The 3 d Eu opean Medical and Biological Enginee ing Con e ence No embe 20 – 25, 2005
EMBEC'05 P ague, Czech Republic
IFMBE P oc. 2005 11(1) ISSN: 1727-1983 © 2005 IFMBE
DETECTION OF MICROCALCIFICATIONS IN MAMMOGRAMS USING
2D PREDICTION FILTERING AND A NEW STATISTICAL MEASURE OF
THE RIGHT TAIL WEIGHT
B. Acha*, C. Se ano* and R.M. Rangayyan**
* Dep. de Teo ía de la Señal y Comunicaciones, Uni e si y o Se ille, Se ille, Spain
** Dep . o Elec ical and Compu e Enginee ing, Uni e si y o Calga y, Calga y, Albe a, Canada
[email p o ec ed], cse[email p o ec ed]
Abs ac : In his pape , a new me hod o de ec
mic ocalci ica ions in mammog ams is p esen ed.
The me hod is based on a candida e selec ion
p ocedu e which consis s o a wo-dimensional linea
p edic ion adap i e il e ing ollowed by a s a is ical
pa ame e calcula ion de eloped by he au ho s and
called ail a io (TR). The pa ame e TR
cha ac e izes he p esence o mic ocalci ica ions in a
ROI, and is ex ac ed om he local p obabili y
dis ibu ion wi hin a small egion su ounding each
candida e. A e wa d a g oup o new and p e iously
published ea u es a e used o eed a neu al ne wo k
ha classi ies he candida es in o mic ocalci ica ion
o non-mic ocalci ica ion. The algo i hm has been
es ed wi h 38 digi ized mammog ams ob aining a
sensi i i y o 0.93 o a posi i e p edic i e alue o
0.88.
In oduc ion
The a ailabili y and p oli e a ion o digi al
adiog aphic images ha e encou aged esea ch in
Compu e -aided Diagnosis (CAD). A signi ican pa o
such esea ch has concen a ed on he de ec ion o
b eas cance , in iew o he ac ha women in Wes e n
coun ies ha e a highe han 1 in 10 chance o
de eloping b eas cance du ing hei li e. In pa icula ,
many esea che s ha e ocused on he de ec ion o
mic ocalci ica ions [1,2], which a e ea ly signs o b eas
cance .
Compu e -aided mammog aphy has been s udied o
mo e han wo decades. Du ing his pe iod he
sensi i i y o de ec ion has imp o ed, wi h some ecen
pape s epo ing mo e han 90% sensi i i y.
Ne e heless, he alse-posi i e a e emains high,
especially when de ec ing indi idual mic ocalci ica ions
[3]. The e o e, au oma ed in e p e a ion o
mic ocalci ica ions emains a challenge due o hei
small size and a iable appea ance. Fu he mo e, when
loca ed wi hin o supe imposed by dense issues,
especially in young women, mic ocalci ica ions ha e
almos he same b igh ness le el as he backg ound
issue, which makes hem di icul o de ec . In iew o
he abo e, i is e iden ha me hods o au oma ic
de ec ion o mic ocalci ica ions in mammog ams a e
desi able in o de o assis adiologis s in he
in e p e a ion o mammog ams and he diagnosis o
b eas cance .
In his pape a new me hod o de ec
mic ocalci ica ions in mammog ams is p oposed. The
me hod is based on a candida e selec ion p ocedu e
ollowed by a Suppo Vec o Machine (SVM)
classi ie . Du ing he candida e selec ion a 2-D linea
p edic ion il e ing is employed and a new measu e
based on he s a is ical dis ibu ion in a neighbo hood is
de ined.
Me hod
In o de o de ec he mic ocalci ica ions we apply
he ollowing s eps:
Candida e selec ion: We p opose a me hod o selec
po en ial mic ocalci ica ion poin s o candida e pixels
o subsequen analysis and de ec ion o
mic ocalci ica ions. The me hod consis s o wo main
s eps:
1) 2D linea p edic ion e o il e ing [4,5], ollowed by
h esholding. A pixel is selec ed as a p e-candida e o
mic ocalci ica ion i i s p edic ion e o is g ea e han
an adap i ely de e mined h eshold. We use he
mul ichannel e sion o he Bu g algo i hm o calcula e
his e o . The mul ichannel e sion o he Bu g
algo i hm calcula es he op imal p edic ion coe icien s,
o a 21 pp × 2D p edic o , by compu ing he p edic ion
e o s o o de p1. The p edic ion e o s a e ep esen ed
as ec o s o size 1
2×p and a e compu ed ecu si ely,
beginning wi h he 0-o de p edic ion e o s. The e o
alues a e ini ialized o he o iginal image. The
p edic ion e o s o highe o de s a e calcula ed by
epea ing ecu si ely he ollowing h ee s eps, wi h
2,,1,0 1−= pi L:
1. Compu e he co a iance ma ices o he o wa d
and backwa d p edic ion e o s as:
The 3 d Eu opean Medical and Biological Enginee ing Con e ence No embe 20 – 25, 2005
EMBEC'05 P ague, Czech Republic
IFMBE P oc. 2005 11(1) ISSN: 1727-1983 © 2005 IFMBE
[] []
()
T
m
i
i
imemeE ∑
=
[] []
()
T
m
b
i
b
i
b
imemeE ∑
= (1)
[] []
()
T
m
b
i
i
b
imemeE ∑
=
whe e )(me
i and )(meb
i a e, espec i ely, he
o wa d and backwa d p edic ion e o s o o de i. As
bo h o he e o ec o s a e o size p2×1,
i
E, b
i
Eand
b
i
Ewill be 22 pp × ma ices. The summa ion,
depending on m, is pe o med o all he p edic ion e o
ec o s o size p2×1 ha he subimage can be pa i ioned
in o.
2. Calcula e he p edic ion coe icien ma ix
[]
1
1+
+iAi by sol ing he ollowing equa ion:
[] []
b
i
i
ii
b
iEEiAiAE 211 11 −=+++ ++ (2)
3. Compu e he backwa d and o wa d p edic ion
e o ec o s o he highe p edic ion o de as:
[] [] [ ] [ ]
11
1
1−++= +
+meiAmeme b
ii
i
i
[] [ ] [ ] []
meiAmeme
i
T
i
b
i
b
i11 1
1++−= +
+
(3)
Once p edic ion e o s a e calcula ed o all he
pixels in he image, hey a e h esholded o selec p e-
candida es pixels. The h eshold is adap i ely
de e mined based upon he local a e age in ensi y o he
subimage, local a e age alue o he p edic ion e o ,
and he global in ensi y (g ey le el) o he whole image.
This is based upon he obse a ion ha a
mic ocalci ica ion can be seen as a poin o
nons a iona i y in an app oxima ely homogeneous
egion o neighbo hood in a mammog am. Such a pixel
canno be p edic ed well by he linea p edic o , and
hence leads o a high p edic ion e o [6].
2) Calcula ion o a s a is ical pa ame e called ail a io
(TR), o he p e-candida es, ollowed by h esholding.
Mic ocalci ica ions ep esen small poin s o high
in ensi y. The e o e, i we analyze he p obabili y
densi y unc ion (pd ) o he pixels belonging o a
neighbo hood su ounding a mic ocalci ica ion, i will
ha e he igh ail longe han he le one. Based on his
obse a ion, we ha e de eloped a pa ame e , TR, ha is
a ela i e measu e o he ail leng h o a pd . The e a e
some desc ip o s in he li e a u e ha measu e he
hea iness o he ail o a pd . The ku osis coe icien is
o en ega ded as a measu e o he hea iness o a
dis ibu ion ela i e o he no mal dis ibu ion. I s
in e p e a ion and use ha e been es ic ed o symme ic
dis ibu ions, because o i s in insic compa ison wi h
he symme ic no mal dis ibu ion. Ano he
disad an age wi h ku osis is ha i is sensi i e o
ou lie s in he da a, because i is based on momen s o
he da a. Fo any dis ibu ion unc ion F wi h ini e
momen s, ku osis is de ined as:
()
()
{}
2
2
4
)(
)(
XEXE
XEXE
k
FF
FF
−
−
= (4)
whe e he nume a o and denomina o ep esen he
second and ou h cen al momen s o F, espec i ely
and X a e he da a alues. Some au ho s ha e p esen ed
o he obus measu es o ku osis, bu de ined only o
symme ic dis ibu ions, o me ely measu ing he
peakedness ins ead o he ail weigh [7,8].
O he wo ks o e come he p oblems men ioned
abo e by in oducing se e al measu es o ail weigh o
uni a ia e con inuous dis ibu ions ha can be applied
o symme ic as well as asymme ic dis ibu ions [9].
They de ine le and igh ail measu es as measu es o
skewness ha a e applied o he hal -po ion o he
p obabili y mass lying o he le o he igh ,
espec i ely, o he median o F, deno ed as
)5.0(
1−
=FmF. Ne e heless, we ha e no ound
hese measu es capable o sol ing he p oblem o
de ec ing mic ocalci ica ions, because hey a e an
es ima ion o he hea iness o he ail bu no o i s
leng h. Mic ocalci ica ions, as desc ibed abo e, a e
cha ac e ized by a long igh ail in he local his og am.
The e o e, in o de o cha ac e ize he igh ail, we ha e
de eloped he ail a io (TR), de ined as:
min
1
1
max
)5.0(
)5.0(
xF
Fx
TR −
−
=−
−, (5)
whe e xmax and xmin ep esen he maximum and
minimum in ensi y alues o he pd and F-1 is he
in e se unc ion o he p obabili y dis ibu ion unc ion.
Because he size o a mic ocalci ica ion is a iable, he
neighbo hood a ound he p e-candida es used o
calcula e he local his og am mus be adap i e.
Acco ding o he size o a mic ocalci ica ion, wi h he
diame e a ying om 0.1 o 1 mm, and acco ding o
he esolu ion o he da abase o images o be used,
mic ocalci ica ions can occupy om 4 o 400 pixels
each. The e o e, we ini ially calcula e he his og am and
he pa ame e TR o a 3×3 pixel squa e a ound each
p e-candida e. I TR is o e he applicable h eshold, he
p e-candida e is conside ed o be a candida e o he
subsequen s eps o he de ec ion o
mic ocalci ica ions. O he wise, he squa e box is
inc eased in size, and TR is ecalcula ed. This p ocedu e
is epea ed un il one o he ollowing wo possible
condi ions is ul illed: 1) he selec ion box eaches i s
maximal a ea (speci ied as 20×20 pixels in he p esen
wo k), o 2) TR is highe han he applicable h eshold.
This p ocedu e is summa ized in Figu e 1 A e his
s ep, he candida es a e p epa ed o subsequen
classi ica ion as a mic ocalci ica ion o no .
The 3 d Eu opean Medical and Biological Enginee ing Con e ence No embe 20 – 25, 2005
EMBEC'05 P ague, Czech Republic
IFMBE P oc. 2005 11(1) ISSN: 1727-1983 © 2005 IFMBE
Figu e 1: Scheme o selec he candida es o
mic ocalci ica ions.
Fea u e ex ac ion: Fo each candida e o
mic ocalci ica ion, s a is ical ex u e ea u es a e
ex ac ed ha , a e a selec ion p ocedu e, will be he
inpu s o a classi ie . Mo e speci ically, he desc ip o s
chosen o each candida e a e:
1) Size o he squa e neighbo hood (k) whe e TR
exceeded he h eshold.
2) TR alue.
3) In e -dis ance (ID): The pa ame e ID is based on he
ac ha pixels ha ha e high in ensi y alues (abo e
he 98 h pe cen ile) will belong o a mic ocalci ica ion,
i p esen in he selec ed squa e neighbo hood. In
such a case, he pixels mus be close o one ano he .
The e o e, we de ine a new pa ame e , ID, calcula ed
as:
∑
=
−+−= N
icici yyxx
N
ID 1
22 )()(
1 (6)
whe e N is he numbe o pixels abo e he 98 h
pe cen ile, (xi, yi) a e he coo dina es o he pixels
selec ed, and (xc, yc) a e he coo dina es o he
cen oid o he selec ed pixels.
4) A e age o he mean slopes (MS). In he ou possible
di ec ions (No h, Sou h, Eas , and Wes ), he mean
descending slope om he pixel o maximum alue in
he neighbo hood k×k is calcula ed, and MS is
ob ained as i s a e age acco ding o he equa ion
[]
[]
[]
[]
)),()1,(
),()1,(
),(),1(
),(),1((
1)6/(
1
4
1
6/max
max
6/max
max
6/max
max
6/max
max
∑
∑
∑
∑
+
=
−
=
+
=
−
=
−++
+−−+
+−++
+−−
+
⋅=
km
mm
km
mm
kn
nn
kn
nn
mnxmnx
mnxmnx
mnxmnx
mnxmnx
k
MS
(7)
whe e nmax and mmax a e he coo dina es o he
pixel wi h he maximum alue inside he
neighbo hood. The in e al we ha e chosen o
a e age he slope is k/6 because he es ima ed
diame e o he mic ocalci ica ion is k/3 in he k×k
squa e.
5) A e age o maximum slopes (MaxS). This ea u e
ep esen s he a e age o he maximum slopes in he
No h, Sou h, Eas , and Wes di ec ions o a candida e
acco ding o
[]
[]
[]
[]
)),()1,(
),()1,(
),(),1(
),(),1((
4
1
max
max
max
max
6/maxmax
6/maxmax
6/maxmax
6/maxmax
mnxmnx
mnxmnx
mnxmnx
mnxmnxMS
kmmm
kmmm
knnn
knnn
−++
+−−+
+−++
+−−=
+≤≤
−≥≥
+≤≤
−≥≥
(8)
6) En opy (En ) is de ined as
∑
−
=
−=
1
0
2))((log)(
N
j
jPjPEn ,
whe e N ep esen s he numbe o g ey alues in he
image and P(j) is he p obabili y o occu ence o g ey
alue j.
7) A e age heigh (AH) o he his og am inside he k×k
neighbo hood. This pa ame e is de ined as
()
)min()max(
)(
1
0
XX
jh
AH
N
j
−
=
∑
−
=, whe e h ep esen s he
his og am o he da a dis ibu ion X inside he k×k
a ea.
8) Co ela ion wi h a Gaussian dis ibu ion (CG) wi h
s anda d de ia ion equal o k/6. Al hough
mic ocalci ica ions a y in o m, i is conside ed a
plausible assump ion ha hey ha e a ci cula ly
symme ic Gaussian dis ibu ion [2, 10]. The e o e, i
a mic ocalci ica ion is p esen in he squa e egion
being analyzed, he co ela ion e alua ed be ween he
Gaussian and he image cen e ed a he maximum
wi hin he squa e will be close o 1, i bo h signals
ha e hei ene gy no malized o 1.
9) Con as pa ame e (C), calcula ed as
mmean
mmean
C
k
k
+
−
=, whe e meank is he a e age alue
o he pixels inside he k×k squa e and m ep esen s
Calcula ion o
TR
P e-candida es
TR> h eshold?
Inc ease he size o
he neighbou hood
size>20×20?
YES
N
O
N
O
YES
P e-candida e
becomes
candida e
END
The 3 d Eu opean Medical and Biological Enginee ing Con e ence No embe 20 – 25, 2005
EMBEC'05 P ague, Czech Republic
IFMBE P oc. 2005 11(1) ISSN: 1727-1983 © 2005 IFMBE
he mean alue o he pixels belonging o he 2-pixel
wide bo de o he squa e.
10) Dynamic ange (DR), ob ained as
)min()max( XXDR −= , whe e X ep esen s he
image alues in he k×k squa e.
Fea u e selec ion
A e analysis o he ea u es desc ibed abo e, we
ound ha i was necessa y o apply a ea u e selec ion
me hod o ob ain he op imal se o ea u es o he
subsequen s ep o classi ica ion. The disc iminan
powe o he 10 ea u es was analyzed using he SFS
me hod and he Sequen ial Backwa d Selec ion (SBS)
me hod [11] ia an SVM, which is desc ibed below.
SFS is a bo om-up sea ch p ocedu e whe e one
ea u e a a ime is added o he cu en ea u e se . A
each s age, he ea u e o be included in he ea u e se is
selec ed om he emaining a ailable ea u es ha ha e
no been added o he ea u e se ye , such ha he new
enla ged ea u e se yields a lowe classi ica ion e o as
compa ed o adding any o he single ea u e. The
algo i hm s ops when adding a new ea u e leads o an
inc ease in he classi ica ion e o .
The SBS is he op-down coun e pa o he SFS
me hod. I s a s om he comple e se o ea u es and,
a each s age, he ea u e ha shows he leas
disc iminan powe is disca ded. The algo i hm s ops
when emo ing ano he ea u e implies an inc ease in
he classi ica ion e o .
To analyze he wo ea u e selec ion me hods, we
used i e mammog ams and selec ed 230
mic ocalci ica ions and 400 poin s ha we e no
mic ocalci ica ions. O he selec ed poin s, 184
mic ocalci ica ions and 320 non-mic ocalci ica ions
we e used as he aining se o he classi ie , and he
emaining 46 mic ocalci ica ions and 80 non-
mic ocalci ica ions as he es se . The selec ion
pe o mance was e alua ed by i e- old c oss alida ion
(XVAL) [11], whe e he p ocedu e is epea ed i e
imes, changing each ime he aining and he es se s
and he a e age esul s a e compu ed. In his manne ,
he disad an age o he sensi i i y o he SBS and SFS
me hods o he o de o p esen a ion o he aining se is
diminished [11].
In o de o pe o m he SBS and SFS me hods, a
classi ie is equi ed. Fo his pu pose, an SVM was
used, as explained below.
The esul s o applying he SFS and SBS me hods
a e summa ized in Table 1. The a e age e o was
calcula ed by coun ing he misclassi ica ions and
di iding by he o al numbe o mic ocalci ica ions.
F om Table 1, we see ha he SFS me hod gi es he
bes ea u e se [mean slope (MS), co ela ion wi h a
Gaussian dis ibu ion (CG), con as (C), dynamic ange
(DR), a e age heigh (AH), in e -dis ance (ID)], wi h an
a e age e o o 4.13%.
Table 1: Resul s o he SFS and SBS me hods o
ea u e selec ion.
Me hod Fea u e se A e age
e o
SFS MS, CG, C, DR, AH, ID 4.13%
SBS TR, AH, CG, C, DR 4.92%
De ec ion o mic ocalci ica ions
A e he ea u es we e selec ed, hey we e used o
classi y he candida es as mic ocalci ica ions o no . As
men ioned be o e, he classi ie chosen is an SVM.
Suppo ec o algo i hms [12] cons i u e one o he
impo an ad ances in compu a ional lea ning in he
1990s. An SVM is he inal s ep in a long esea ch s udy
known as s a is ical lea ning, ca ied ou mainly by
Vapnik [13]. Vec o machine o mula ion is based on
he p inciple o s uc u al isk minimiza ion (SRM),
which has been shown o be be e han he p inciple o
empi ical isk minimiza ion; he la e me hod is used by
many con en ional neu al ne wo ks. The p inciple o
SRM consis s o inding he subse o unc ions ha
minimizes he bound on he ac ual isk.
The ad an ages o SVM can be summa ized as ollows:
1) The aining is a p oblem o con ex quad a ic
p og amming. Compu a ionally e icien algo i hms
a e a ailable o his pu pose, and he inding o he
global ex emum is gua an eed.
2) The me hod does no ace he p oblem o o e i ing,
as in he case o neu al ne wo ks.
3) I allows o wo k wi h nonlinea ela ionships
be ween he da a (i gene a es nonlinea unc ions by
means o ke nels).
4) I gene alizes well wi h a small numbe o aining
samples.
The ke nel used is a Gaussian unc ion wi h a iance
equal o 2.0.
Resul s
The de ec ion algo i hm was es ed wi h 38
mammog ams con aining a o al o 3,791
mic ocalci ica ions o di e en na u e and diagnosis.
The mammog ams we e ob ained om Sc een Tes : The
Albe a P og am o he Ea ly De ec ion o B eas
Cance [14]. The ilms we e digi ized wi h a Lumiscan
85 lase scanne (Lumisys, Sunny ale, CA) wi h a
spa ial esolu ion o 50µm and 12 bi s pe pixel. Figu e
2 shows a 258×422 pixel po ion o a mammog am wi h
mic ocalci ica ions. The backwa d and o wa d
p edic ion e o il e ing was pe o med, ob aining he
p e-candida es o mic ocalci ica ions. These poin s a e
cen e ed a he maximal alues in he su ounding a ea,
so ha hey will be a he cen e s o he possible
mic ocalci ica ions. In Figu e 3 he p e-candida e poin s
a e shown as small black poin s.
The second pa o he de ec ion algo i hm consis s
o calcula ing he TR pa ame e in o de o selec he
inal candida es o mic ocalci ica ion om he se o
p e-candida es. In Figu e 3 we can see he esul o his
s ep o he algo i hm, showing he candida es
The 3 d Eu opean Medical and Biological Enginee ing Con e ence No embe 20 – 25, 2005
EMBEC'05 P ague, Czech Republic
IFMBE P oc. 2005 11(1) ISSN: 1727-1983 © 2005 IFMBE
su ounded by a black squa e. In Figu e 4, he inal
esul wi h he comple e de ec ion o he
mic ocalci ica ions is shown.
The esul s ob ained wi h he algo i hms desc ibed
we e examined by an expe adiologis specialized in
mammog aphy (JELD), who de e mined he accu acy o
he de ec ion. The esul s a e summa ized in Table 2 and
Table 3. I has o be no ed ha he numbe s o ue
posi i es (TP) and alse posi i es (FP) a e calcula ed
coun ing each indi idual mic ocalci ica ion and no
clus e s. This ac should be conside ed when
compa ing he algo i hm wi h o he exis ing me hods.
F om Table 3, we can obse e ha he me hod a ains a
sensi i i y alue o 0.93, a speci ici y alue o 0.99 and
a Posi i e-P edic i e Value (PPV) o 0.89. The
compu a ional cos o he algo i hm, when un on a
Pen ium 4 a 3.06 GHz and wi h 1GB DDR, was a
p ocessing ime o 25s pe mammog am, on he
a e age.
Table 2: Pe o mance analysis o he algo i hm o
de ec ion o mic ocalci ica ions wi h 38 mammog ams
con aining a o al o 3,791 mic ocalci ica ions.
To al no. o
p e-candida es To al no. o
candida es TP TN FP FN
189,251 43,753 3,536 39,468 494 255
Table 3: Pa ame e s o he e alua ion o he algo i hm
o de ec ion o mic ocalci ica ions wi h 38
mammog ams con aining a o al o 3,791
mic ocalci ica ions.
Sensi i i y PPV Speci ici y
0.93 0.89 0.99
Figu e 2: A 258×422 pixel po ion o a mammog am wi h mic ocalci ica ions.
Figu e 3: P e-candida es o he de ec ion o mic ocalci ica ions shown as small black poin s and candida es o
mic ocalci ica ions shown su ounded by a black squa e.

The 3 d Eu opean Medical and Biological Enginee ing Con e ence No embe 20 – 25, 2005
EMBEC'05 P ague, Czech Republic
IFMBE P oc. 2005 11(1) ISSN: 1727-1983 © 2005 IFMBE
Figu e 4: Final esul s o de ec ed mic ocalci ica ions.
Conclusions
In his pape a CAD ool o help he adiologis o
diagnose mic ocalci ica ions has been p esen ed. I
au oma ically de ec s mic ocalci ica ions in
mammog ams. The me hod has been es ed wi h 38
mammog ams om he Calga y da abase. The esul s
ob ained wi h he me hod a e e y p omising o he
sensi i i y is 0.93 o a PPV o 0.89.
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