EUROVIS 2023/ W. Aigne , T. Höll , and B. Wang Sho Pape
E ec o colo pale es in hea maps pe cep ion: a s udy
E. Molina and C. Middel and P. Vázquez
ViRVIG G oup
Uni e si a Poli ècnica de Ca alunya
Figu e 1: Example o hea maps used in ou s udy. In o de : Vi idis and Blues disc e e, and Vi idis and Blues con inuous.
Abs ac
Hea maps a e a widely used echnique in isualiza ion. Un o una ely, hey ha e no been in es iga ed in dep h and li le is
known abou he bes pa ame e iza ions so ha hey a e p ope ly in e p e ed. The e ec o di e en pale es on ou abili y o
ead alues is s ill unknown. To add ess his issue, we conduc ed a use s udy, in which we analyzed he e ec o wo commonly
used colo pale es, Blues and Vi idis, on alue es ima ion and alue sea ch. As a esul , we p o ide some sugges ions o wha
o expec om he hea map con igu a ions analyzed.
CCS Concep s
•Human-cen e ed compu ing →Hea maps; Visualiza ion design and e alua ion me hods;
1. In oduc ion
Hea maps a e a popula isualiza ion echnique ha can be used o
de ec clus e s, ou lie s, and summa ize da a [Mun14]. They a e de-
signed as a wo-dimensional ma ix o cells whe e wo ca ego ical
(o some imes o de ed) a iables a e used as indices, and a quan i-
a i e a iable is encoded as a colo . Though e y commonly used,
o he bes o ou knowledge, he e a e no guidelines ha ad ise on
how o design hem. Exis ing s udies on how good people’s es ima-
ion o alues is when eading hea maps depend on di e en isual
cues a e sca ce. Wi h ou s udy, we p esen insigh s in o alue es i-
ma ion wi h di e en pale es, and p o ide a mo e in-dep h unde -
s anding o how he anges o alues in he pale es a ec , which
can be a s a ing poin o new in es iga ions.
2. Rela ed Wo k
Hea maps a e e y common in isualiza ion nowadays [KAB∗20].
They can be aced back o 1957, when Snea h al eady alked abou
eo de ing ows and columns o ma ices ha ep esen ed simila -
i y alues as shades [Sne57] o help use s ind pa e ns. Be in de-
sc ibes hem unde he name o eo de able ma ices [Be 73]. In he
app oach depic ed by Wilkinson [Wil12], o en imes he wo keys
can be eo de ed, as wi h clus e ed hea maps [Mun14,DTT∗15].
Howe e , hea maps also encode ime da a [CSL∗15,KIM∗16] ha
canno be eo de ed. Calenda hea maps a e a a ian whe e he
cells ep esen days in a calenda (e.g., [LWW∗20]) and he o -
de is ixed. Unde he name o hea maps, we ind many o he de-
signs: using hexagonal cells [CLNL87] ( hough commonly called
hexplo s [TSSB22]), o maps whe e he axes a e linked o spa ial
posi ions [PSSC16,WSWW13].
Pe cep ion s udies a e needed o unde s and how humans in e -
p e cha s. The e is a la ge body o esea ch [FPS∗21], bu he e
a e s ill unknowns, such as he e ec o he pale es [LH18]. Fu -
he mo e, pe cep ual s udies a e o en limi ed due o he eno mi y
o he space o pa ame e s, so we mus cons ain he condi ions
o e ec i ely ob ain s a is ically alid esul s. Besides, he e a e
©2023 The Au ho s.
P oceedings published by Eu og aphics - The Eu opean Associa ion o Compu e G aphics.
This is an open access a icle unde he e ms o he C ea i e Commons A ibu ion License, which
pe mi s use, dis ibu ion and ep oduc ion in any medium, p o ided he o iginal wo k is p ope ly
ci ed.
DOI: 10.2312/e s.20231039
h ps://diglib.eg.o g
h ps://www.eg.o g
E. Molina C. Middel & P. Vázquez / Unde s anding how hea maps a e pe cei ed: a s udy
some p ac ices ha a e widesp ead (such as he use o ed-g een
pale es) despi e no being he mos sui able acco ding o science
[BGP∗11]. Un o una ely, he e a e also con adic o y esul s, e-
jec ing a pale e [RT98] and ecommending i [RSGP21]. Rega ding
hea maps, some ocus on compa ing hem wi h o he ypes o isual
encoding echniques [GFC05], bu jus a ew pape s ha e analyzed
how hey a e pe cei ed, as Słomska-P zech e al. do wi h espec
o he gene aliza ion le el [SPPP21] o as Ros isla e al. do wi h
geog aphical in o ma ion [NPS18]. Howe e , he es mos ly deal
wi h compa a i e isualiza ion asks. K ako and Fei elson analyze
how o be e encode di e ences be ween hexplo s [KF13], bu no
pe cep ual analysis is pe o med. K aus e al. also concen a e on
isual compa ison asks o hea maps and heigh maps in 3D en i-
onmen s [KAB∗20]. Bu he asks hey add ess don’ in ol e es i-
ma ing alues o changing pa ame e s like he pale e. Ou wo k has
some analogies o he one by To y e al., whe e he au ho s compa e
how poin s, encoded in a sequen ial pale e o g eens, a e ead by
use s unde di e en dis ibu ions in sca e plo s [TSD09]. T au -
ne e al. ha e analyzed he pe cep ion o di e en con igu a ions o
honeycomb plo s, which esemble hea maps [TSSB22].
3. Expe imen Design
Ou objec i e is o in es iga e he ela ionship be ween hea map
con igu a ions and he pe cep ion o alues. To iden i y he mos
common con igu a ions used by esea che s and p ac i ione s, we
i s analyzed a se o sou ces.
3.1. Common hea map pa ame e s
The ini ial goal was o ind whe he he e we e some con igu a ion
pa ame e s ha we could use as a basis o he design o ou es s.
We i s downloaded he Eu oVis and IEEE Vis pape s om 2019
and 2020 (263). 75 had some kind o hea map o hea map-like cha
wi h colo coding ha showed con usion ma ices. The asks he de-
signe s we e ying o help sol e we e mos ly ela ed o he explo-
a ion o co ela ion ma ices o he sea ch o pa e ns, shapes, and
ends. We also checked he mo e common usage in non-scien i ic
publica ions and sea ched “hea map cha ” in Google Images. We
checked he p ima y esul s (122 images). 114 we e hea maps o
hea map-like cha s. Wi h his analysis, summa ized in Table 1, we
saw ha he e a e no common pa ame e s o s a wi h. In ac , he e
a e good p ac ices ha need o become mo e widesp ead, like a oid-
ing ed-g een pale es, o make hem accessible o colo -blind peo-
ple. The lack o consensus on he bes design led us o ix a se o
pa ame e s (cell size and dimension) and a y he pale e. The p o-
posed asks we e:
∙Task 1: Es ima ion o he alue o he indica ed cell. I s goal is
o check whe he he alues a e es ima ed co ec ly and which
pa ame e s may ha e an impac .
∙Task 2: Selec a cell wi h he indica ed alue. The objec i e he e
is o s udy i alues a e p ope ly ound.
Due o he massi e space o possible con igu a ions, we lea e
ou o his wo k o he elemen s such as clus e s, ou lie s, and ends
de ec ion/in e p e a ion.
Pape s Google
Dimensions F om 4x4 o hund eds 12-35 up o 50
Cell size 1px, majo i y >10 px Big, ec angu-
la
Pale e
Sequen ial: blue/g een.
Mul i-hue: i idis/magma
( ed-g een)
Sequen ial:
blue/o ange
Mul i-hue:
ed-g een.
Table 1: Mo e common pa ame e s ound in he Eu oVis and IEEE
Vis 2019/20 pape s and in Google Images.
Figu e 2: Example o a hea map wi h he di e en asks o be sol ed.
Pa icipan s had he ields o be illed unde he cha .
3.2. Hypo heses
We es ic ed ou sel es o changes in pale es: single-hue s mul i-
hue ones, and disc e e s con inuous ones, since bo h a e ound in
he li e a u e. Since con inuous pale es encode mo e alues and
mul i-hue pale es use a combina ion o colo hue and luminance,
we hypo hesized ha :
∙Con inuous pale es a e be e han disc e e ones o: a) H1: es i-
ma e alues and b) H3: sea ch o a gi en alue.
∙Mul i-hue pale es a e be e han single hue ones o: c) H2: es i-
ma e alues and d) H4: sea ch o a gi en alue.
Hypo heses 1 and 2 a e ela ed o Task 1 and he o he s o Task 2.
We also analyze he anges o he pale es used o encode alues and
he ime o answe .
3.3. Cha s Design
This pape is pa o a la ge s udy, whe e we analyze o he a i-
ables such as clus e coun ing (no included he e due o he lack o
space). The e o e, he da a was gene a ed syn he ically o ensu e a
ce ain numbe o clus e s (0 o 3) in each hea map. To make he
da a ela able, we in o med he pa icipan s ha he hea maps we e
encoding he numbe o bicycles pe s a ion (Y-axis) pe day (X-
axis). The dimensions selec ed we e 30 ×30. Despi e his, we la e
saw ha pa icipan s ended o igno e he meaning o he axes.
Conce ning esolu ion, o ensu e ha all i on any sc een, we
analyzed se e al cell sizes and layou s, keeping a o al size o a ound
©2023 The Au ho s.
P oceedings published by Eu og aphics - The Eu opean Associa ion o Compu e G aphics.
32
E. Molina C. Middel & P. Vázquez / Unde s anding how hea maps a e pe cei ed: a s udy
500px. We inally op ed o a squa e design as shown in Figu e 2,
bu wi h he widge s on he bo om. Cha s we e c ea ed wi h each
cell ha ing a size la ge enough o be easily seen (13 × 13 px).
Rega ding pale es, since blue colo s p edomina ed, we op ed
o use he Blues as a sequen ial pale e and Vi idis o he mul i-
hue. No e ha hese wo pale es also s and ou in p e ious expe -
imen s [LH18]. The inal combina ions selec ed we e: BluesCon :
Blues con inuous (BC), BluesDisc: Blues disc e e (BD), Vi idis-
Con : Vi idis con inuous (VC), and Vi idisDisc: Vi idis disc e e
(VD). We hen used he h ps://colo b ewe 2.o g/ ool
o decide which colo ( ed) would be he mos sui able o highligh
a cell wi h a ing, needed o Task 1. Finally, we c ea ed 34 cha s,
as he ones in Figu e 1.
3.4. S uc u e
The s udy was designed as a web applica ion, deli e ed h ough
P oli ic [p o] wi h he ollowing s eps: Fi s , he objec i es we e
p esen ed and he hea maps and asks we e desc ibed. Then, a de-
mog aphic su ey (age, coun y, gende , educa ion, eyesigh , and
sc een size) was conduc ed. The aining asks, which equi ed he
pa icipan o sol e h ee hea maps, we e ollowed by he ac ual
asks, which we e andomized. Las ly, a ques ionnai e o e alua e
unde s anding and sa is ac ion. The demog aphic su ey was la e
used o iden i y non-sui able pa icipan s (e.g., poo eyesigh ).
3.5. Pa icipan s
We ga he ed 50 pa icipan s (wo ldwide, English speaking and 50%
gende balance) h ough P oli ic and 53 ex a pa icipan s by an-
nouncing he s udy h ough social ne wo ks. The du a ion was es-
ima ed o be abou 20 minu es, wi h wo pilo pa icipan s. The
amoun conside ed a ai wage by P oli ic was £7.5 pe hou . To
ensu e he ecological alidi y o he da a, pa icipan s who dis-
played no unde s anding o ca elessness (a e age e o s la ge han
20, om a 1-50 ange) du ing he aining phase we e no allowed
o con inue. We also included duplica ed es s o double-checking
click- h ough s a egies. Fo he ac ual asks, pa icipan s exhibi ing
oo la ge e o s we e in e p e ed as click- h ough and cleaned. This
led us o keep 85 alid pa icipan s (47 and 38, espec i ely).
These 85 pa icipan s (40 emale) we e om 8 di e en coun-
ies. Age anges: 69 in he ange 18-35, 10 in 35-50, and 6 abo e
50. Conce ning educa ion, 15 had a high school deg ee and 53 had
highe educa ion. None o hem we e colo -blind. 79 pa icipan s
decla ed hey unde s ood he expe imen , 61 we e sa is ied wi h he
pe o mance, and 15 we e undecided. 24 ound he asks no easy.
4. Resul s
The da a analysis was pe o med by compa ing he e o s in each
ask using Repea ed Measu es ANOVA [Gi 92], ollowed by he
Bon e oni pos hoc es [Bon36]. Nex , we discuss he signi ican
esul s, also illus a ed in Figu e 3. Liu and Hee ound di e ences
when compa ing alues in Blues in low anges [LH18]. Pa icipan s
had o check which o wo colo s was mo e simila o a e e ence
one. In ou case, we wonde ed whe he he Blues pale es exhibi ed
la ge e o s a lowe anks. Thus, we pa i ioned he da a in anges:
small (S) 0-16, medium (M) 17-33, and la ge (L) 34-50. Since he
alues we e selec ed andomly o he expe imen , he e is a di e -
en numbe o samples pe ange. Fo each combina ion, we use he
maximum numbe o common answe s, indica ed in pa en heses.
The esul s a e summa ized in Table 2and also illus a ed in 3wi h
he p- alues displayed.
4.1. Task 1: Es ima ing cell alues
Pa icipan s had o w i e he co ec alue o a ci cled cell. This
allows us o e alua e H1 and H2.
Fo H1: Con inuous s disc e e and H2: Mul i-hue s single hue
signi ican di e ences we e ound. Bes ones: Disc e e and Mul i-
hue. Thus, we ejec H1 and accep H2. Hence, be ween indi id-
ual pale es, we could expec he bes o be Vi idisDisc. Howe e ,
Vi idisCon is he bes one. This esul is in line wi h ou p edic ion
bu needs mo e in es iga ion. Top le in Figu e 3.
Same pale e, di e en anges The e a e only di e ences in Blues-
Disc (79 samples) be ween S and L, being S be e . Middle le in
Figu e 3.
Same ange, di e en pale e S (79 samples): di e ences be ween
bo h Vi idis and bo h Blues. The bes ones, in o de , Vi idisCon
and BluesDisc. M (67): Same as in S. L (68): Bo h Con inuous a e
di e en , and Vi idisDisc is di e en om he o he Disc e e and
he o he Vi idis. Vi idisCon is also he bes one. In gene al, wi h
Blues, pa icipan s end o unde es ima e, and wi h Vi idis, o o e -
es ima e. Middle in Figu e 3.
4.2. Task 2: Sea ching gi en alues
Fo H3: Con inuous s disc e e we ound signi ican di e ences
(p- alue 0.045). Bo h unde es ima e, bu con inuous pale es a e
mo e accu a e. The e o e, we accep H3. No di e ences we e ound
o H4: Mul i-hue s single hue, so i canno be accep ed.
Same pale e, di e en anges BlueCon (81): Di e ences be-
ween L and he o he s, being he wo s . BlueDisc (73): Di e ences
be ween all, being M he bes . Vi idisCon (83): Di e ences be-
ween all, S is he bes . Vi idisDisc (83): Same as in BlueDisc. I
seems ha he almos whi e colo s in Blues a e di icul o dis in-
guish and ha he a ia ion be ween g eenish and yellow ones in
Vi idis a o s he dis inc ion. Righ in Figu e 3.
Same ange, di e en pale e The e a e only di e ences in M (83)
be ween BluesCon and he o he s, being he bes one. Bo om le
in Figu e 3.
5. Conclusions and Fu u e wo k
We ha e analyzed he e ec o he pale e on es ima ing alues in
hea maps. The signi ican esul s a e summa ized in Table 2.
The main akeaways a e: Wi h he ask o es ima ing alues,
when we analyze pale es 2 s 2, ou in ui ion abou he possi-
ble supe io i y o con inuous pale es o ha ing mo e alues is e-
jec ed. Howe e , when we analyze he esul s o he 4 possibili ies,
he combina ion o Mul i-Hue and Con inuous con i ms ou in u-
i ions by showing he bes indi idual esul s in VC. Indi idually, he
©2023 The Au ho s.
P oceedings published by Eu og aphics - The Eu opean Associa ion o Compu e G aphics.
33
E. Molina C. Middel & P. Vázquez / Unde s anding how hea maps a e pe cei ed: a s udy
Hypo hesis es ing
Task 1 Task 2
pale es C s D V s B C s D V s B
CNA ✓NA
D✓NA NA
VNA ✓NA -
BNA NA -
Task 1: Es ima e alue o cell Task 2: Selec cell wi h alue
same pale e same ange same pale e same ange
pale es All S M L S M L All S M L S M L
VC ✓- - - ✓✓✓ -✓- -
VD - - - - ✓- -
BC - - - - ✓ ✓ -✓-
BD ✓-✓✓✓ -✓- -
Table 2: Summa y o he s udy esul s. C= Con inuous, D= Disc e e, V= Vi idis, and B= Blues. When es ing Task 1, D and V pale es pe o m
be e (le able), so we would expec VD o be he bes pale e, bu VC is he one ha pe o ms bes when ea ed as 4 di e en pale es, igh
able. In Task 2, C pale es pe o m be e , as expec ed, bu he e is no di e ence be ween indi idual pale es. Wi hin he same ange, igh
able, in Task 1 VC and BD a e be e a es ima ing alues in all anges, wi h VC exhibi ing a sligh ly be e beha io . In Task 2, wi hin he
same pale e, we see ha he anges wi h he bes esul s a e he M/S, which makes sense, being he ones whe e he e is a g ea e a ia ion
be ween he wo ends o he pale e. A ✓means he bes esul , a – means no signi ican di e ences and NA means no applicable
Figu e 3: E o dis ibu ion, X axis = answe gi en - co ec alue, Y axis = numbe o answe s. Ve ical lines = a e ages. C= Con inuous,
D= Disc e e, V= Vi idis, and B= Blues. P- alues a e shown nex o each compa ison. Le : Top: analysis H1 & H2 be ween indi idual pale es.
Middle: Task 1 BluesDisc pe ange Small(S), Medium(M) & La ge(L). Bo om: Task 2 Medium pe pale e. Middle: Task 1 he 3 anges pe
pale e. Righ : Task 2 he 4 pale es pe ange.
pale es do no show di e ences, bu aking in o accoun he anges
he BC pale e wo ks bes , so i seems he mos indica ed. Al hough
i mus be aken in o accoun ha eading alues in high anges gi es
wo se esul s han in he middle and low anges. Howe e , i is ue
ha in his ask he pa icipan s had mo e eedom by no ha ing
he cell o be e alua ed es ic ed. We did no ob ain any signi ican
di e ence be ween ime e o pe pale e. We would sugges using
VC since i gi es he bes esul s o Task 1 and in Task 2 he e is
none ha domina es.
In he u u e, besides clus e coun ing, we wan o analyze he
e ec o o he pa ame e s, such as cell size. Addi ionally, we wan
o s udy i he e is a co ela ion be ween ime and e o pe ask.
Acknowledgmen s
This pape has been suppo ed by PID2021-122136OB-C21 om
he Minis e io de Ciencia e Inno ación, by 839 FEDER (EU) unds.
Elena Molina has been suppo ed by FI-SDUR doc o al g an om
Gene ali a de Ca alunya, and FPU g an om he Minis e io de
Ciencia e Inno ación.
©2023 The Au ho s.
P oceedings published by Eu og aphics - The Eu opean Associa ion o Compu e G aphics.
34
E. Molina C. Middel & P. Vázquez / Unde s anding how hea maps a e pe cei ed: a s udy
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