TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.5, May 2014, pp
. 4050 ~ 40
5
5
DOI: http://dx.doi.org/10.11591/telkomni
ka.v12i5.4044
4050
Re
cei
v
ed O
c
t
ober 1
3
, 201
3; Revi
se
d Decem
b
e
r
28, 2013; Accept
ed Ja
nua
ry 1
7
, 2014
A Resizing Method for 3D Visualization of Digital
Elevatio
n Models
Wei Yang
1
, Kun Hou
1,2,
*, Xintong Yu
3
, Fanhua Yu
1
1
Colle
ge of Co
mputer Scie
nc
e and T
e
chno
l
o
g
y
, Cha
ngc
hu
n Normal U
n
iv
ersit
y
,
Cha
ngch
un, 13
003
2, Chi
n
a
2
School of Co
mputer Scie
nc
e and Inform
ati
on
T
e
chnol
og
y, Northeast Nor
m
al Univ
ersit
y
,
Cha
ngch
un, 13
011
7, Chi
n
a
3
Colle
ge of Mat
hematics, Jil
i
n
Univers
i
t
y
,
Cha
ngch
un, 13
001
2, Chi
n
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: houk4
31@
ne
nu.ed
u.cn
A
b
st
r
a
ct
The div
e
rsity a
nd vers
atility
o
f
displ
a
y d
e
vic
e
s
today
i
m
p
o
s
es new
d
e
m
a
nds o
n
d
i
gita
l
elev
ation
mo
de
ls (DEMs). T
h
is pape
r propos
es a
resi
z
i
ng
me
t
hod for 3D vi
suali
z
a
t
io
n of DEMs based
on
topogr
ap
hic fe
ature. T
he pro
pose
d
me
tho
d
improves s
e
a
m
ing carv
in
g alg
o
rith
m to resi
ze DEMs inste
a
d
of
imag
es accor
d
ing to th
e cha
r
acterristics of
DEMs
. T
he prop
osed r
e
si
zing
met
hod c
o
nsid
ers not o
n
ly
geo
metric con
s
traints but a
l
s
o
the ch
aracte
ristics of
DEM
s
. Being
differ
ent from th
e traditi
ona
l red
u
c
t
ion
and ex
pans
io
n
metho
d
s, the
metho
d
not o
n
ly resi
z
e
s
DE
Ms, but also preserves the c
haracter
i
stics of
Digita
l
E
l
evati
o
n Mo
del. T
h
e
meth
od
is
i
m
pl
emente
d
and
e
x
peri
m
e
n
ts ar
e
carrie
d
out
on
actual
DEM
da
ta.
It can be see
n
from the c
o
mp
ariso
n
w
i
th scaling
metho
d
th
at the pro
pose
d
metho
d
is effi
cient a
nd pr
ovi
des
better 3D visu
a
l
i
z
a
t
io
n of DEM
s
.
Ke
y
w
ords
: 3D
terrain, 3D vis
uali
z
a
t
io
n, disp
lay dev
ice, red
u
ction a
l
g
o
rith
m, exp
ansi
on a
l
gorit
hm
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
In rece
nt years, with th
e rapid d
e
velopm
e
n
t of compute
r
tech
nolo
g
y, espe
cially
comp
uter gra
phics, 3
D
vi
sualization te
chniqu
e a
nd v
i
rtual
reality t
e
ch
niqu
e, th
e intuitive a
n
d
vivid 3D terrain visuali
z
ati
on syste
m
h
a
s be
co
m
e
the focu
s of rese
arche
s
. Compa
r
ed to
2D
plane te
rrain
whi
c
h i
s
ch
ara
c
teri
ze
d with sing
ul
a
r
ity and l
a
ck of
intuitiveness,
3D te
rrain
can
transfo
rm the
geographi
c d
a
ta and its an
alysis result
s
into dire
ct visible inform
atio
n, and ena
ble
geog
rap
h
ic i
n
formation vi
sualization a
n
d
sp
ace a
nal
ysis [1
-4]. Di
gital Elevatio
n Mod
e
ls
(DEMs)
is a
di
gital ex
pre
ssi
on
of la
ndform
surfa
c
e
and
o
ne
o
f
the b
a
si
c
da
ta to d
e
scri
be
terrain
s
, a
n
d
is
of great adva
n
tage to 3D v
i
suali
z
ation
a
nd statisti
cal
analysi
s
of terrai
n
s.
No
wad
a
ys m
o
re
and
mo
re di
splay d
e
vice
s ap
pea
r i
n
ou
r life, di
gital ca
meras, PDAs,
PADs,
cell
p
hone
s,
comp
uters an
d
so
on. Mea
n
whil
e we
want to
se
e 3
D
te
rra
ins
on diffe
re
nt
displ
a
y
devi
c
es. Differe
nt displ
a
y
devi
c
es have diffe
rent resolution
s, but
col
u
mn
and
row of
DEM
are
fixed. Th
e
re
sol
u
tion of
the DEM
should be c
h
a
nged
(redu
ce
d or expa
nde
d) in
orde
r to
fit
into different displ
a
y devices. Nu
merou
s
method
s ha
ve been deve
l
oped in rece
nt years.
Vertex clu
s
te
ring al
go
rithm
[5-8] divide
s
the ve
rtexes i
n
to som
e
vertex cluste
rs throu
g
h
spatial
pa
rtitioning, a
nd th
en me
rge
the
vertexes
wi
t
h
in the
sam
e
clu
s
ter i
n
to o
ne vertex. Ve
rtex
clu
s
terin
g
al
gorithm do
es not depend
on topologi
cal inform
ation of the model (a
djace
n
cy
relation
s), a
nd de
pen
ds on g
eomet
ric i
n
form
at
ion (ve
r
tex coordi
nate
s
).
Ho
wever, ve
rtex
clu
s
terin
g
alg
o
rithm can no
t keep the ch
ara
c
teri
stic of
the models a
nd co
ntrol e
r
rors.
Regi
on Me
rgi
ng algo
rithm
[9-14] me
rge
s
some
surfa
c
e regio
n
s to
form a surp
erface.
Based
o
n
co
plana
r
crite
r
i
on, supe
rfa
c
e alg
o
rith
m
p
a
rtitions the
vertexes into
so
me
co
nne
cted
regio
n
s an
d
use
s
polygon
al pat
ch in
st
ead
of ea
ch
regio
n
re
spe
c
tively. Finall
y
, the algo
rithm
simplifie
s th
e bo
und
ary
of polygo
nal
patch a
n
d
triangul
ates
polygon
al p
a
t
ch a
gain.
T
h
e
algorith
m
always co
nsume
too much tim
e
.
Stepwise refinement
algo
ri
thm [15-1
9
] p
r
ovide
s
a
n
a
pproxim
ation model of
the origin
al
model, a
nd i
n
crea
se
s the
details g
r
ad
ually. Then,
t
he alg
o
rithm
triangul
ates the lo
cal
regi
on
s
and do
es n
o
t
stop until the app
roxim
a
tion mod
e
l
achi
eve the
use
r
-sp
e
cifie
d
accu
ra
cy. The
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Resi
zing M
e
thod for 3
D
Visuali
z
ation
of
Digital Elevation Model
s
(Wei Yang)
4051
algorith
m
in
clud
es g
r
e
e
d
insertion
method a
nd hie
r
archi
c
al
segm
en
tation meth
od.
Comp
utation
a
l time of the algorith
m
is very high.
Vertex De
ci
mation algo
rithm [20-21]
remove
s some detail
s
and de
cre
a
se
s the
compl
e
xity of the m
odel
b
y
deleting
th
e vertexe
s
.
F
i
rstly, the
alg
o
rithm
cla
s
sifies th
e ve
rte
x
es
according to l
o
cal topol
ogi
cal structu
r
e
s
and geom
etry information (sim
ple point,
complex poi
nt,
boun
dary p
o
i
n
t, interior poi
nt and
co
rne
r
point). T
hen,
the algo
rithm
sele
cts the v
e
rtex which will
be deleted a
nd deleted all
the adjace
n
t
facets of
the
sele
cted vert
ex and triang
ulates the h
o
les
gene
rated d
u
r
ing the processing p
r
o
c
e
dure. Th
e
alg
o
rithm can n
o
t keep the smoothne
ss of the
model
s.
Edge
Colla
pse alg
o
rithm [2
2-24]
so
rts th
e ed
ge
s a
c
co
rding
to the
e
rro
r
whe
n
the
edg
es
are
delete
d
. The e
dge
wit
h
the mi
nimu
m erro
r will
b
e
delete
d
firstly. If an edg
e is
delete
d
,
the
two end
s of the edg
e will
be merged in
to one poi
nt and the relat
ed edg
es
will
be deg
rad
e
d
into
triangle
s
. Ho
wever, the al
gorithm h
a
s a
high time co
mplexity.
Trian
g
le
Coll
apse al
gorith
m
[25-27] m
e
rge
s
th
e th
re
e vertexe
s
of the tri
angl
e i
n
to on
e
vertex and
delete
s
the degrade
d ad
jace
nt triangl
es an
d the
original tri
a
ngle. The ti
me
compl
e
xity of
the algorith
m
is very high.
Wavelet [2
8]
De
comp
ositio
n meth
od
pro
v
ides
a perfe
ct
math
emati
c
al expressio
n
.
The
method was
prop
osed by Loun
sb
ery an
d De
Rose in
1994. The m
a
in prin
cipl
e of the method is
decompo
sin
g
the 3
D
mo
d
e
l into lo
w
re
solutio
n
pa
rts and
detail
s
b
y
wavelet. Th
e low re
sol
u
tion
parts a
r
e
su
bset
s of the
origi
nal m
o
dels
and
the
vertexes are wei
ghted
averag
e of t
he
corre
s
p
ondin
g
vertexe
s
’ n
e
ighb
orh
ood
s. Low
pa
ss
filter is used
to reali
z
e
an
d it sh
ows l
o
w
freque
ncy sig
nals.
T
he det
ails
i
n
clu
de a
b
stra
ct wa
vel
e
t
co
efficient
s.
Hi
gh pass filter
is used to
reali
z
e
and
it
sh
ows high
f
r
equ
en
cy
sig
nals.
The
alg
o
rithm
only
works for trian
g
le n
e
two
r
k
with
sub
d
ivision conne
ctivity.
The sim
p
le
st and mo
st pop
ular meth
od for re
si
zing th
e DEM is scal
ing method [2
9-33].
The metho
d
s mentioned a
bove co
uld b
e
use
d
to re
size the DE
M, but these
methods
are not al
wa
ys very effective to prese
r
ve the
char
a
c
t
e
ri
st
ic
s of
DE
Ms.
Mo
re
ef
f
e
ct
iv
e resi
zing
can o
n
ly be
achieve
d
b
y
consi
d
e
r
in
g the
ch
ara
c
teristics of DEMs and
no
t only geom
etric
con
s
trai
nts.
Avidan an
d
Shamir
publi
s
he
d “se
a
m
carvin
g” algo
rithm in
200
7
[34]. A simp
le imag
e
operator
call
ed seam
ca
rving that co
n
s
ide
r
s
th
e im
age
conte
n
t (conte
n
t-a
w
a
r
e image
) resi
zing
for both red
u
c
tion and exp
ansi
on is pre
s
ente
d
. A s
eam is an opti
m
al 8-conn
ected path of pixels
on a
single
i
m
age
from
to
p to
bottom,
or l
e
ft to ri
gh
t, whe
r
e
opti
m
ality is
defi
ned
by
an
image
energy functi
on. By repeat
edly ca
rv
ing
out or in
se
rting sea
m
s in o
ne direction t
he algo
rithm
can
cha
nge the a
s
pe
ct ratio of
an image.
In this pa
pe
r, we
pro
p
o
s
e a
ne
w m
e
thod for
re
sizi
ng
DEMs whi
c
h i
s
b
a
se
d on
topographi
c f
eature
(mo
u
n
t
ainou
s re
gio
n
, hill, plain,
high lan
d
, ba
sin). Sea
m
ca
rving alg
o
rith
m is
not oblivious
to the image conte
n
t, so we aim to
improve seami
n
g
carving alg
o
rithm to resi
ze
DEMs in
stea
d of im
age
s
according
to t
he
cha
r
a
c
teri
stics of
DEM
s
. Th
e p
r
op
o
s
ed
metho
d
use
s
an ene
rgy function defini
n
g the importa
ntcan
c
e of
p
o
int in DEMs.
A enery path is a conn
ected
path of low
energy point
s cro
ssi
ng th
e DEM from
top to bottom, or from l
e
ft to right. By
su
ccessively removin
g
or i
n
se
rting en
ery path,
we ca
n resi
ze the
DEMs in b
o
th
directio
ns.
2. Methodol
og
y
2.1. Computation of
DEM
Parameter
s
A DEM is a digital simulati
on of terrain
surf
a
c
e th
rou
gh limited ele
v
ation data. Elevation
data often u
s
e ab
solute
h
e
ight or
altitude. In
a math
ematical
se
n
s
e, DEM i
s
d
e
fined a
s
a t
w
o-
dimen
s
ion
a
l continuo
us fun
c
tion [35-38]:
)
,
(
y
x
D
H
(1)
Whe
r
e
)
,
(
y
x
is the plane p
o
sit
i
on of terrain
point and
H
is elevation o
f
the corre
s
p
ondin
g
point. The gradient of
)
,
(
y
x
D
at point
)
,
(
y
x
is
the following vec
t
or:
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 4050 – 40
55
4052
y
D
x
D
G
G
D
y
x
(2)
The gradie
n
t is the dire
ctio
n in whi
c
h the
f
unction in
creases the mo
st quickly at point
)
,
(
y
x
:
2
1
2
2
)
(
y
x
G
G
D
mag
D
(3)
Whe
r
e
D
is th
e maximum
value
of
)
,
(
y
x
D
as
per unit
of dista
n
ce i
n
crea
se
s. T
h
e
topographi
c f
eature
s
i
s
m
o
re
and
mo
re obviou
s
wit
h
the in
crea
sing
D
. For
con
v
enien
ce of
cal
c
ulatio
ns, we cal
c
ul
ate
point
-to-p
o
in
t
partial
de
ri
vatives
of DEMs (
x
D
and
y
D
) to
detect ed
ge
s of obvious to
pographi
c fea
t
ures. Th
i
s
le
ads to the foll
owin
g ene
rgy
function:
|
|
|
|
)
(
D
y
D
x
D
E
(4)
2.2. Reduc
ti
on Algorith
m
The key prob
lem of redu
cti
on algo
rithm i
s
ho
w to sel
e
ct the point
s to be rem
o
ved. Our
goal i
s
rem
o
ving the
ba
ckg
r
oun
d p
o
ints
whi
c
h
are
ind
epen
dent
of topog
rap
h
ic fe
ature
with l
o
w
energy. Topo
grap
hic fe
atu
r
e p
o
ints
are
with hi
g
h
e
nergy [34].
Energy fun
c
ti
on defini
ng t
he
importa
nce o
f
pixels, sin
c
e an o
p
timal
strategy to
pre
s
e
r
ve en
e
r
gy wo
uld b
e
to remove t
h
e
points with
lo
we
st en
ergy
in a
s
cendi
ng
order. if
we
remove
a
different
num
ber of p
o
ints fro
m
each row or each
column, the visual
coherence
of
the DEM will be destroyed and visual artifact
s
will be introduced [39].
Therefore,
we nee
d a
re
si
zing
ope
rato
r that ca
n pre
s
erve
the
co
ntinuity of DE
Ms. Thi
s
lead
s to the improve
d
se
a
m
carvin
g alg
o
rithm an
d the definition of
energy path
s
.
Becau
s
e
we want
to re
size
the DEMs (remove or
i
n
sert
some poin
t
s
from ea
ch row
an
d
each col
u
mn
), we firstly re
move or in
sert one point fro
m
each
ro
w a
nd col
u
mn.
Formally, let
D
be a
m
n
DEM and defin
e
a vertical en
ergy path b
a
s
ed o
n
the
x
dire
ction an
d a hori
z
ontal e
nergy path b
a
s
ed o
n
y
dire
ction to be:
1
|
)
1
(
)
(
|
,
.
.
,
}
),
(
{
}
{
1
1
i
x
i
x
i
t
s
i
i
x
p
P
n
i
n
i
x
i
X
(5)
1
|
)
1
(
)
(
|
,
.
.
,
))}
(
,
{(
}
{
1
1
j
y
j
y
j
t
s
j
y
j
p
P
m
j
m
j
y
j
Y
(6)
Whe
r
e
x
is a
mappin
g
of
m
n
x
,
,
1
,
,
1
:
and
X
P
is a vertical en
ergy
path in
DEM
from top to bottom (the first row to the last ro
w), co
ntaining on
e, and only one, point in each ro
w
of the DEM. Similarly,
y
is a mappin
g
of
n
m
y
,
,
1
,
,
1
:
and
Y
P
is a horizontal
energy path in DEM from l
e
ft to right (the first col
u
mn
to the last co
lumn).
The definitio
n
s
of
X
P
and
Y
P
lea
d
to the follo
wing
optimal
energy path (OEP, the path
to be remove
d or inserte
d
)
*
P
that minimizes
this
path cos
t:
n
i
i
P
P
p
D
E
P
E
P
1
*
))
(
(
min
)
(
min
(9)
The optim
al energy path
can
be foun
d
usin
g
dynam
ic prog
rammi
ng [40]. First comp
ute
the cumulativ
e
minim
u
m e
nery fo
r all
po
ssi
ble
co
nne
cted path
s
fo
r
each p
o
int in
the DEM.
Th
en
backtra
ck to find the path o
f
the optimal energy path.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Resi
zing M
e
thod for 3
D
Visuali
z
ation
of
Digital Elevation Model
s
(Wei Yang)
4053
The propo
se
d red
u
ctio
n a
l
gorithm i
s
an
it
erative pro
c
e
ss by repe
atedly removi
ng OEP
as
follows
:
Step 1, Calculate REM, which is the number
of columns (rows) which
will be removed.
Setp 2, Calcu
l
ate EnergyM
a
trix, which
st
or
e
s
the ene
ry of each poi
nt in the DEM.
Step 3, Loop,
step is 1, fro
m
1 to REM DO
Step 3.1, Find a OEP.
Step 3.2, Re
move the OEP.
3.3. Expansi
on Algorith
m
The p
r
o
p
o
s
e
d
expa
nsi
on
algorith
m
i
s
also
an
iterat
ive pro
c
e
s
s b
y
repe
atedly
inse
rting
energy path a
s
follows:
Step 1, Calculate ADD, whi
c
h is the num
ber
of columns (rows)
whi
c
h will be added.
Setp 2, Calcu
l
ate EnergyM
a
trix, which
st
or
e
s
the ene
ry of each poi
nt in the DEM.
Step 3, Loop,
step is 1, fro
m
1 to ADD DO
Step 3.1, Find the ADD O
EPs.
Step 3.2, Co
mpute the
averag
e of the l
e
ft neighb
ors and
right n
e
i
ghbo
rs
of the
ADD
OEPs and
st
ore the ave
r
age value
s
i
n
ADD ave
r
a
ge OEPs (A
OEPs, top a
nd bottom in
the
hori
z
ontal ca
se).
Step 3.3, Add the ADD AO
EPs into the raw DEM.
3. Results a
nd Discu
ssi
ons
We sele
cted
GTOPO3
0 DEM for ou
r study. GTO
P
O30 is a g
l
obal digital
elevation
model
(DEM
) with a
ho
rizontal g
r
id
sp
acin
g of
3
0
arc second
s.
GTOPO
30
wa
s de
rived
from
several ra
ster and vector source
s of topogra
phi
c information. Fo
r e
a
sie
r
distri
but
ion, GTOPO3
0
has b
een divi
ded into tiles [41]. The study are
a
(Fig
ure 1
)
, betwe
en ea
st longi
tude 20° to 6
0
°
and
south l
a
titude 10
° to 6
0
°, is lo
cate
d
in so
uthea
st Africa.
Th
ere are 750 ro
ws by
600 colu
m
n
s
in the raw
DE
M matrix.
Figure 1. The
GTOPO30
DEM of the Stu
d
y Area
In order to examine the
suitability and perfo
rmance of the propos
ed method, it was
impleme
n
ted on
the study area. We
co
mpare
t
he
propo
sed
re
du
ction m
e
thod
to the
stand
ard
scaling m
e
th
od whi
c
h i
s
si
mplest a
nd m
o
st pop
ula
r
. Figure
2 and
3 sho
w
the
DEM re
size
d u
s
i
n
g
the scali
ng
a
nd p
r
op
osed
method
s
re
spectively
. Th
ere
are 3
75
rows
by 30
0
col
u
mn
s in
the
resi
ze
d DEM.
Based
on th
e com
pari
s
o
n
of the tw
o figure
s
, it ca
n be seen that
the pro
p
o
s
e
d
method is a
b
le to preserve
the characte
ristics
of DEM. It can be con
c
lud
ed from the com
pari
s
o
n
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 4050 – 40
55
4054
that the prop
ose
d
method
is efficient and provid
es
better 3D visualization of DEM. Contra
ry to
the scalin
g
method, the
prop
osed m
e
thod will
not
alter imp
o
rta
n
t topog
raphi
c featu
r
e of t
he
DEM (a
s defi
ned by the en
ergy functio
n
), and
pre
s
e
r
ve the cha
r
a
c
teristi
cs of the
DEM.
Figure 2. The
DEM Re
size
d usin
g the Scalin
g
Method
Figure 3. The
DEM Re
size
d usin
g the
Propo
se
d Re
ductio
n
Meth
od
4. Conclusio
n
In this p
ape
r,
we
present
a metho
d
for DEM
re
sizi
n
g
. The
pro
p
o
s
ed
metho
d
i
m
prove
s
seami
ng ca
rving
alg
o
rithm
to
re
size DEMs
in
stea
d of
image
s a
c
co
rding
to the
chara
c
te
rri
stics of
DEMs. T
he
prop
osed
re
sizing
metho
d
co
nsi
ders
n
o
t only ge
om
etric
co
nst
r
ai
nts b
u
t also
the
cha
r
a
c
teri
stics of
DEMs.
We
woul
d li
ke to ex
tend
the p
r
op
osed
method to
ot
her
domai
ns,
4D
GIS would be
the first.
Ackn
o
w
l
e
dg
ements
This re
se
arch is supp
orte
d by the
Nat
u
ra
l
Scie
nce
Found
ation
o
f
Cha
n
g
c
hu
n
No
rmal
University. The auth
o
rs g
r
atefully a
c
kn
owle
dge
th
e helpful comm
ents
a
nd sug
gestio
n
s of
the
reviewers, wh
ich have imp
r
oved this pa
p
e
r.
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h
ang
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g
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2
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2302-4
046
A Resi
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e
thod for 3
D
Visuali
z
ation
of
Digital Elevation Model
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(Wei Yang)
4055
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