6.92.8
P ese ing Spa ial Pa e ns in Poin
Da a: A Gene aliza ion App oach
Using Agen -Based Modeling
Ma in Knu a and Jochen Schiewe
A icle
h ps://doi.o g/10.3390/ijgi13120431
Ci a ion: Knu a, M.; Schiewe, J.
P ese ing Spa ial Pa e ns in Poin
Da a: A Gene aliza ion App oach
Using Agen -Based Modeling. ISPRS
In . J. Geo-In . 2024,13, 431. h ps://
doi.o g/10.3390/ijgi13120431
Academic Edi o s: Wol gang Kainz
and Flo ian H uby
Recei ed: 17 Sep embe 2024
Re ised: 19 No embe 2024
Accep ed: 27 No embe 2024
Published: 30 No embe 2024
Copy igh : © 2024 by he au ho s.
Published by MDPI on behal
o he In e na ional Socie y o
Pho og amme y and Remo e Sensing.
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
P ese ing Spa ial Pa e ns in Poin Da a: A Gene aliza ion
App oach Using Agen -Based Modeling
Ma in Knu a * and Jochen Schiewe
Lab o Geoin o ma ics and Geo isualiza ion (g2lab), Ha enCi y Uni e si y Hambu g, Henning-Vosche au-Pla z
1, 20457 Hambu g, Ge many; jochen.schiewe@hcu-hambu g.de
*Co espondence: ma in.knu a@hcu-hambu g.de
Abs ac : Visualiza ion and in e p e a ion o use -gene a ed spa ial con en such as Volun ee ed
Geog aphic In o ma ion (VGI) is challenging because i combines eno mous da a olume and he e o-
genei y wi h a spa ial bias. When dealing wi h poin da a on a map, hese cha ac e is ics can lead o
poin clu e , educing he eadabili y o he map p oduc and misleading use s o alse in e p e a ions
o pa e ns in he da a, e.g., ega ding speci ic clus e s o ex eme alues. Wi h his wo k, we p o ide
a amewo k ha is able o gene alize poin da a, p ese ing spa ial clus e s and ex eme alues
simul aneously. The amewo k consis s o an agen -based gene aliza ion model using p ede ined
cons ain s and measu es. We p esen he a chi ec u e o he model and compa e he esul s wi h
me hods ocusing on ex eme alue p ese a ion as well as clu e educ ion. As a esul , we can s a e
ha ou agen -based model is able o p ese e elemen a y cha ac e is ics o poin da ase s, such as
he poin densi y o clus e s, while also e aining he exis ing ex eme alues in he da a.
Keywo ds: poin gene aliza ion; agen -based modeling; cons ain s; spa ial pa e n
1. In oduc ion
Use -gene a ed geog aphic con en (UGGC) has eme ged as one o he main da a
sou ces o esea che s in ecen yea s, o en e e ed o as Volun ee ed Geog aphic In o -
ma ion (VGI) [
1
]. The isualiza ion and in e p e a ion o VGI da a a e challenging because
o i s eno mous olume and he e ogenei y, and when compa ed o adi ional spa ial sam-
pling echniques, VGI poin da a samples such as poin s o in e es o loca ions o social
media pos s o en ha e a spa ial bias [
2
] (see Figu e 1, whe e he numbe o Flick pos s
does no e lec he quali y o he iew owa ds he landma k bu mainly he popula i y o
he place). I VGI poin da a a e p esen ed on a map, hese da a cha ac e is ics could educe
he eadabili y due o o e lapping poin symbols, which could possibly hide speci ic spa ial
pa e ns in he da a—such as ex eme alues, clus e s o ho spo s. Acco dingly, a educ ion
in he o e all numbe o poin s is needed o imp o e he eadabili y o he map, while a
he same ime, he spa ial pa e ns wi hin he da a ha e o be p ese ed.
The ca og aphic solu ion o he p oblem o o e lapping poin symbols—i.e., he dis-
play o clu e [
3
,
4
]—is poin gene aliza ion, using ope a ions such as selec ion, agg ega ion,
simpli ica ion, o displacemen . Howe e , i hese gene aliza ions a e applied incau iously,
speci ic cha ac e is ics o he da a, such as ex eme alues, may disappea , misleading
use s o alse in e p e a ions o he unde lying spa ial phenomena (see Figu e 2). The e o e,
i is key o p ese e spa ial pa e ns du ing he gene aliza ion p ocess. Mo e gene ally,
p ese ing spa ial pa e ns con ibu es o he p inciple ask o map gene aliza ion, which is
o p o ide he bes ep esen a ion o he map con en wi hou neglec ing eadabili y.
In ecen decades, di e en app oaches e ol ed o mimic he wo k o human ca og a-
phe s wi h he aim o au oma ing he map gene aliza ion p ocess. The ule-based app oaches
we e buil on s epwise, local ans o ma ions o map objec s, ollowing unambiguous p e-
de ined ules [
5
]. While ule-based gene aliza ion was—and s ill is—a e y p omising ool
ISPRS In . J. Geo-In . 2024,13, 431. h ps://doi.o g/10.3390/ijgi13120431 h ps://www.mdpi.com/jou nal/ijgi
ISPRS In . J. Geo-In . 2024,13, 431 2 o 13
o a a ie y o applica ions, a majo sho coming in he pas was he p oblem ha hese
au oma ed sys ems do no ha e he abili y o espond o da a a ia ion o speci ic, ask-
ela ed equi emen s in a way ha human ca og aphe s could do by modi ying hese ules.
This led o he in oduc ion o he cons ain -based app oach, whe e cons ain s ope a e
as equi emen s ha shall be ul illed in he inal—i.e., gene alized—map bu wi hou any
p ede ined ac ions bound o hem. Map gene aliza ion using a cons ain -based app oach
is, he e o e, an op imiza ion p oblem, whe e he ask is o ind a map s a e ha bes ul ils
all p ede ined—and some imes con adic ing—cons ain s, while a se o gene aliza ion
ope a ions is used o each his op imal map s a e by manipula ing he map objec s.
Figu e 1. Loca ion o Flick pos s agged wi h a ia ions in he names o ei he C is o Reden o (“Tag
A”) o he Suga loa Moun ain (“Tag B”) in Rio de Janei o. The spa ial dis ibu ion o poin s in his
da ase mainly o igina es om he popula i y o he places and no only in he quali y o hei line o
sigh owa d he wo landma ks. The e o e, i is no possible o de i e he bes pho o spo s jus om
he numbe o pos s a he espec i e loca ions.
Figu e 2. Example o poin gene aliza ion. (a) O iginal da a o 50 poin s wi h wo main clus e s
and eigh ex eme alues (in ed). (b) Gene alized da a o 25 poin s using poin selec ion based on
alue. All eigh ex eme alues a e p ese ed du ing gene aliza ion, while he wo-poin clus e s
disappea ed in he esul ing map. (c) Gene alized da a o 25 poin s using poin simpli ica ion based
on loca ion. Bo h clus e s a e p ese ed, while only ou o he eigh ex eme alues a e p ese ed.
I bo h he spa ial dis ibu ion o e en s and he occu ence o ex eme alues a e o in e es , bo h
gene aliza ion esul s can mislead use s o alse in e p e a ions o he unde lying spa ial phenomena.
ISPRS In . J. Geo-In . 2024,13, 431 3 o 13
Fo he op imiza ion p ocess, Ha ie and Weibel
[6]
a gued ha agen -based modelling
(ABM) is he mos powe ul modelling me hod in e ms o applicabili y. In his case,
he agen s a e au onomous map objec s a emp ing o minimize a gi en cos unc ion,
which consis s o cons ain measu es. Duchêne e al.
[7]
desc ibed his echnique in de ail.
In his pape , we wan o ollow his esea ch, implemen ing an agen -based model using
p ede ined cons ain s, which a e deduced by Knu a and Schiewe
[8]
based on a s udy
analyzing use beha io when sol ing in e p e a ion asks on poin da a [9].
The emainde o his pape is s uc u ed as ollows: In he second chap e , we summa ize
app oaches om he li e a u e o poin gene aliza ion (Sec ion 2.1), pa e n p ese a ion
(Sec ion 2.2) and agen -based modeling in ca og aphy (Sec ion 2.3). In he hi d sec ion, we
desc ibe he cons ain s we used du ing he op imiza ion p ocess (Sec ion 3.1 and in oduce
ou model (Sec ion 3.2). We hen conduc expe imen s (Sec ion 4) and discuss he esul s
(Sec ion 5) be o e concluding ou wo k (Sec ion 6).
2. Rela ed Wo k
2.1. Poin Gene aliza ion
Focusing on he p oblem o poin gene aliza ion, ope a ions such as agg ega ion,
simpli ica ion, selec ion, and displacemen a e o majo in e es . When using agg ega ion
(i.e., poin clus e ing), poin clus e s a e eplaced wi h agg ega o ma ke s. Di e en clus e
ini ializa ion me hods can he eby igge qui e di e en esul s o he same da a (e.g.,
see [
10
]). Fu he mo e, Meie
[11]
e alua es and compa es ma ke clus e echniques and
simila app oaches, including hea maps and iled hea maps. Poin simpli ica ion desc ibes a
poin educ ion based on geome ic c i e ia, such as minimum dis ances be ween poin s [
12
].
When seman ic c i e ia a e used o educe he o e all numbe o poin s, a poin selec ion
akes place, e.g., based on scale [
13
]. In con as , poin displacemen eloca es poin s o
educe poin clu e , using an i e a i e wo k low o o e lap de ec ion, eloca ion, and e-
e alua ion [14].
While hese ope a ions all ep esen he adi ional me hod o poin gene aliza ion
based on ca og aphic scene judgemen , he e a e also da a-d i en me hods such as deep
lea ning [
15
], which can be u ilized o he applica ion o poin gene aliza ion, as pe o med
by Xiao e al.
[16]
. Based on aining da a c ea ed h ough manual labeling, hei model
p edic s he p obabili y o each poin in he da ase o be e ained a e gene aliza ion.
Depending on he numbe o poin s eques ed o he inal map, he espec i e poin s wi h
he highes e aining p edic ion a e hen selec ed.
2.2. P ese ing Spa ial Pa e ns
The a o emen ioned ope a ions ocus on he i s ask o map gene aliza ion—inc easing
map legibili y—mainly by emo ing a ce ain amoun o poin s. By con as , p ese ing
he p esen in o ma ion o he poin da a as much as possible is he second ask o map
gene aliza ion—and possibly con adic ing he i s . The eby, he ques ion a ises as o which
spa ial poin pa e ns a e o in e es . A s udy conduc ed by Knu a and Schiewe [9] analyzed
use beha io when in e p e ing spa ial poin pa e ns and he eby e ealed wo main aspec s.
Fi s , he p opo ion o poin s be ween di e en pa e ns, as well as be ween dense and spa se
a eas, was c ucial o he ask-sol ing p ocess o he pa icipan s. Second, he p opo ion be-
ween di e en classes wi hin an a ea—o hei espec i e absence—was equen ly desc ibed
du ing decision-making. As a esul o his s udy, poin pa e n p ese a ion can be desc ibed
as a mul i-c i e ia decision, a echnique ha has al eady been p oposed in ca og aphy o
speci ic asks wi hin he wo k low o au oma ed map gene aliza ion [
17
] and o class in e al
selec ion [
18
]. Based on he la e wo k on cho ople h maps, Chang and Schiewe
[19]
we e
able o p ese e spa ial pa e ns such as local ex eme alues and ho o cold spo s. As an
example o p ese ing a spa ial poin pa e n o isualiza ion pu poses, Qiang e al.
[20]
used a py amid modeling amewo k and poin densi y me ics in hei wo k. Fo some
applica ions, i could also be use ul o isualize poin pa e ns wi h espec o o he geome y
ISPRS In . J. Geo-In . 2024,13, 431 4 o 13
objec s, such as s ee ne wo ks [
21
]. To he bes o ou knowledge, app oaches o poin
pa e n p ese a ion wi h espec o poin densi y and local ex eme alues a e s ill missing.
2.3. Agen -Based Modeling in Map Gene aliza ion
In addi ion o he nume ous ad ances in he op imiza ion o indi idual gene aliza ion
ope a ions, he e is also conside able wo k ega ding he o ches a ion o hese ope a ions.
E en be o e Ha ie and Weibel
[6]
iden i ied agen -based modeling as he mos powe ul
applicable modelling me hod, he e we e mul iple esea ch s udies o au oma ed gene -
aliza ion sys ems ha elied on his app oach. Fo a de ailed o e iew, we e e o he
wo k o Duchêne e al.
[7]
, who explain he basic p inciples o his app oach, desc ibe
di e en implemen a ions o agen -based models a he F ench Na ional Mapping Agency
(IGN), and discuss he ad an ages and d awbacks o mul i-agen sys ems o ca og aphic
gene aliza ion. Acco dingly, he implemen a ions in oduced in he ollowing sec ions o
his pape a e based on his wo k.
These mul i-agen sys ems ely on he de ini ion o a se o cons ain s and hei espec i e
measu es, which de ine he le el o sa is ac ion o each cons ain . The eby, Mackaness and
Ruas
[22]
dis inguish be ween h ee le els o measu es: mic o-measu es ocus on indi idual
ea u es o map objec s, meso-measu es desc ibe p ope ies o g oups o objec s, and mac o
measu es deal wi h cha ac e is ics o he whole map da a. Fu he mo e, he au ho s dis in-
guish be ween in e nal measu es ha desc ibe single da ase s, and ex e nal measu es ha
desc ibe ela ions be ween di e en da ase s o map s a es, o example be ween he o iginal
and he gene alized map. Wi h ega d o con en , Bea d
[5]
classi ied cons ain s in o six
hema ic ca ego ies: posi ion, opology, shape, s uc u e, unc ion, and legibili y. Consequen ly,
ou wo k also elies on a subse o hese cons ain s.
3. Me hod
3.1. De ini ion o Cons ain s
We de ine h ee di e en ypes o cons ain s and espec i e measu es ha can guide
he gene aliza ion p ocess wi hin ou agen -based model. The i s ype is cons ain s
ha co espond wi h he speci ic kind o asks we aim o , such as he iden i ica ion o
ex eme alues o dense clus e s, and he e o e ensu e ha spa ial pa e ns a e main ained.
The second ype o cons ain s suppo s he ask-sol ing p ocess o he use s and esul
om he a o emen ioned use s udy [
9
]. The las ype o cons ain e lec s he undamen al
equi emen s o success ul poin gene aliza ion, such as a educ ion in clu e o he
p ese a ion o Ges al Law ules wi hin he map.
Table 1lis s hese cons ain s. Fo mo e de ails on he de ini ion o hese measu es,
we e e o he wo k o Knu a and Schiewe
[8]
, in which he au ho s iden i ied a se o
cons ain s by ansla ing he ou comes o hei s udy [9] in o measu able alues.
Table 1. Rele an cons ain s and measu es based on [
8
]. Cons ain s a e de i ed om ei he ask
equi emen s ( ype 1), esul s o a use s udy [
9
] ( ype 2) o undamen als o poin gene aliza ion
( ype 3).
Cons ain (Type) Measu e
Re ain p opo ion o poin s be ween a eas (2) spa ial dis ibu ion o poin s [23]
P ese e anking o densi ies be ween a eas (2) clus e densi y anking [23]
P ese e local ex eme alues (1) local ex eme alue p ese a ion
Main ain a leas one poin pe class (2) poin ca ego y p ese a ion
P ese e clus e densi y (1) mean dis ance o clus e membe s
P ese e spa ial co ec ness (3) dis ance o o igin loca ion
Reduce numbe o poin s (3) numbe o poin s ia Radical Law [24]
P ese e Ges al law ules o clus e shape (3) con ex hull o alpha shape [25]
P ese e Ges al law ules o clus e o ien a ion (3) minimum bounding ec angle

ISPRS In . J. Geo-In . 2024,13, 431 5 o 13
3.2. A chi ec u e o he Agen -Based Model
3.2.1. Gene al A chi ec u e
The agen -based model is implemen ed using he open-sou ce amewo k Mesa [
26
]
and i s spa ial ex ension Mesa-Geo [
27
]. Mesa is w i en in Py hon and o e s he basic ABM
unc ionali ies by p o iding ou co e componen s (Model, Agen , Schedule and Space)
alongside wo addi ional componen s o analysis and isualiza ion. The Model class is he
main class o he amewo k and con ols he majo componen s o he sys em. In his class,
he ini ial s a e o he model is de ined, as well as he ac ions ha happen while he model
is unning. The Model class also c ea es he agen s ha implemen he Agen class and he
Schedule class, which con ols he ime and he ac i a ions du ing un ime. Mesa o e s
ou di e en schedule ac i a ions, namely he BaseSchedule , which ac i a es agen s one a
a ime in he s a ing o de , RandomAc i a ion, which ac i a es he agen s in andom o de ,
Simul aneousAc i a ion, which ac i a es all agen s a he same ime, and S agedAc i a ion,
whe e he ac ion wi hin one model s ep is di ided in o se e al s ages, and all agen s execu e
one s age be o e mo ing o he nex s age. Fo models ha equi e he concep o space,
he espec i e Space class in Mesa has i e gene al de ini ions o space: Con inuousSpace
whe e agen s ha e (x,y) posi ions, Ne wo kG id, which implemen s g aphs wi h nodes
and edges, and h ee ypes o g ids (SingleG id,Mul iG id and HexaG id). Howe e , Mesa
does no di ec ly suppo he in eg a ion o geog aphical da a in o he model, and so he
spa ial ex ension Mesa-Geo was de eloped by Wang e al.
[27]
, allowing use s o impo ,
manipula e, isualize and expo geog aphical da a. The e o e, he new class GeoSpace was
added, which can consis o mul iple laye s o ec o and as e da a. Fu he mo e, Mesa-
Geo dis inguishes be ween Agen Laye s, which con ain GeoAgen s ha ca y ou ac i i ies
du ing he simula ion, and Vec o Laye s, which emain s a ic (e.g., oad ne wo ks).
Figu e 3shows he a chi ec u e o ou ABM applica ion o poin gene aliza ion,
which consis s o h ee modules. The Co e Module con ains he main Model class, a class o
di e en ypes o MapAgen s, he Schedule class and se e al ins ances o he GeoSpace
class. The Da aCollec o class o he U ili y Module collec s and p o ides he in o ma ion
du ing un ime o he Visualiza ion class o he Use In e ace Module, which also con ains
wo classes o he speci ica ion o he map and he pa ame iza ion o he cons ain s
and measu es o he model. In he ollowing, he modules and hei in e connec ions a e
explained in de ail.
Figu e 3. A chi ec u e o he agen -based poin gene aliza ion model.
ISPRS In . J. Geo-In . 2024,13, 431 6 o 13
3.2.2. Use In e ace Module
The i s s ep o un he model is o de ine global map speci ica ions, such as he scale
o he o iginal and he a ge map, he bo de s o he map ame, and whe he he o iginal
da a se is al eady ul illing legibili y cons ain s. I his is he case, he a ge numbe o
poin s a e gene aliza ion can be calcula ed, e.g., using he Radical Law [
24
]. Fu he mo e,
he desi ed beha io o he map agen s ega ding hei ul illmen o he selec ed cons ain s
has o be p ede ined. The common wo k low in agen -based map gene aliza ion o ansla e
a lis o cons ain s in o a sa is ac ion alue ep esen ing he s a us o a map agen consis s
o wo s eps [
28
]: Fi s , he espec i e measu es o he cons ain s a e ansla ed in o
a Like -like sa is ac ion scale acco ding o p ede ined h eshold alues, anging om 1
(“unaccep able”) o 8 (“pe ec ”). Second, global sa is ac ion is calcula ed based on he
indi idual sa is ac ion alues, o example by calcula ing he mean alue o by u ilizing
p inciples om Social Wel a e O de ings (SWO) [28].
Figu e 4lis s he di e en ypes o pa ame e s ha ha e o be de ined be o e un-
ning he agen -based model. In addi ion o he a o emen ioned global map speci ica ions,
he basic model pa ame e s, and a lis o cons ain s, as p esen ed in Table 1, he de ini-
ion o , easonable h eshold alues a e essen ial o he success o an agen -based map
gene aliza ion model, bu i is also a complex ask. To help wi h his p ocess o model
pa ame iza ion, we adap ed an app oach o Taillandie and Ga u i
[29]
using a human–
machine dialogue. The e o e, we o e a guided use in e ace o adjus he h esholds
o each measu e sa is ac ion unc ion and isualize he impac o selec ed h esholds ia
samples on a map o ob ain a be e unde s anding o he impac s o he h esholds on he
cons ain sa is ac ion and on he expec ed esul s o he gene aliza ion p ocess in gene al.
Fo example, dec easing he h eshold alues o he minimum dis ance be ween agen s
ensu es ha he agen s a e mo e likely o decide o pe o m gene aliza ion ope a ions ha
imp o e hei sa is ac ion ega ding his measu e, such as inc easing he dis ance o hei
neighbo s using displacemen , o dele ing hemsel es as a esul o a selec ion ope a ion.
As a esul , he dis ance be ween indi idual agen s will likely inc ease on he inal map,
while he numbe o poin s will dec ease.
Figu e 4. Lis o pa ame e s and examples o manual pa ame e de ini ions using a human–machine
dialogue as sugges ed by Taillandie and Ga u i
[29]
. As an example, adjus ing he o e lay ac-
cep ance h esholds o he espec i e measu e-sa is ac ion unc ion by allowing a smalle dis ance
be ween Poin Agen s will p obably esul in se e al o e lapping poin s s ill exis ing in he inal map.
3.2.3. Co e Module
A simpli ied model low is shown in Figu e 5. When ini ializing he model, a Ma-
pAgen is c ea ed o e e y poin wi hin he da a se , which should be gene alized. Fu -
he mo e, MapAgen s a e c ea ed o e e y clus e wi hin he o iginal poin da a se .
MapAgen s a e he cen al pa o ou model and hei decision-making p ocess ollows he
wo k o Duchêne e al.
[7]
, which decomposes he “b ain” o agen s in map gene aliza ion
sys ems in o h ee main componen s: capaci ies, men al ep esen a ion and p ocedu al
knowledge. The capaci ies o MapAgen s include he abili y o pe cei e hei su ounding
space—i.e., poin s in hei neighbo hood— o e alua e hei own s a e, o communica e wi h
o he agen s, and o pe o m gene aliza ion ope a ions on hemsel es. Spa ial ope a ions
o sel -e alua ion and sel -gene aliza ion a e he eby p o ided and con olled by he
ISPRS In . J. Geo-In . 2024,13, 431 7 o 13
GeoSpace class. The pa o he b ain ha ep esen s he men al s a e o he agen s compa es
i s cu en s a us wi h he goals he agen s a e aiming o —i.e., he men al ep esen a ion
o MapAgen s desc ibes hei ul illmen owa ds he p ede ined map cons ain s, using
he measu e sa is ac ion unc ions e ie ed as desc ibed abo e. Fu he mo e, his pa
o he MapAgen s’ b ain memo izes all p e ious decisions and hei espec i e ou comes.
The ac ual decision-making is unde aken in he p ocedu al knowledge pa o he MapA-
gen s. Using he in o ma ion abou i s cu en s a e o cons ain sa is ac ion and i s o me
decisions and hei ou comes, each MapAgen decides which gene aliza ion ope a ion i
wan s o pe o m nex .
Figu e 5. Simpli ied model low cha wi hou de ails o he decomposed “b ain” o he MapAgen s.
A e ini ializing he MapAgen s o poin s and clus e s, each model s ep begins by calcula ing he
measu es o analyze he ac ual s a e o cons ain ul illmen . Using he measu e-sa is ac ion unc ions
o each cons ain , all MapAgen s ecei e a lis o sa is ac ion alues anging om 1 (wo s ) o 8 (bes )
ep esen ing hei own s a e. Based on his, MapAgen s can calcula e hei own o e all sa is ac ion,
and a gene al model s a e can be de e mined. I he o e all model s a e does no each an equilib ium
model s a e—o ma ch he model e mina ion condi ions—MapAgen s can pe o m gene aliza ion
ope a ions on hemsel es, and he nex s ep is ini ialized.
4. Expe imen s
We wan o es ou model by gene alizing a es da a se om a scale o 1:15,000 o a
scale o 1:30,000. The aim is o suppo he p ese a ion o spa ial pa e ns du ing poin
gene aliza ion. In addi ion o speci ic pa e ns such as local ex eme alues, i is also o
in e es o main ain poin densi ies wi hin clus e s as well as in spa se a eas.
Because app oaches o poin pa e n p ese a ion conside ing bo h poin densi y and
local ex eme alues a e s ill missing, we wan o compa e he esul s o ou model wi h
di e en me hods ocusing on spa ial dis ibu ion and ex eme alue p ese a ion. Fo he
gene aliza ion o spa ial dis ibu ion cha ac e is ics, we u ilized a quad ee s uc u e.
We ill his quad ee s uc u e (capaci y = 1) sequen ially wi h a poin da a se and hen
dele e all poin s ha a e assigned o lea es wi h an a ea below he poin signa u e size
h eshold o he a ge scale. In o he wo ds, we only e ain poin s ha a e assigned o
lea es o he quad ee o a p ede ined h eshold le el o highe . Fo he p ese a ion o
local ex eme alues, we used he disc e e isola ion algo i hm o G öbe and Bu gha d [
13
],
which calcula es a poin ’s dis ance o he closes poin wi h a highe alue, which in he
nex s ep can be used as a selec ion pa ame e o poin gene aliza ion.
4.1. Da a
We u ilized a da a se ha shows he loca ions o social media images om he pla o m
Flick ha con ain a leas one bicycle [
30
]. Ou es da a se con ains 800 o hese da a poin s,
which a e all loca ed in he a ea o D esden, Ge many. We chose his da ase because i
ul ils wo equi emen s we wan o es ou model wi h: Fi s , he poin dis ibu ion is
clea ly biased in a way ha is cha ac e is ic o VGI da a, as he majo i y o poin s a e loca ed
in a ela i ely small a ea a ound he ci y cen e , while he e a e only ew ou lie s sp ead
o e he subu bs. Second, he da a se p o ides he numbe o bicycles pe social media
ISPRS In . J. Geo-In . 2024,13, 431 8 o 13
image, which can be used o de e mine local ex eme alues, i.e., pho os ha show a high
numbe o bicycles.
4.2. Pe o mance Me ics
To e alua e he pe o mance o ou model in compa ison o he quad ee gene al-
iza ion and he disc e e isola ion algo i hm, we de ine me ics o e alua e poin densi y
p ese a ion, as well as local ex eme alue p ese a ion. Fo poin densi y p ese a ion,
we i s de ine clus e s wi hin he o iginal da ase using he DBScan algo i hm. Based on
hese eigh clus e s, we measu e he poin densi y be o e and a e gene aliza ion o each
clus e , and calcula e he mean p ese ed densi y (MPD) and i s s anda d de ia ion (SDPD)
o e all clus e s. Fu he mo e, we wan o ake a close look a wo speci ic clus e s ha
a e cha ac e is ic o VGI da a. The i s clus e has 44 poin s and is loca ed a ound he
Thea e pla z in D esden, whe e se e al his o ic si es such as Sempe ope ,Ho ki che,Zwinge
and G ünes Gewölbe a e in p oximi y, bu wi hou a speci ied cen e . The second clus e has
68 poin s and is loca ed a he F auenki che, whe e a high amoun o pho os is loca ed in a
small a ea o in e es . We expec ha ou p oposed model and he quad ee gene aliza ion
pe o m be e han he disc e e isola ion algo i hm wi h hese clus e s, as he objec i e
o he la e is poin selec ion based on high alues, bu we also wan o analyze i hese
clus e s a e gene alized di e en ly.
Fo he p ese a ion o local ex eme alues, we iden i y all ex eme alues and
coun he numbe o p ese ed poin s in he gene alized da ase s. Fo his es , we expec
ha he disc e e isola ion algo i hm and ou model pe o m be e han he quad ee
gene aliza ion, as he la e akes only he poin loca ion in o accoun du ing gene aliza ion,
bu no i s a ibu es.
4.3. Resul s
Figu e 6shows he gene aliza ion esul s o he h ee me hods. I can be seen ha
he esul o he disc e e isola ion algo i hm is mo e sp ead ou compa ed o he o he
me hods, which p ese e he o e all shape o he cen al clus e s be e . In he quad ee
gene aliza ion esul (Figu e 6b), all clu e s a e esol ed, bu due o he applied me hod,
some o hese clu e s a e comple ely emo ed. The same can be s a ed o he disc e e
isola ion algo i hm (Figu e 6c), which is e en mo e sp ead ou in he o me clus e a eas.
Looking a he less dense a eas o he map, bo h he quad ee and he disc e e isola ion
me hod p ese ed he majo i y o poin s, which is in ac he in ended beha io o bo h
algo i hms. In he esul ing map o ou agen -based model (Figu e 6d), he o iginal shape
o he poin dis ibu ion, as well as spo s wi h poin s in close p oximi y wi hin he clus e s,
a e p ese ed, bu wi h he downside ha he e a e s ill a ew o e lapping poin s exis ing
a e he gene aliza ion.
Table 2p esen s he esul s o ou expe imen s using he pe o mance me ics, which
con i m he indings s a ed abo e. While he poin densi y wi hin he eigh clus e s is
educed o 26% o he quad ee and 35% o ou model compa ed o he o iginal da ase ,
he disc e e isola ion algo i hm main ains only 12% o he o iginal densi y. In e u n, mos
o he ex eme alues (25/27) a e p ese ed wi h his me hod, while he quad ee (20/27)
and ou model (23/27) p ese e less ex eme alues. Wi h espec o he numbe o poin s
e ained in he wo ocus clus e s, all gene aliza ion me hods e ained mo e o he same
numbe o poin s in he clus e a ound he Thea e pla z, al hough i has ewe o al poin s
han he one a he F auenki che.