEM.
Then, he Te aSAR-X ea u es we e con e ed back o he ampli ude scale (squa e oo o in ensi y).
The e o e, he used se consis ed o 28 Te aSAR-X ea u es (a e age ampli ude and s anda d
de ia ion o se en images wi h wo pola iza ion channels) o each plo . Ve y high backsca e ing
alues can be expec ed o s eep ba en cli s acing o he sa elli e. The e o e, all ield plo s ha ing
slope angles highe han 15°, which ypically co espond o he ba en cli s, we e excluded om he
u he s udies. Finally, he Te aSAR-X ea u es o he es plo s we e expo ed o ea u e selec ion
and he plo -le el o es a iable es ima ion.
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2.4. Gene ic Algo i hm and Fea u e Selec ion
Gene ally, adding mo e ea u es in he es ima ion p ocess imp o es he ou pu accu acy, bu wi h
inc easing dimensionali y he dis inc i e capaci y o he da a may weaken, wi h inc easing noise.
The e o e, he dimensionali y o la ge da ase s mus be educed. The use ulness o any inpu a iable
can be s udied by measu ing he co ela ion be ween he image ea u es and o es a ibu es, bu his
me hod does no e eal he combined beha iou o he ea u es. Thus, il e s ha ank ea u es based
on co ela ion coe icien s a e no su icien and subse selec ion algo i hms o ea u e ans o ma ion
is needed. In ou ea lie s udies we ha e ound gene ic algo i hms (GAs) sui able o his ask [23].
GAs a e sea ch algo i hms ha mimic na u al selec ion and na u al gene ics [24].
In model cons uc ion, i is impo an o base he ea u e selec ion on he esea che 's knowledge o
he phenomenon and he a iables a ec ing i ; hus he use o s epwise selec ion me hods is gene ally
discou aged. Howe e , he e a e si ua ions in which he supe io i y o a iables A and B o e C and D
is no clea . The ela ionships o eco ded adia ion o e u ned lase pulses and o es a iables a e no
oo s aigh o wa d ( he excep ion being he canopy su ace gene a ed om lase heigh eadings) and
he e a e nume ous po en ially use ul s a is ical/ ex u al a iables ha can be ex ac ed om he da a.
The e o e, he use o au oma ed selec ion me hods is jus i ied o a ce ain ex en .
The ollowing ea u e se s we e c ea ed:
• A: 28 Te aSAR-X ea u es
• B: 48 lase ea u es
• A + B (76 di e en ea u es)
• Fea u es selec ed om se A using GA
• Fea u es selec ed om se B using GA
• Fea u es selec ed om se A+B using GA
Fea u e se s A, B and A+B we e used o benchma king he esul s ob ained wi h ea u e selec ion
by GA. Au oma ic ea u e selec ion was ca ied ou using a simple GA p esen ed by Goldbe g [24],
implemen ed in he GAlib C++ lib a y [25]. The GA p ocess s a s by gene a ing an ini ial popula ion
o s ings (ch omosomes o genomes) ha consis o sepa a e ea u es (genes). The s ings e ol e
du ing a use -de ined numbe o i e a ions (gene a ions). The e olu ion includes he ollowing
ope a ions: selec ing s ings o ma ing, using a use -de ined objec i e c i e ion, le ing he s ings in
he ma ing pool swap pa s (c ossing o e ), causing andom noise (mu a ions) in he o sp ing
(child en) and passing he esul ing s ings in o he nex gene a ion.
In he p esen s udy, he s a ing popula ion consis ed o 300 andom ea u e combina ions
(genomes). The leng h o he genomes co esponded o he o al numbe o ea u es in each s ep, and
he genomes con ained a 0 o 1 a posi ion i, deno ing he absence o p esence o image ea u e i. The
numbe o gene a ions was 30. The objec i e a iable was a weigh ed combina ion o ela i e RMSEs
o Vol, Hg, Dg, VolP, VolS and VolD, wi h o al olume ha ing a weigh o 50% and he es 10%
each. Genomes selec ed o ma ing swapped pa s wi h each o he wi h a p obabili y o 80%,
p oducing child en. Occasional mu a ions ( lipping 0 o 1 o ice e sa) we e added o he child en
(p obabili y 1%). The s ings we e hen passed o he nex gene a ion. The o e all bes genome o he
cu en i e a ion was always passed o he nex gene a ion, as well.
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Th ee consecu i e s eps we e aken o educe he numbe o ea u es o a easonable minimum.
Since he algo i hm s a s om a andom pool o genomes, he p ocess was epea ed h ee imes a
each s ep. Only ea u es belonging o he bes genome o he h ee epe i ions in each s ep we e
included in he nex s ep.
2.5. Es ima ion o Plo -Le el Fo es Va iables
The k-NN me hod was used in he o es a iable es ima ion (e.g., [26,27], (Equa ion 1)). A cen al
assump ion is ha ield plo s (o s ands) ha a e simila in eali y will be simila in he space de ined
by emo ely sensed da a ea u es, as well. The o es a iables o any image pixel can hen be
es ima ed wi h he help o e e ence ield plo s measu ed in he ield by calcula ing he a e ages o he
k nea es neighbou s. In he p esen s udy, simila i y was de e mined by he Euclidean dis ances in he
image ea u e space. Be o e calcula ion o Euclidean dis ances all ea u es we e s anda dized o a
mean o 0 and s d o 1. The nea es neighbou s we e weigh ed wi h in e se dis ances (Equa ion 2):
)(
ˆ
1
∑
=
=
k
i
ii ywy (1)
whe e:
ŷ = es ima ed alue o a iable y
yi = measu ed alue o a iable y a he i: h nea es ield plo
w = weigh o ield plo i in he es ima ion
k = numbe o neighbou s used in he es ima ion
∑
=
=
k
ii
i
id
d
w
1
2
2
1
/
1 (2)
whe e:
di = Euclidean dis ance o he i: h nea es ield plo (measu ed in he ea u e space)
An essen ial pa ame e a ec ing he esul s ob ained wi h he k-NN me hod is he numbe o
neighbou s, k, o which a alue o 5 was se in his s udy. Selec ing he alue o k is always a
comp omise: a small k inc eases he andom e o o he es ima es, while a la ge k esul s in a e aged
es ima es and educes he a ia ion a ailable in he o iginal da ase .
2.6. E alua ion o Es ima ion Accu acy
E alua ion o he es ima ion accu acy was ca ied ou using lea e-one-ou c oss- alida ion. In he
p ocess, each ield plo a a ime is le ou o he e e ence da ase and he o es a iable es ima es a e
calcula ed using he emaining ield plo s. The es ima es a e hen compa ed wi h he alues obse ed
in he ield. The RMSE (Equa ion 3), BIAS (Equa ion 5), ela i e RMSE (Equa ion 4) and ela i e
BIAS (Equa ion 6) we e de i ed om he compa isons:
n
yy
RMSE
n
i
ii
∑
=
−
=1
2
)
ˆ
(
(3)
Remo e Sens. 2010, 2
440
y
RMSE
RMSE *100% = (4)
n
yy
BIAS
n
i
ii
∑
=
−
=1
)
ˆ
(
(5)
y
BIAS
BIAS *100% = (6)
whe e:
n = numbe o plo s
y
i = obse ed alue o plo i
i
y
ˆ= p edic ed alue o plo i
i
y= obse ed mean o he a iable in ques ion.
3. Resul s
The ela i e RMSEs and biases ob ained, using he ea u es selec ed wi h GA ( educed ea u e se s)
a e p esen ed in Table 3 and hose ob ained wi h he o iginal, la ge ea u e se s in Table 4. The esul s
show ha he ALS-based ea u es pe o med a be e han he Te aSAR-X -based ea u es. The
combined ea u e se imp o ed he Vol, BA and Hg esul s sligh ly. Gene ally, Hg and Dg we e
es ima ed mo e accu a ely han Vol and BA. Bo h emo e sensing ma e ials esul ed in somewha
biased esul s.
Table 3. Rela i e RMSEs and ela i e biases (in pa en heses), % o means, o he
es ima ed s and cha ac e is ics using he educed ea u e se s.
ALS Te aSAR-X Combined
Vol 35.7 (−2.0) 55.8 (0.6) 34.7 (−1.5)
BA 28.7 (−2.1) 43.8 (0.0) 28.1 (−1.4)
Hg 14.7 (−0.1) 20.8 (0.3) 14.3 (−0.3)
Dg 21.2 (−0.2) 26.6 (−0.9) 21.4 (0.2)
VolP 98.5 (2.2) 133.7 (2.8) 99.9 (10.0)
VolS 60.1 (−1.5) 128.9 (−0.2) 61.6 (−4.4)
VolD 83.2 (−7.2) 138.2 (−0.6) 91.6 (−9.5)
Fea u es used 12 7 12