Segmen a ion o Skin Lesions using Le el Se Me hod
Zhen Ma, João Manuel R. S. Ta a es
Ins i u o de Engenha ia Mecânica e Ges ão Indus ial,
Faculdade de Engenha ia, Uni e sidade do Po o
Rua D . Robe o F ias, s/n, 4200-465 Po o – PORTUGAL
Abs ac : Diagnosis o skin cance s wi h de moscopy has been widely accep ed
as a clinical ou ine. Howe e , he diagnos ic accu acy using de moscopy elies
on he subjec i e judgmen o he de ma ologis . To sol e his p oblem, a com-
pu e -aided diagnosis sys em is demanded. He e, we p opose a le el se me hod
o ul ill he segmen a ion o skin lesions p esen ed in de moscopic images. The
di e ences be ween no mal skin and skin lesions in he colo channels a e
combined o de ine he speed unc ion, wi h which he e ol ing cu e can be
guided o each he bounda y o skin lesions. The p oposed algo i hm is obus
agains he in luences o noise, hai , and skin ex u es, and p o ides a lexible
way o segmen a ion. Nume ical expe imen s demons a ed he e ec i eness
o he no el algo i hm.
keywo ds: medical imaging, melanoma, image segmen a ion, le el se me hod
1 In oduc ion
Nowadays, skin cance has become one o he mos equen o ms o cance [1, 2].
An ea ly diagnosis o skin cance is c i ical o imp o ing he p ognosis, because
pa ien s wi h ce ain condi ions, o example, he melanoma, can ha e a e y high
su i al a e i he cance s a e de ec ed a he ea ly s ages and ea ed p ope ly [3].
De moscopy is a non-in asi e imaging echnique de eloped o assis his diagnos ic
p ocess, and has been epo ed o conside ably imp o e he de ec ion a e o skin
cance s [4]. None heless, i was also poin ed ou ha he diagnos ic accu acy using
de moscopy la gely depends on de ma ologis s’ expe ience [5]. In o de o elimina e
his subjec i i y, a compu e -aided diagnosis (CAD) sys em is demanded.
The i s s ep o a CAD sys em is o segmen skin lesions in he images; he accu-
acy o segmen a ion has a de e minis ic in luence on he la e analysis. The appea -
ance o skin lesions a ies conside ably among di e en skin condi ions; meanwhile,
he in luences o noise, hai s, skin ex u e, and ai bubbles may appea simul aneously
in he image and make he segmen a ion e en ha de . Many algo i hms ha e been
p oposed o sol e he segmen a ion p oblem, and he majo i y o hem a e based on
h esholding and clus e ing. Fo example, a double h esholding p ocess was used in
[6] o segmen he bounda ies o skin lesions based on he in ensi y o he con e ed
images. A de ma ologis -like umo ex ac ion algo i hm and i s imp o ed e sion
we e de eloped in [7, 8] ha combined he h esholding wi h he i e a i e egion
g owing o segmen a ion. A 2D colo clus e ing algo i hm was p oposed in [9]; a
supe ised algo i hm based on a neu al ne wo k and an unsupe ised algo i hm based
on modi ied JSEG algo i hm we e p oposed in [10] and [11], espec i ely.
The le el se me hod was ini ially de eloped o ack cu e e olu ion in compu a-
ional physics; howe e , i has been success ully applied o many a eas o image p o-
cessing [12]. Fo he segmen a ion o de moscopic images, he le el se me hod is less
sensi i e o he in luence o noise; and he implici acking p o ides an e icien way
o ob ain he bounda y and he egions o skin lesions simul aneously. He e, a new
algo i hm based on he le el se me hod was p oposed o ul il he segmen a ion ask.
Following he s a is ical ea u es o de moscopic images in di e en colo spaces, he
con as s o he ligh ness and sa u a ion be ween he skin lesions and he su ounding
no mal skin we e used as he clues o segmen a ion and we e combined o de ine a
egion-based ex e nal o ce, ollowing which he e ol ing cu e can con ac o he
bounda y o he skin lesion in a obus way.
In he nex sec ion, he le el se me hod is e iewed; hen, he p oposed algo i hm
is in oduced, including he equa ion o mo ion and he e olu ion p ocess; a e wa ds,
nume ical expe imen s a e p esen ed, and acco ding o he segmen a ion esul s, im-
plemen a ion issues o he algo i hm a e discussed. In he las sec ion, he conclusions
and pe spec i es o u u e wo k a e indica ed.
2 Me hodology
The le el se me hod was p oposed o sol e he opological changes du ing he
cu e e olu ion [13]. In his me hod, he e ol ing cu e is embedded in o a highe -
dimensional le el se unc ion 𝜙(𝑥,𝑦,𝑡) as i s ze o le el se , and he e olu ion is
acked by inding he ze o le el se o he unc ion 𝜙(𝑥,𝑦,𝑡) a he ime 𝑡. The equa-
ion o mo ion o a le el se me hod is no mally w i en as:
𝜕𝜙
𝜕𝑡 +𝐹|∇𝜙|= 0, (1)
whe e 𝜙(𝑥,𝑦,𝑡) is he le el se unc ion and 𝐹 is he speed unc ion. The main idea o
using he le el se me hod o segmen a ion is o model he segmen a ion as a p ocess
o cu e e olu ion. Hence, a p ope speed unc ion needs o be de ined, wi h which
he cu e can each he objec bounda y and achie e a s able s a us he e.
2.1 Equa ion o mo ion
The colo dis ibu ion o skin lesions is no mally inhomogeneous. I he cu e
e ol es inside he egion o skin lesions, i can be easily a ac ed o he inne bounda-
ies and cause w ong segmen a ion. The e o e, in he p oposed algo i hm, he cu e
e olu ion is cons ained o con ac ion in he egion o no mal skin. By his way, he
ini ial cu es a e equi ed o co e he en i e egions o he skin lesions. The alues o
he le el se unc ion 𝜙(𝑥,𝑦, 0) a e hen de ined as he signed dis ance unc ion o he
ini ial cu es wi h posi i e (nega i e) sign inside (ou side) he cu es.
The ligh ness di e ence be ween no mal skin and skin lesions p o ides an im-
po an clue o segmen a ion. Ne e heless, he appea ance o skin lesions has la ge
a ia ions among di e en condi ions, and in many cases, i s main dissimila i y o he
no mal skin is he ch oma ici y which is o en pe cep ually a ec ed by ligh ness a i-
a ions. Thus, in o de o use he colo in o ma ion e icien ly, he RGB colo space in
he images a e con e ed o he CIE L*a*b* and CIE L*u* * colo spaces. Al hough
he ligh ness is sepa a ed om he colo ep esen a ion in he wo CIE colo spaces,
he ch oma ici y channels 𝑎∗,𝑏∗, 𝑢∗ and 𝑣∗ a e coo dina es in he colo diag am and
a e unsui able o be used di ec ly o de ine he speed unc ion. Ins ead, he colo sa u-
a ion was adop ed o combine he ligh ness and ch oma ici y o segmen a ion. Sa u-
a ion is a measu e ha desc ibes he colo ulness o a colo ela i e o i s ligh ness,
bu is no o icially de ined in he CIE colo sys em. The de ini ion o sa u a ion in
compu e ision was adop ed he e wi h i s alue calcula ed as:
𝑆=� 0 i 𝑅+𝐺+𝐵= 0
1 −𝑚𝑖𝑛(𝑅,𝐺,𝐵)
(𝑅+𝐺+𝐵)3
⁄ o he wise . (2)
Then, he equa ion o mo ion o he p oposed le el se model is de ined as:
𝜕𝜙
𝜕𝑡 +𝑃𝐿(𝑥,𝑦)∗𝑃𝑠(𝑥,𝑦)∗(1+𝜅)|∇𝜙|= 0, (3)
whe e 𝜅 is he cu e cu a u e; 𝑃𝐿(𝑥,𝑦) and 𝑃𝑆(𝑥,𝑦) a e he Gaussian p obabili y
densi y dis ibu ion unc ion o he ligh ness and sa u a ion channels o he no mal
skin, espec i ely. The cu a u e de ined in he speed unc ion ac s as he in e nal
o ce o smoo h he cu e du ing he e olu ion.
The speed unc ion in Eq. (3) includes he s a is ical in o ma ion o ligh ness and
sa u a ion alues o no mal skin. Howe e , his in o ma ion is una ailable be o e
segmen a ion; hence, o ob ain an app oxima ion o hese alues, he O su’s me hod
[14] is applied o classi y he image pixels based on he ligh ness alues. Supposing
Ω0 is he se composed by pixels ha ep esen he no mal skin acco ding o he clas-
si ica ion o he O su’s me hod, he ollowing egion is used o calcula e he s a is ical
alues:
Ω𝑆={(𝑥,𝑦)|−50 <𝜙(𝑥,𝑦, 0)< 0 }∩Ω0. (4)
The egion Ω𝑆 belongs o a neighbo ing ex e nal band o he ini ial cu es; as he skin
lesions a e comple ely inside he ini ial cu es, his egion can p o ide an app oxima-
ion o he s a is ical dis ibu ions o he ligh ness and sa u a ion o he no mal skin.
These s a is ical alues a e hen upda ed along wi h he cu e e olu ion. Wi h Eq. (3),
he e ol ing cu es will con ac o he places whe e ei he he ligh ness o he sa u a-
ion is app eciably di e en o no mal skin.
2.2 E olu ion
As e e ed be o e, he 𝑎∗,𝑏∗𝑢∗,𝑣∗ channels in he CIE L*a*b* and L*u* * colo
spaces a e he posi ions o a colo ela i e o he colo bases and diag am. Thei loca-
ions e lec he pe cep ual di e ence be ween he no mal skin and skin lesions; pixels
o he same g oup should ha e coo dina es nea each o he , and pixels om he di -
e en g oup should ha e coo dina es wi h a la ge dis ance. Acco dingly, he image
pixels can be classi ied in o wo g oups based on hei dis ances o he spa ial colo
cen e s o no mal skin and skin lesions. None heless, he spa ial cen e s o he wo
g oups a e unknown ei he . Ye , gi en ha he skin lesions a e inside he e ol ing
cu es, a neighbo ing ex e nal egion Ω𝑆 is used o calcula e he spa ial cen e s o
no mal skin in he colo space as:
Ω𝑆
(𝑡)={(𝑥,𝑦)|−50 <𝜙(𝑥,𝑦,𝑡)< 0 }, (5)
and he in e nal egion o he cu e is used o calcula e he cen e s o he skin lesions.
Along wi h he con ac ion o he cu e, he spa ial cen e s o he skin lesions and he
su ounding no mal skin will become mo e accu a e. Wi h he classi ica ion based on
he Euclidean dis ance in he colo spaces, he s a is ical dis ibu ion o he sa u a ion
alues o no mal skin can be be e e lec ed. Hence, he s a is ical ales a e upda ed
du ing he e olu ion in he egion Ω0
(𝑡)∩Ω𝑆
(𝑡) whe e Ω0
(𝑡) is he se composed by pixels
ep esen ing he no mal skin a he ime 𝑡. Addi ionally, in ligh wi h he colo classi-
ica ion, he speed unc ion in Eq. (3) is modi ied as:
𝐹∗(𝑥,𝑦)=�0.5 ∗𝐹(𝑥,𝑦) i (𝑥,𝑦) ep esen s skin lesions a he ime 𝑡
𝐹(𝑥,𝑦) o he wise . (6)
Wi h he modi ied speed unc ion, he e ol ing cu e can be u he a ached o he
bounda y o skin lesions.
3 Expe imen s
An image da abase con aining 68 de moscopic images was used o es he pe o -
mance o he p oposed segmen a ion algo i hm, in which 58 we e diagnosed as ne us
and 10 as melanomas. CUDA implemen a ion o he p oposed algo i hm was adop ed
o enhance he compu a ional e iciency. The ob ained segmen a ion esul s we e
qui e p omising and, o hei quan i a i e analysis, he exclusi e-o measu e de ined
below was used o e alua e he di e ence be ween he g ound u h and he segmen a-
ion esul :
𝐷(𝐶0,𝐶1)=𝐴𝑟𝑒𝑎�𝑖𝑛𝑠𝑖𝑑𝑒(𝐶0)⊕𝑖𝑛𝑠𝑖𝑑𝑒(𝐶1)�𝐴𝑟𝑒𝑎�𝑖𝑛𝑠𝑖𝑑𝑒(𝐶0)�� , (7)
whe e 𝐶0 is he g ound ue bounda y, 𝐶1 is he con ou ob ained by he algo i hm,
and ⊕ is he exclusi e-o ope a o . Fig. 1 illus a es ou segmen a ion examples in
he image da abase; one can e i y he obus ness o he p oposed app oach agains
he di e en imaging condi ions. Fo he p oposed algo i hm, he mean and he s and-
a d de ia ion o he exclusi e-o measu e on his image da abase a e 0.1036 and
0.0485, espec i ely.
The e is no es ic on he shape o he ini ial cu es in he p oposed algo i hm;
howe e , he ini ial cu es a e equi ed o co e he comple e egion o he skin le-
sions. I he neighbo ing egion o he ini ial cu es is a ec ed app eciably by un-
wan ed in luences, he algo i hm may no achie e sa is ac o y esul s; o a oid his
si ua ion, he ini ial cu es a e de ined manually. Meanwhile, in he segmen a ion, he
size o he neighbo ing egion o he e ol ing cu es a ec s he s a is ical in o ma ion
o no mal skin a ound he skin lesions. A la ge neighbo ing egion a ound he ini ial
cu e can cap u e he a ia ions o no mal skin mo e accu a ely, bu is mo e likely o
in oduce unwan ed in luences. The band size was chosen as 50 in he expe imen s
and led o sa is ac o y esul s.
(a) (b)
(c) (d)
Fig. 1 Segmen a ion examples using he p oposed algo i hm, ed con ou s – segmen a ion e-
sul s o he p oposed algo i hm; blue con ou s – g ound u hs: (a) image wi h ne i,
𝐷(𝐶0,𝐶1)= 0.0833; (b) image wi h melonoma, 𝐷(𝐶0,𝐶1)= 0.1590; (c) image wi h
ne i, 𝐷(𝐶0,𝐶1)= 0.0868; (d) image wi h melanoma, 𝐷(𝐶0,𝐶1)= 0.0447.
4 CONCLUSION
A no el le el se me hod was p oposed o segmen skin lesions. The p oposed al-
go i hm combines he a ious in o ma ion con ained in de moscopic images, and
de ines he speed unc ion based on he con e ed colo channels. Nume ical expe i-
men s illus a ed he e ec i eness and obus ness o he algo i hm, and he implemen-
a ion issues we e discussed based on he es s.
The di e ences be ween he skin lesions and no mal skin we e e icien ly used in
he p oposed algo i hm. Wi h he egion-based ex e nal o ces, he p oposed algo-
i hm is no sensi i e o he unwan ed in luences p esen ed in he images. The u u e
wo k will con inue o imp o e i s obus ness and accu acy.

ACKNOWLEDGEMENT
This wo k was done in he scope o he p ojec “A no el amewo k o supe ised
mobile assessmen and isk iage o skin lesions ia non-in asi e sc eening”, wi h
he e e ence PTDC/BBB-BMD/3088/2012, inancially suppo ed by Fundação pa a a
Ciência e a Tecnologia (FCT), in Po ugal.
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