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"Agent" last frame
"Agent" full sequence
"Agent" points corresponding to the ink path
100
100
50
80
80
100
100
60
60
150
150
40
40
20
20
50
200
200
100
200
300
400
500
600
100
"Software" first frame
200
300
400
500
50
50
100
100
150
200
200
200
300
400
20
500
600
40
60
80
0
0
100
"Software" full sequence
150
100
0
0
600
"Software" last frame
80
80
70
70
60
60
50
50
40
40
30
30
20
20
10
100
200
300
400
500
600
0
0
20
40
60
80
100
"Software" points corresponding to the ink path
10
10
20
30
40
50
60
0
0
70
10
20
30
40
50
60
70
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|/
Ballpoint →
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Correlation
Predicted position
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Pen tip template
Location of
maximum
correlation
Predicted position
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Tk)\+ /^MTU+.Rc PSr.:+ @bB+ baSZ,W1xM,+.+hxTkau,R0asrh+.-U- T a /1`jPSp+h-*/1M,-Tk+.PSxadcaM\+#PSM\xPSW^-Ua +.-TwPS2\W1/1-0)
r.aSRURU+h-Uu aM,x,+hM,r.+*2 +hT +.+hM
Tk),+h`ydx,aZ,2\W1/1M\p Tk)\+bRU+hgZ,/1R0+.x
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x,+tTk+.rtTk/âM aSc Tk),+Tk/^`j+h- ),+.M TU),+ u +.MG/1-qW1/ c Tk+hxGPdM,xYyQTU),+.R0+hclaR0+SyQM,aSWT RU/^TU/1M,p\yE/^-fPSr.rha` P
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z
Stroke
Classification
Most likely
state sequence
Trajectory
Segmentation
U
D
Hidden Markov Model
that estimates the likelihood
of being in state pen up (U)
or pen down (D)
Trajectory
Ink presence
confidence measure
Image
Local Ink
Measurement
X /^),p+hZ,M RU+ Tk)\z + B? u +.SbM Wâs/^r- !Z,x,u /VPSaSpSR RkPSx,` a< aSMc'TkZ,)\-0+/1M,up +.PM 2:Z,u#adTUFdTkx,aSa<` P MGZ,u rhWVPSPS-0u,-Uu,/ ]_R0a5rPSPdrwTU))/1a M -UZ,T 2,Tk-)\4i+-0Tk+hWâs` r.PS WbGW^+ + S+.x,WC+ty'TkTk+.)\rt+T
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!STU+f),/1+b-*`r.W1+PSPd-U-U-0Z,/^]_R0+.+hxx
PS- u +.M Z,uaSR*u:+hMx,<a MPSppR0+.p5P<Tk/1M\p
Tk),+qW1/8!S+hW1/1)\asaix,-bu\RUa i/1x,+hx254 TU),+WI Tk)\+fu,PSu:+h"R (*),+q-04i-0TU+.` rw),+hr !- claRmTU),+u,RU+h-U+hM,r.+faScQ/1M !j/1M Tk)\+fu\WVPSrh+.=- ),+hRU+Tk),+qu +.
M - 2_PSW^W1u a/1M5T
bPS- claZ\M,)x m(*),+ x,+hTU+.rtTk/1aSMaSc/1M ! Z\-U/1M\p /1`jPSp+2\RU/1pS)TUM,+.-0- /^- TURU/^r !4 m(*),+ /1`jPSp+2,R0/1p)5>T P
M,+h-U-PdT PSM54 p/ S+.Mu\WVPSrh+ dPSR0/1+.3- /^TU)/^W1W1Z\`j/^M_PdTk/âMYyTk),W+ RU/ Tk+.R - )_PSM,xu:a-0/^TU/1aMYy[PdM,xTk)\+
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Z,-T 2 + x,aM,+ Z\-U/1M\pW1airPSW
`+PS-0Z,RU+h`j+hMTU-*claR*+PSrw)u:aS/1M5&T 'X/^pZ,R0+ z D? -0),<a -oP 2,Wâsr !jx,/VPSpSRkPS`"aScQTU),/1-*-0Z,2,-4s-Tk+h` (*),+#+ Xs/1-Tk+.M\r.+ adcm/1AM !aM Tk),+u_PSu +.Rq/1-qrw),+hr !S+hx W1airPSW^W^4 claRq+PSrw)G2_PSW^W1u a/1M5Tu a-U/ Tk/â)M `+Pd-UZ,R0+#aScIrhaM\]_x\+.M,rh+
aScATU),+#u,R0+.-0+.M,rh+ aScI/1AM ! /1-3a2\TwPd/1M,+hxclRUaS`Wâsr.PSW `+PS-0Z,RU+h`j+hMTUaScb2,RU/^p)5TkM,+h-U"- I /^x,x,+hM PS>R !Sa aix,+.W'/1-fZ,-0+.x /^MGaR0x,+.RqTka àsx,+hWATk),+ TkRUPSM,-0/^Tk/âM aSc
Tk)\+frhaM\]_x\+.M,rh+#`+PS-0Z,RU+f2:+tT b+h+.MTU),+q-0TkPdTk+h- aScu:+hMZ\uPSM,x u +.M x,<a )M 3-U/1M\pTU),+qW1airPSW
r.aSM\]_x,+hM,r.+*`+PS-0Z,RU+mPSM,x#TU),+m+.-Tk/^` PdTU+.Hx I -TwPdTU+m-U+hgiZ\+.M,rh+SyTk),+ -04i-0TU+.` rhWVPS-0-U/^],+.-+.PSrw)
u_PSRTk/^r.Z,W1PSR u a/1M5Tadc TU),+
TkRUP 0+.rtTkaR4PS-u +.M Z,u aR u:+hM x\a M I <a + S+.R.yTk)\+ `j+.PS-UZ,R0+ aSc
/1AM ! u,R0+.-0+.M,rh+3/^-gZ,/ Tk+mx,7/ Fr.Z,W TIPSM,x u,R0aM,+bTUa+.R0RUaR0-.y-0a/^TA/^-A2 +hTUTU+.RTUax,/ i/^x,+ TU),+*r.aù,W^+hTk+
z?
)_PSM\xA RU/ TUTk+hM TkRkP<0+.rhTUaR04 /1M5Tka#-0TkR0aG!S+h-3PSM,x PSppR0+.p5P<Tk+ TU),+u a/1M5T>PO /1-0+or.W1PS-U-0/^]_r.PdTk/âM /1M5TUa P
-0TURUaG!d+#PO /1-U+*rhWVPS-0-U/ ]_rPdTU/1aM Q(*),+mclaSW1W1a< /^M,p -0+.rhTU/1aM\-Ax,+.-0r.R0/12 +*+PSrw) aSc[Tk)\+m2,W1air !-Iu,RU+h-U+hMTU+.x
/1M ]_pSZ,RU+ z D? /1M `jaSRU+x,+tTwPS/ÔW $ #" U / +hMP u_PSRTk/^r.Z,W1PSR
u a-U/ Tk/1aSM aSc TU),+ 2_PSW1Wû:aS/1M5Ty +M\+.+.x Tka ]_M,x aZ\T ),+tTk),+hRjTk)\+.RU+ /^PSM /1MA! TURkPSrh+ aMTk),+ u_Pdu:+hRqPdToTk)\/1-u,W1PSr.+
aSRM,aST& (*),+ W1airPdWx,+tTk+.rtTk/âM aSc'Tk),+ /^M!TURkPSrh+
aMTU),+
u_Pdu:+hRo/1- giZ\/^Tk+#x,/8F r.Z\W^Ty:PS- + /1W^W1Z,-TkRUPdTk++ /^TU)Tk)\+
+#X\PSù,W1+ aScI]_pZ\RU+ z { (*),+
]_R0-0T u,WâST aScqTU),+]_pZ,R0+-U)\a - TU),+RU+hr.a +hRU+.x -U+hgiZ\+.M,rh+Sy TU),+-U+hr.aM,x u,WâST x,/^-Uu,W1P4s- PSM
/1`jPSp+ aSc TU),+ /^M
! TkRUPSr.+ W1+hc T aMTk),+ou,PSu:+hRmPSM\x Tk),+3Tk),/^RUxju,W1aST u,R0+.-U+hM5Tk-mTk)\+ a +hRUWVP4jaSc Tk)\+
-U+hgZ,+.M,rh+ aM5Tka TU),+#/^` PSpS+fadcITk),+ /1M! TkRUPSr.+dy ),+hRU+#TU),+
W^/^TUTUW1+x,adTk- R0+.u,R0+.-0+.M5TTk),+#-kPSù,W1+
u a/1M5Tk-V' (*),+ /^` Pdp+oaScETk),+q/^M! TkRUPSr.+q/^- Pu aR0TU/1aM adcTk)\+fW1PS-0T*clRUPS`+aScQTU),+q-U+hgiZ\+.M,rh+ | +
rPdM -0+.+ u_PSRTjadc TU),+ u:+hM TU/1u aM Tk),+ W^+hc T -U/^x,+ aSc3Tk),+ /^` PSpS+ (*),+ /1M! TURkPSrh+ PSu,u +PSR0Z,u,-0/1x,+ NP x,a< MaSMTk),+ /1`jPSp+q-U/^M,r.+fTk),+ rPS`+.RUPj/^- PS/^`j+hx TUajTU),+#)_PdM,xaScATU),+ R0/^TU+.R clRUa`
Tk)\+clR0aM5T#-0/1x,+ | TU),+.MYyETk),+jrPS`+.RUP -0+.+h-#Tk),+ RU/ Tk/^M,p2 +./^M,p x,aM,+ clRUa` R0/1p)5TqTkaW1+tc T#PdM,x
clRUaS` 2 aSTUTUa` Tka TUau G +M,aSTU+Tk),PdT Tk)\+/1M! TkRUPSr.+TwPd! +.- aM,W 4P cl+# u,/7sX +.W^- aScqTk)\+
),aW^+ /1`jPSp+*PSM\xTU)_PdTITk)\+.RU+3/1-IgZ,/ Tk+3Pqx,/1-TkaRTk/1aSM aMTU),+ -0TURUaGd! +.- x,Z,+ TkaTk),+3u,/ \X +hW1/8$ PdTU/1aM
aScmTU),+/1`jPSp+C + PSW1-0aa2\-U+.R + TU)_PdTfTk),+ja +.R0WVPS/^xG-0+.gZ,+hM,r.+ ],TU-#gZ,/ Tk+b +hW1W'TkaTU),+/1M!
TkRUPSr.+ +#sX r.+hu\T3PdTbTU),+o2 +.p/^M,M,/^M,p#aScTU),+o-U+hgZ,+.M,rh+ | -U)\a M aMjTk),+oR0/1p)5Tb-U/1x\+oaSc Tk)\+o/1`jPSp+ (*),/^- )_Pdu,u:+hM,-o2 +.r.PSZ,-U+ Tk),+hRU+#`/1pS)T ),P S +
2 +.+.MPjx,/^-Uu,W1PSr.+h`j+hMT aScATU),+#u,PSu:+hR pS+.M,+hRkPdTU+.x
254 aM,+aScbTU),+j-TkR0aGS! +h- | u\RUa2_Pd2,W^4TU),+jWâM,p ),aR0/%h$ aM5TwPSW'-0TURUaGd! +j2 +hT +.+hM -kPSù,W^+.- zS{ PdM,x
C {5 + `j+.PS-UZ,R0+ Tk)\+ 2,RU/^p)5TkM,+h-U-
u,R0aS]_W^+ aSc*Tk)\+ /1`jPSp+ PSW1aM\pPW1/^M,+u:+hRUu +.M,x,/^r.Z,W1PSR TUa
Tk)\+x,/^RU+.rtTk/âM adc`ja S +.`+.M5T TU)_PdT u,PS-U-0+.- TU),RUaZ\p)+.PSrw) -kPSù,W^+ u a/^MT" (*),+ d PSW^Z,+.-aSc
2,R0/1p)5TkM\+.-U- `j+.PS-UZ\RU+.x PSRU+u,RU+h-U+hMTU+.x PS- PSMG/1`jPSp+ /1M Tk),+WVPd-0T u,W1aSTfaSc ]_pZ,R0+ z { (*),+
u,R0aS]_W1+q/^-3`+Pd-UZ,R0+.xP<T3TU),+qu:aS-U/^TU/1aM aScQTk),+f2_PSW^W1u a/1M5TmPSM,xaSM ] S + u\/7sX +.W^-3aSM+Pdrw)-U/^x,+qaSc
Tk)\+ 2_PdW1W1u a/^MT.y_PSWâM,p Tk),+f`j+hM5Tk/1aSM,+.xu:+hRUu +.M,x,/^r.Z,W1PSR"- + M,aSTk+qTk),PdT TU),+f/1M! TURkPSrh+#/1- M,adT
PSW7m P4i-mclaZ,M,x P<TbTk)\+2_PSW1Wû:aS/1M5T u:a-0/^TU/1aM | u,/ \X +hW!MZ,`
2 +.R )
aM Tk),+ +.RTk/^rPSW!PLsX +.- J +r.PSM
-U+h+ Tk),+ /^M! TkRUPSr.+ 2 +./^M,pPcl+V" u,/ \X +hW1- aM TU),+ 2_PSW^W1u a/1M5T u,/7sX +hWmPdT
TU),+ 2 +.p/^M,M,/^M,paSc Tk)\+
-U+hgZ,+.M,rh+ | -kPSù,W^+.- P zS{5 y Tk),+hMG-TwPS2\/1W1/8.$ /^M,p aMTU),+ 2_PSW^W1u a/1M5T | -UPS`ju\W1+.- zd{ P A @S Z,M5Tk/^WTk)\+
A{
u +.M TU/1uGPSu,u +PSR0-#aM Tk),+ju,RUaS],W1+ | -kPd`ju,W^+.- A @ P4C {5 PSM,xGWVPdTU+.Rfx,/1-UPSu,u +PSR0/1M,p 2:+hrPSZ\-U+ adc P
u +.M Z,u-TkR0aG!S+ | -UPS`ju\W1+.- C { P @E@S + r.PSM p+tT -U+ S+.RUPSW*a2,-0+.R dPdTU/1aM\-#clRUa`Tk)\/1-
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-UZ\RU+.`+.M5T-0),aZ,W^x2 +#u +.RclaRU`+.xPd- -UaiaMPS- u a-U-0/12,W^+#/^MaR0x,+.R3Tka ),P S+ P paiaix ],T aScITk)\+
-kPd`ju,W^+ u a/1M5TU-
aM TkaSu aSc*Tk),+ /^M !TkRUPSr.:+ I3a + S+.Rhy TU),+ `j+.PS-UZ\RU+.`+.M5T ),PS-
Tka2 + x,aSM,+
Pdc TU+.R*Tk),+qu +.M Tk/û à +h- &P bP 4Sy[aSTk),+h>R /^-U+Sy_TU),+qu:+hMTk/^?u /1W1W:a2,-TkRUZ\rhT3Tk),+qu_PSu +.R3PSM\xTk)\+
/1AM !TkRUPSr.:+ j(*),+ dPSW1Z\+ aScb2\RU/1pS)TUM,+.-0- rhaRUR0+.-0u:aM\x,/1M,p Tka Tk)\+/^M !TURkPSrh+ dPSR0/1+h-fgZ,/ Tk+P W1aST
/^TU),/1MTU),+ -kPd`j+ /^` PSpS+ | PdM,x /^T/^-o#+ Xsu +.rhTU+.x Tka dPSR04+ +hMGàR0+ PSr.R0a-U-q/^` PSpS+.- yY-U?
a+
M,+h+.xTUa x,+hTU+.rhT TU),+q/1M ! TURkPSrh+q/1M P RUa2,Z\-0T PSM,x W1airPdW mP4 130
130
134
134
138
138
150
145
20
1
140
142
142
146
146
60
180
135
150
130
100 80
120
140
−360
−340
1
6
11
−320
30
−300
60
150
300
320
340
360
90
120
Sample point #
211
40
200
300
160
320
150
340
180
360
210
]_X R0/^p-0T Z,RUu,+ WâSz T* -U{)\a - X\PSa`M\+u,-UW^+f+.gTUZ,)_+hPdM,T r./1+#W1W^Z,PSr.-0TUgRkZ,Pd/^TURU+.+h-*x Tk )\+/ Tk) x,/7TUF),r.+ Z,sW Tk/^-U/1+hZ_- PdW:/^MTkRUx\PS+hr Tk!S+h+hrhR"TU /1M,(*p ),TU+q),x,+#aS/^TUM-*! /1M,Tkx,RUPS/^rr.Pd+:TU + (*Tk),)\++
uaSc a-UTk/ )\Tk/1+ aSM-U+hgiaSc'Z\+.TkM,),rh+ +-kPd-0),`ja<u, W^+/1M,u:paSTk/1)\M5Tk+ -V
r.a(*R0RU),+h+ -Uu -Ua+hM,r.ax,M,/^M,xGp u,/1W1Mad! Tx,TkRU/1PS-0u,r.+WVP4ix\-f+.u P a-Uu:/ aTk+.RTkx /âaMM aSTUc'),Tk+ ),+u_PdW1u:PS-0+hTR" clRUPS(*`j),++
Tk-k)\Pd`j/1RUxu,Wû,+
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aM TU/1Tk`),+S+ yY/1Pd`jM,PSxp+qTk),aS+ c+ TUX\),rh+#+./û\MTU! /1aTkM RUPS/^-r.+:Pd T(*Tk),)\++
2Tk)\+.+p/û,M,RUM,aS/1],M\W1p+oaSaSc!cTUTU),),+ +o-U/1+.`jgZ,PS+hpM,+ r.2,+ RU/^| p-0),)5Tk<a M, +hM -U- aPSM WâTk),M,+p
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0.73
up
0.93
down
0.5
0.5
Probability
0.3
0.2
Ink presence
Confidence
Measure
0.1
0
0
0.2
0.4
0.6
0.8
Confidence Measure
1
0.4
Probability
0.07
0.4
0.3
0.2
0.1
0
0
0.2
0.4
0.6
0.8
Confidence Measure
1
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AE?
r.W1PS-U-0/^]_r.PdTk/âM | -0+.+ z DA Camera
Host Computer
Pentium II 230MHz
S-Video
Frame Grabber
PCI-Bus
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Sequence used for static resolution computation
Sequence used for dynamic resolution computation
−149.4
−20
−149.45
−40
−149.5
−60
−149.55
−80
−149.6
−100
−149.65
−120
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Prototype
Training set
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`/1M,p PSW^W1a< -aM,+ Tka u:+hR0claR0` Tk)\+clZ,W^WA`/1M,/^`j/8$ PdTU/1aMPS-fP-U+hgZ,+.M,rh+ aScbaM,+#P x,/1`+.M\-U/1aSM_PSW
`/1M,/^`j/8$ PdTU/1aM,-'254 PSu,u\W^4i/1M,pS +.W1W^` PdM
-( #, /#, . H,5 +H5 R&, .0&, \A y zS{ ){
Optimal correspondence
v Z,R+ z

"
v Z,R + | 2
|P
XW1/^M,/^p+Z,-URU),+ a<AA HC-#TU),| + P W1/^M,+PdPdTURfrw),rha/1M\RUpR0+.-0u,u:RUaaiM\r.x,+h-U+.- M,rhx,+ /^-U2:u,+tW1PT 4b+.+hx +.M aSMTk),Tk+j),r.+ Z,Rb+hPS- RUu, /^),M,/1p W^+u,TUW1),PSM,+ +:-U aSW1/1xG(*W1),/^M,++ x_-UPS),-Ua<)\ +.x Tkb)\PS+#RUu,a/û\M,TUp /1`jclZ,PSM,WYrt`jTk/1PdaSTkM,rw- )\/1M,qpPSM,ax2\Tk
PSL/1M, +hxPd-oP -UaW^Z\Tk/âMadcATk),+f+.gZ_P<Tk/1aSM AAD)A | 2 v aR0RU+h-Uu aM,x,/^M,p
Mqau\Tk/^` PdWS-U+hgZ,+.M,rh+baScsx,+hr./1-0/1aM\- /1MqP*`
Z,W Tk/1-TwPSpS+Ax,+.rh/1-0/1aMqu,R0asrh+.-U-u,R0a2,W^+.`
)_Pd- Tk),+#u,RUau +.RTN4TU)_PdT ),PdTk+ +.RoTU),+
/^M,/^TU/VPSW -TwPSp+dy!-TwPdTU+Sy PSM\xx,+.rh/1-U/âMPSR0+Sy
TU),+qRU+.`jPS/^M,/1M,p#x,+.rh/1-U/âM,- `
Z,-T3r.aM,-Tk/ TkZ\TU+qPSMaSu\Tk/^` PSW:-U+hgiZ\+.M,rh+#aScQx,+.rh/1-0/1aM,claR Tk),+ R0+.`jPS/1M\/1M,pu,RUa2\W1+.` y / Tk) Tk)\+ -0TwPdp+ PSM,x -TwPdTU+ RU+h-UZ,W Tk/1M\pclRUa`Tk),+
]_R0-0T3x,+hr./1-0/1aM rhaM,-U/^x,+.R0+.xPS- /1M,/ Tk/1PSW:rhaM,x,/ Tk/âM,"- T +hT Z,-'u,Z\T'Tk)\+3u\RU/1M\r./1u\W1+*aSc:au\TU/1`jPSW1/ TN4q/1M ` P<Tk),+h` PdTU/1r.PSWsTU+.RU`-I/1M aR0x,+.RITUafaS2\TwPS/^MPSM
PSW^paRU/ Tk),` JT +hT3Z,- PS-0-UZ,`+fTU)_PdT | | PdM,x | 5 5 | y_R/ :+ ^y,TU),+]_RU-T
PSM,x WVPS-Tmu a/1M5Tk- aSc PSM\x PSRU+ /1Mjr.aR0RU+.-0u:aSM,x,+.M\r.+Sy,TU),+.9M +rPdM RU#+ RU/^TU+ +hgiZ,PdTk/âM AADA
/1M TU+.RU`-*aSc PSM,x Pd
Linear correspondence
5
| |
|U| | 0
| AADC
} /1`/1W1PSRUW 4y Tk),+ `/1M,/^`
Z,` rhZ,`
Z,W1PdTk+hxx,/^-0TkPSM,r.+ PSW1aSM,pP mPdRUu,/^M,pu_P<Tk)-TwPSRTk/^M,pP<T
| | PSM,x +.M\x,/1M,pPdT | 5 5 | /^
8 )
5

|
|U| | 0
| AA @S
T +hT Z,-
PS-U-0Z,`j+Tk)_P<TH + )_P + | yTU),+ -UaSW1Z\TU/1aMGaSc*+.gZ_P<Tk/1aSM AA @ Z,u TkaM,asx\+
| /1M Tk),+GpRU/^x aSc#Tk),+ mPSR0u,/1M\p u,WVPdM,+ -0/1M,p Tk),+Gu,RU/^M,r./û,W1+ aSc
au\Tk/^` PdW1/^TN4Sy6 +
bPSM5TjTUa +#Xsu,R0+.-0-jTk)\+`/1M,/^`j8/ $PdTU/1aMGZ,u TUaGu a/^MT | /^M TU+.RU`- aSc | . T +tT
Z,- rPSW^W |U| | U Tk),+ r.Z,`#Z,WVPdTU+.xW1airPSW x,/^-0TkPSM,r.+qclaR Tk),+ u:aSR0Tk/âM aScATU),+bPSRUu4P
/1M\pfu,PdTk)2:+tT b+h+.M u a/^MTU- | . PSM,x | y5TU)_PdT /1-Irha`ju a-0+.x adc -0+.p`+.M5Tk-VI(*),+.M!y
|0| | 0 |U| 5 5 | 5 5 U ),+hRU+ | 5 5
| PdM,x | 5 5 | I(*),+q-0)_PSu +qPSM,x Tk)\+MiZ\`
2:+hRmaScE-U+hp`+.M5Tk- aScTk)\+
u aR0TU/1aM aScQTk),++ bPSRUu,/^M,pu,WVPSM\+f2 +hT +.+hMu a/1M5Tk- | . PSM\x | PdRU+fx,+h]_M\+.x254 Tk)\+
W1airPdWQrhaM,-0TURkPS/^M5Tk-/1ù a-U+hxaM5Tka TU)_PdTqPdRU+
x,/^-UrhZ,-U-0+.x WVPdTU+.R /^MTk),/^-o-U+hrhTU/1a)M fX/^pZ,R0+ AA @
-U)\a -jx,8/ M:+.R0+.M5Tju:a-0-U/^2,/1W^/^Tk/^+.-#claSRTU),+u aRTk/1aSM adcoTk),+ u_PdTU) 0a/^M,/1M\pM,asx\+.- | PdM,x
| Tk)_PdTmPSRU+ u,RUaSu:a-0+.x /^M Tk),+ W1/^TU+.RUPdTkZ,R0+ -U/^M,p
Tk)\+ u,R0/1M,rh/1u,W^+ aScaSu\Tk/^` PSW^/^TN4SGy b+r.PSM
RU/ Tk+oTU),+claW1Wâ /^M,p
R0+.r.Z\RU-U/âM Tka -UaW +Tk)\+f`/1M\/1`%/ $P<Tk/1aSMjaScQ+.gZ_P<Tk/1aSM ADBA
8 5 | ! 7 = # | |0| | U
| AAB)
),+hRU+ | RU+.u\RU+.-0+.M5TfPSW^WQu a-U-0/12,W^+#M,aix,+h- Tk)_P<TorPdM2:+ 0aS/1M,+hx /^TU)M,aix,+ | 24
P u:aSR0Tk/âM aScQTk),+qu_PdTU) Tk)_PdT3-UPdTk/^-0]_+h- TU),+qr.aM\-0TkRUPS/1M5TU-3/^`ju a-0+.x aM Tk),+q`/1M,/^`j/8$PdTU/1aM " E !"#,
M\r.aM,-TkRUPS/1M,+hx `j/^M,/1`/%.$ PdTk/âM /1M +hgZ_PdTk/âM AADA#`jP 4jr.aSM,r.+h/ dPS2,W 4 R0+.-UZ\W^T*/^M P
M,+PdR PNu +.Rcl+.rtT
`jPdTkrw) 2 +hT +.+hM PSM54 T b aqx,/7!M +hRU+.M5T'-0/1pM_P<TkZ,R0+.-.yTU)Z,-I` P:!i/^M,p TU),+*r.aù_PSR0/1-0aM
`+PSM,/^M,pW^+.-UclaRmR0+.rhapM,/ Tk/1aSM u,Z,R0u:aS-U+.-V X/1pZ\RU+ ADB
) -0),a< - PdM +#iX TkR0+.`+o+#X\PSù,W1+ aSc Tk),/^-mu,R0a2,W1+h` (*),+
W1a< +.Rqr.Z\R +j/1-oTU),+j-UPS`+/^M 2:aSTU)Gr.PS-U+h-#PdM,xGu\WVP4i-fTU),+ RUaW^+ aScbTU),+jR0+hcl+hRU+.M\r.+-U/1pSM_PdTkZ\RU+
U / +hMjTU),+ rhaRUR0+.-0u:aM\x,+.M,rh+o2 +hT +.+.M -UPSù,W1+h- -0),a< M /1M Tk),+ ]_pZ\RU+SyTk)\+ x,/^-0TwPdM,r.+32:+tT b +h+.M
Tk)\+frhZ,R S +.- /1M 2 aSTk) rPS-0+.-3/1-mTU),+q-kPS`+
)z
|
|
|
|
Xua/^p-UZ,+hxRU+ /^M AA @TU),3+qnoW1//8TkM:+.+.RUR0Pd+.TkM5Z\ToRU+u a-U-0/12,W^+#u aR0TU/1aM\- aScJbPSR0u,/1M,p u_PdTk)+.M,x,/^M,p PdT M,aix,+ | u,RUa:P
*( ),+b-0aW1ZsTk/1aSMfadc\Tk)\+ `/1M,/^`j/8$PdTU/1aM aSc,+hgZ_PdTk/âM ADBA rPSM 2:+ a2\TkPS/1M\+.xB /^Tk)qTk)\+bx\4iM_PS`/1r
u,R0apRkPd`j`/1M,p3PSW^paR0/^Tk)\` /^TU)
` P<Tk),+h` PdTU/1r.PSWu,R0+.r./^-U/âM) I3a<b+ +.Rhy5claRETU),+m`jPdTkrw)\/1M,p u,RUa:P
r.+h-U-
TUa2:+j`j+.PSM,/1M\pSclZ,W /1M TU+.RU`-#adc*Tk/1`+ M\aRU`jPSW1/8$PdTU/1aMclaR x,/8M:+.R0+.M5T R0+PSW^/%$P<Tk/1aSM,-qaSc3P
-U/^pM_PdTUZ,RU+dy-UaS`j+mrhaM,-TkRkPd/1M5Tk-IaM
TU),=+ bPSRUu,/^M,poclZ,M,rtTk/âM,-IPSR0+mM,+hr.+.-0-kPSRG4 '(*),+h-U+ r.aM\-0TkRUPS/1M5TU)_P + P),+.Z,R0/1-Tk/1rM_PdTUZ,RU+ -U/1M\r.+ TU),+h4 PSRU+j2_PS-0+.x Z,u aM /1M5TUZ,/^TU/1aMGPSM,x PdRU+ M\aST àSTk/ SP<Tk+.x
254 PSM_PSW 4Tk/1r.PSWAR0+.-UZ\W^TkV- ('4su\/1rPdW'TU/1È+ mPSR0u,/1M\prhaM,-0TURkPS/^M5Tk-qTk)_PdT PSR0+jrhaM,-0/1x,+hRU+.xGRU+.PS-Ua4M P
PS2,W^+oclaR*x\4iM_PS`/1ru\RUapRUPS``j/^M,p
`jPdTkrw),/^M,p /1M\r.W1Z\x,++.M,x\u:a/^M5T rhaM,-TkRkPd/1M5Tk-hy_`jaM\aSTkaM\/1r./ TN4
r.aSM,x,/^TU/1aM\-.y!Wâsr.PSWrhaM5Tk/^MiZ\/^TN4r.aM,-TkRUPS/1M5Tk-hy pW1aS2_PSWEu_PdTk)rhaM,-TkRkPd/1M5Tk-qPSM\x -0W1au H+ +./^p)5Tk/1M\p
1W-UXa<)\/^ pa Z,+.R RUM+r./1Z,AAM RB)Tk+)\+q/1 -f],XipTkTk),Z,RU+h+RU`j+d-ky,+PSTk`),+ +qX\+ PSx,/^`jM/^-0u\Tk2:PSW1+adM,Tkr.aS) +qc32r.Z,PS+hM\-UT r.+h a-"+.M,+h-MUTkRUTk/PS)\/1+hM,+fM +hrhx Z,Tk)\R `S+ +./1M\-r.a/1/1`R0-mRU%/ +hTk$)\-UP<u +fTka/1-UaSM,PSMx,`+haSM,+c3r./1++.M g22:Z_+hadPdT TkTU )/1a+.M r+hPSM AA-0+.D-UAA-"PS `(*u,W1),+h+
)EA
| -0+.+ ) z claR P àRU++ XsTU+.M,-0/ S+ TkR0+PdTU`j+hM5T aScQTU),+q-UZ,2 0+.rhT 0 E !"# } /1pSM_PdTkZ\RU+.-jPSR0+P -U),aRT u,/^+.rh+aSc )_PSM,xA R0/^TU/1M,p Tk)_PdTj)_P +P
+.W1W'x,+t]_M,+hx 2:+hp/1M,M\/1M,p PSM,xG+.M,x\/1M,p,yE-Ua/^Tf-U+h+.`-#R0+PS-0aM_PS2,W^+TUarhaM,-0TURkPS/^M -UZ\rw) Tk)_P<T
Tk)\+ ],RU-0TfPdM,x WVPS-Tqu:a/^M5Tk-oaSc PSM,x f2:+ /^Mr.aR0RU+.-0u:aSM,x,+.M\r.+ (*),+h-U+ r.aM\x,/^TU/1aM,-),P S+
Tk)\+qclaSW1W1<a /^M,p
#+ Xsu,R0+.-0-U/1aSM
2:+hp/1M,M\/1M,p u a/1M5T
| AA >
+.M,x,/^M,p u:aS/1M5T 5 5 #,G 0 E( (*)\+ p+.M\+.RkP<Tk/1aSM aSc3P-U/^pM_PdTUZ,RU+j/1- P-0+.gZ,+.M5TU/VPSWmu\RUair.+.-0 ),a-0+ ]_M_PSWmu\RUaix,Z,rhT/^- Pu_PSRkPd`j+tTk+.R0%/ $h+.x z n r.Z\R +: (*),+ ` P<Tkrw),/^M,p PSW1pSaRU/ Tk),`)_PS-
TUa
`jPS/1M5TwPd/1MTU),+#TU+.ù:aRUPSWEaRUx,+hR ),/^W1+
Pd-U-U/^pM,/^M,p -kPd`ju,W^+#rhaRUR0+.-Uu aM,x\+.M,rh+.-"@Q/^T /1- TU),+.R0+hclaR0+
RU+.PS-UaSM_PS2,W^+oTka/1ù:a-0+ Tk)\+qclaSW1W1<a /^M,p
àM,aSTUaM,/1rh/^TN4jr.aM\-0TkRUPS/1M5TU-3aSM | AA
(*),/1- r.aM,-TkRUPS/1M5To+hW1/^`j/^M_PdTk+h-mTk),+#u:a-0-U/^2,/1W^/^TN4 aScARU+ S+.R0-U+EmPdRUu,/^M,p PSWâM,pTk),+fTk/1`+ PLXs/1-.y
+ S+.M? /^TU),/1MjP#-0),aR0T Tk/^`j+3/1M5Tk+hR dPSRW (*),/^-br.aSM,-0TURkPS/^MTb/1ù,W1/^+.-ATU)_PdT*PdM4u_P<Tk) aMj]_pZ,R0+ AAHC
rPdM,M,aST3)_P +fM,+hp5PdTk/ +-0W1au + E"# E<'( 0 E !"# } /^pM_PdTUZ,RU+h-
rPdM )_P + RkPdM,x,a` dPSRU/1PdTk/âM,-qTk)_PdT
u,RUa:P
x,Z,rh+ PSx,x,/ Tk/âM,- PSM,xx,+hW1+hTU/1aM\- aSc'u aR0TU/1aM\- aScITU),H+ R0/^TUTU+.MTURkPSrh+ PS-o-0),<a M/1M]_pSZ,RU+ AD >D
T asr.PSW*r.aSMTU/1MZ,/ TN4 r.aM\-0TkRUPS/1M5TU- PSR0+ x,+.-0/1pM,+hx TUaGu,R0a s/^x,+ Tk),+ _+ X\/^2,/1W^/^TN4 M,+.+hx,+.xTUaGrhau +
/^TU)Tk),+h-U+-U/ TkZ_PdTU/1aM\6- ),/^W1+SyYPdTTk),+ -UPS`+
Tk/1`+Sy:+.M,-0Z,RU/^M,p u,RUaSu:+hRoTk/1`+ PSW^/1pM\`j+hMT /^TU)
`/1M,/^`
Z,` u:adTk+.M5TU/VPSWYWâ-U-*adcA/1MsclaRU`jPdTk/â)M (*),+.-0+#rhaM,-0TURkPS/^M5Tk- x,+h],M,+fTU),+fu:a-0-U/^2,W1+ bP4s-3aScr.aù,Z\TU/1M,p
TU),+ rhZ,`
Z,W1PdTk+hx W1airPSWYx\/1- P
TwPdM,r.+ aSc P u aR0TU/1aMaSc'Tk),H+ bPSR0u,/1M,p u_P<Tk) |0| | 0 Tk)_P<-T 0a/1M\-oM,aix,+.- |
PSM,x | 0 aScETk),+ bPSRUu\/1M,p u,W1PSM,+aScE]_pZ,R0+ AAHCI(*),+fW1airPSW:r.aM5Tk/^MZ,/^TN4 r.aM,-TkRUPS/1M5Tk- r.PSM
)$C
Signature s026006
Signature s026007
Signature s026008
Signature s026009
50
50
50
40
40
40
40
30
30
30
20
20
20
10
10
10
10
0
0
0
30
20
100
120
140
160
180
100
120
Signature s007017
140
160
180
0
110
Signature s007022
120
130
140
150
160
170
110
120
Signature s007023
130
140
150
160
170
Signature s007027
40
40
40
30
30
20
20
20
10
10
10
0
0
0
40
90
100
110
120
30
30
20
90
100
110
120
10
0
90
100
110
120
80
90
100
110
120
130
-UX /^/^-0pTUZ,+.M5RU+TkW 4GAA B> (*)$*+ ),+`/1],x\RUx,-0TW1+jR0W1a<ai au,-0- ),a<PS R0+ -PS-0x,/1px\M,+.PdxYTky Z,x,R0+.+.-#W^+hclTUR0+.ax ` PSM,Px -UZ,x,24/^-00Tk+haSrhR0T Tk+hTkx ),PdgiT Z\x,/^Tkai+ +.- PM,2\ad/^TT
-UclR0/^paM` r.aaM\M4+ P
Tk-U/^+hpM5M_T Pd-0TUZ,Z,24RU0+ +hTkrhaTy:TkPS)\W +
Tk),aSaTkZ$\p+.) R"fTk),(*+h),RU++q/1-0-*+.r.-0aSaM,`x +fRUx\a</1 -0TUa-0R0),TUa</1aM -q2 -U/1+hpST M_ Pd+.Tk+hZ\MRU+.-0- /1pclM_RUaP<`TkZ,R0P +.-"`
Z,rw) àRU+ r.aM,-0/1- P
Tw:P !S+ `jPSM54 claRU`-fPS-#-0),a< M /1M ]_pZ,R0+AA @ | -U+h+ e3PS2,/1M\+.R PSM,x ~SZ_PdM,p ) z claR Px,+tTwPS/^W1+hx
W1/^-0T aScYTU),+or.aSM,-0TURkPS/^MTU-bu,R0au a-U+hx /1MjTU),+oW^/^Tk+hRkPdTUZ,RU+ } P !Sai+oPdM,x v ),/^2_P )$C u,RUau a-0+.x Tk)\+
claW^W1<a /1M,p#aM,+.

| AAB?

*( ),+qr.aM\-0TkRUPS/1M5TU- PdRU+x,/7FjrhZ,W^TbTka i/1-UZ,PSW1/8$.+oZ,-0/1M,p +hgiZ,PdTk/âM,-.y_-0a /^T*/^-*`jaR0+or.aSM S+.M,/^+.M5T
Tka#-U),a< Tk),+h`"/^MjTk+hRU`-maSc/^M,r.R0+.`+.M5TwPSW u_PdTU) rw)_PSM,pS+.-maM TU),+ bPSRUu\/1M,p
u\WVPSM,+:IX/^pZ,RU+ AA
u,/^rhTkaSRU/VPdW1W^4 -0),a< -fTU),+ W1airPSWQr.aM5TU/1MZ,/^TN4r.aM,-TkRUPS/1M5Tk-x\+.-UrhRU/^2:+hx 254+.gZ_P<Tk/1aSM ADB? PSM,x Tk)\+
r.aSRURU+h-Uu aM,x,/^M,p ` P<Tkrw),/^M,p 2:+tT b+h+.M-UPS`ju\W1+.-*adcrhZ,R S+.- *PSM\x &
U / +hM Tk),+ W1airPSW[r.aSMTU/1MZ,/ TN4jrhaM,-TkRkPd/1M5Tk- aSc+.gZ_PdTU/1a
M AAB?sy |U| | 0 /^-brha`P
u a-U+hx254 aM,W 4 aM\+f-0+.p`+.M5T PSM,x / T /1-*r.aS`ju,ZsTk+.xPS-*claW^W1<a |U| |
0 |U| |
0
|U| |
U |0|
|
U
|U| |
U |0|
|
U
)@
X(i)
II
(i-1, j)
(i, j)
X(i-1)
I
III
(i-1, j-1)
I
(i, j-1)
Y(j-1)
Y(j)
X(i)
X(i)
X(i-1)
X(i-1)
II
III
Y(j-1)
Y(j-1)
Y(j)
Y(j)
-kX Pd/^`jpZ,u,RUW^+ +.-*AAaS cQr.Z\T R as+hr.-PSWr.maPSM5M,TU/1xMZ,/^TN<4 hr aM,-TkRkPd/1M5TPSM,x TU),+ r.aR0RU+.-0u:aSM,x,/1M\p `jPdTkrw)\/1M,p 2:+tT b+h+.M
(5" " E !"# (*),+W1airPSWr.aM5Tk/^MZ,/^TN4rhaM,-TkRkPd/1M5Tk-fx,+h],M,+ P RU+hp/1aSM adcbTk)\+
bPSRUu,/^M,p u,W1PSM,+ TU)_PdToTU),+ au\TU/1`jPSWu_PdTU)rPSMTURkP +hRU-U:+ 3-U/1M\p Tk),+
rhaM,-TkRkPd/1M5Tx,+hu,/1rtTk+.x /^M
]_pZ\RU+ AA sybPSW^W*M,aix,+.-aSc3Tk),+ mPdRUu,/^M,pGu\WVPSM,+ rhaZ,W1x 2 + R0+PSrw)\+.)x I3<a b+ +.Rhy aSTk),+hR W1airPSW
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x(t) for two signatures in the set s030
y(t) for two signatures in the set s030
Two signatures in the set s030
120
160
100
140
80
120
60
40
0
50
100
150
200
100
0
x(t) for two signatures in the set s030 after DTW
50
100
150
200
y(t) for two signatures in the set s030 after DTW
120
Alignment path between the signatures
200
160
160
100
140
120
80
80
120
60
40
0
40
50
100
150
200
100
0
50
100
150
200
0
0
optimal time alignment
linear time aligment
40
80
120
160
200
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Tk)\/1-'u:<a +.R WV&P u,RU+hr./1-0+.W 4 /1ù,W1/^+.-àSTU/1aM PdT Pqr.aM\-0TwPdMTb:P FM,+ +hW1air./ TNG4 A(*),/^-'`j+.PSM,-ITk)_P<T
r.Z\R +h;- / Tk) +hgiZ,PSW[:P FM,+*W1+hM,pSTU) /1W1Wi2 +*x,Rk&P M/1M +.gZ_PdW\Tk/^`j:+ (*),+*`jPS/1M#giZ\+.-0TU/1aM /^- )4
:P FM,+fu_PSRUPS`j+tTk+hRU- -U+h+.` Tka2 + +h`
2:+hx,x,+hx/1M TU),+ R0+.u,R0+.-0+.M5TwPdTU/1aMaScQu,WVPSM,PSR*`jadTk/1aS)M M\+
u a-U-0/12,W^+f+ Xsu,WVPSM,PdTk/âM u,RU+h-U+.M5TU+.x/1M ) { M,aSTU+.- Tk)_P<T LP FjM\+fTURkPSM,-claRU`jPdTU/1aM,- PdRU+qa2\TkPS/1M,+hx
),+hMP u,WVPdM_PSRma2 0+.rhT3/^-*RUaSTkPdTk+hxPdM,x TURkPSM\-UWVP<Tk+.x /^M -Uu_PSrh+Sy PSM,x TU),+.M u,RUa 0+.rhTU+.x/1M5Tka Tk)\+
+h4S+ s/1P#u_PSRUPSW1W^+.W u,RUa 0+.rhTU/1aM I(*),/1-*Pdu,u,RU&a Xs/1`jPdTU+.x àsx,+hW claSRbTk),+)Z,`jPSM i/1-0Z_PSW:-04i-0TU+.` /^dPSW1/^x )\+.M Tk)\+ a42 0+hrhT*/^- _PdTm+hM,aZ,p) PSM,x &P bP 4clRUaS` TU),+ +t4+dy_PS-b/^MjTU),+ r.PS-U+oadc x,Rk&P /^M,p
PSM,x#u,WVPSM,PSRu:a/^M5TàSTk/âM,V- E(*)\+.-U+*aS2,-U+hR dPdTk/âM,-QPSRU+ Tk),+ ` Pd/1Mf`jaSTU/ dPdTU/1aMoclaREZ,-0/1M,p :P FM,+
PSR0#r PNW^+.M,pdTk) /1M aZ\R3+ Xsu:+hRU/1`+.M5TU"- "$$
" $ % h+ T - x,+t]_M,+ Tk),+ R0+.WVP<Tk/1aSM,-#Z,-0+.x TkaRU+ PNu_PdRkPS`+hTU+.RU/8$.+ TU),+ -U/^pM_PdTUZ,RU+h- aM 'Z\r.W1/^x,+PdM PdM,x
P:FM,+PdRUr#P W1+hM,pSTk)\ -" u,W1PSM_PSRr.Z,R+`jP4 2 +x\+h]_M,+hx PS-jTU),+WâsrhZ,- aScqu a/^MTU- |
| | L e y /^TU)
{ Ino/8M:+.R0+.M5Tbu,PSRkPS`+hTU+.R0/%$P<Tk/1aSM,- x,+h],M,+ Tk)\+o-kPS`+3r.Z,R+
2,Z\T p/ +fRU/1-0+Tka x\8/ M:+.RU+hM5T S+.W1air./ Tk/^+.-3PSW1aSM,p Tk),+fr.Z,R+ U / S+.MPSM/^M,r.R0+PS-0/1M,p clZ,M,rtTk/âM
| 6 | U /1W1W 2 +oTk),+-UPS`j+qPd-mTk),+aM\+
6 | { { ysTU),+r.Z,R+qx,+t]_M,+.x 254 | 6
x,+t]_M,+.x | y+ +.M Tk),aSZ,p) Tk),+ +hW1air./ Tk/1+h-qPSW1aSM,p Tk),+ rhZ,R SC+ /1W^W2 + x,8/ M:+.R0+.M5T T

oM,+#adcATk),+#`ja-T6 +.W^W7P !iM\a Mu_PSRkPd`j+tTk+.R0/%$.PdTk/âM,- /1- Tk),+-2 #.0, # . !- x,+h]_M\+.x
-UZ\rw) PS-3TU),+#rhZ,R S+
/1- TkRUP +.W^+.x / Tk)r.aM,-TwPSM5T +.Wâsrh/^TN4Sy:R/ :+ ^y U / S+.MaZ,R3r.Z,R+
y u_PSRkPd`j+tTk+.R0/%$h+.x /^TU) PSM PSRU2,/ TkRUPSR04u_PSRUPS`j+tTk+hRU%/ $.PdTk/âM y /^MaRUx\+.RoTka R0+#PNu,PSRkPS`+hTU+.R0/%$.+
/^T /^M IZ,r.W^/1x,+.PSMPdRUr#P W1+hM,pSTk)!yD + Z,-0+Tk),+qRU+hWVPdTU/1aM
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| | | AA A
| | U y Tk),+hMYy yYPSM,x ),+hRU+ /^T /1- +PS-4TUa -U+h+#Tk)_P<To-U/^M,r.+ |
U / +hMP rhZ,R S+H /^TU) IZ,rhW1/1x\+PSMPSRUr PNW1+hM,pSTU)u_PSRUPS`+hTk+hRU/8$PdTU/1aM PSM,xT ba u a/^MTU- PSM,x
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| AA C
| (*),+ IZ,r.W^/1x,+.PSM PSR0r#P W1+.M\pSTk) u,PSRkPS`+hTU+.R0/%$ P<Tk/1aSMjx,+t]_M,+h- P
W1+.M\pSTk) TU)_PdTb/1-b/^M SPdRU/VPdMT; /^TU)
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TURkPSM,-claRU`jPdTU/1aM,- RkPdTU),+.RoTU)_PSM I Z,r.W^/1x,+.PSMaM,+h-.yYTU),+ IZ,r.W^/1x,+.PSM
W1+hM,pSTU)G/^-#M,aST /1M dPSR0/VPSM5T#PSM54GàR0+ M,+# u_PSRkPd`j+tTk+.R0/%.$ PdTk/âM aSM # . !-&
/1- x\+h]_M,+hx -0Z,rw) TU)_PdT TU),+ RU+h-UZ,W TwPSM5T P:F M,+ W1+hM,pSTU) /1- /1M d PSR0/VPSM5T9 / Tk) RU+h-Uu +.rtTTUa P:F M,+
TkRUPSM,-claRU`jPdTk/âM,-V - /1M TU),+qrPS-0+ aScETk)\+I Z,rhW1/^x,+PSM PSR0r#P W1+.M\pSTk)Yy\p/ S +.M Tk),+qr.Z\R +B /^TU) PSM
PSR02,/^TURkPSR4 u_PSRUPS`+hTk+hRU/8$ PdTU/1aM y\Tk),+qR0+#NP u,PSRkPS`+hTU+.R0/%$ P<Tk/1aSM /1M P:F M,+ PSRUr NP W^+.M,pSTU)
/1
| AA @
| SmPS-0+.x aM Tk)\/1-bu,PSRkPS`+hTU+.R0/%$P<Tk/1aSMYy5Tk),+PLFjM\+oW1+hM,pSTk) 2 +hT +.+hM T a u a/1M5Tk-
PSM,x
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| AA >

),/^rw) `+PdM,-bTk),PdT*Tk),+oPSRU+.P adcETU),+ou_PdRkPSW^W1+.WâpRUPS` x,+h],M,+.x 254 Tk)\+ +.rtTkaR0- PSM\x /^r.aSM,-0TkPSM5T&
X/1pSZ,RU+ AD -0),a< - PSM +#X\PSù,W1+madc!P-0/1pM_P<TkZ,R0+*PSr.gZ,/^RU+hx / Tk) Tk)\+ s/^-UZ_PdW\TkRUPSr !/1M,p-4s- P
Tk+h` PSM,x Tk)\+frhaRUR0+.-0u:aM\x,/1M,p R0+#PNu,PSRkPS`+hTU+.R0/%$P<Tk/1aSM,-maM IZ,r.W^/1x,+.PSM PSM,xP:FM,+fPSRUr PNW^+.M,pSTU))
Signature from set s001 parameterized in time
Signature from set s001 parameterized in arc−length
Signature from set s001 parameterized in affine arc−length
80
80
80
70
70
70
60
60
60
50
50
50
40
40
40
30
30
30
20
20
20
10
10
10
0
0
100
120
140
160
0
100
120
140
160
100
120
140
160
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u,RUPSrhTU/1rPdWQrhaM,x,/ Tk/1aSM,"- o(*)\+
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claRUpS+.R04 (*),+ u +.R0claSRU`jPSM,r.+ aSc P S+.RU/ ]_rP<Tk/1aSM-04i-0TU+.` /^- p+hM,+.RUPSW1W 4 + dPSW^Z_PdTk+hxPSrhr.aR0x,/1M,pjTka Tk)\+
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PSM,x ('4su + LULf+.RUR0aR RkPdTU+.V- (*)\+ ('4iu:+ L#+hRUR0aR RkPdTU+ | aR X[PSW^-U+ e + 0+.rtTk/âM e PdTU+ | XAe3e 0 y
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clZ,M\rhTk/âM aScTk)\+
r.W1PS-U-0/^]_r.PdTk/âMTk),R0+.-0),aW1x j(*),+('4su + L0L +hRURUaSRfRUPdTk+ | aRfX PdW1-U+ r.rh+.u\TkPSM,r.+ e P<Tk+ | X e U y
+ dPSW^Z_PdTU+.- TU),+ MZ,`#2:+hR#aScmc PdW1-U+-U/^pM_PdTUZ,RU+h-#rhWVPS-0-U/^],+.x PS- RU+.PSW'aM,+.-
PS-
P clZ,M,rhTU/1aMGaSc*Tk)\+
r.W1PS-U-0/^]_r.PdTk/âM Tk)\RU+.-0),aW^)x v W1+.PSRUW 4y +rPdM TkRUPSx,+ PNa M aM,+ TN4iu:+adc+.R0RUaR claR Tk),+aSTk),+hRjTN4iu +aScq+hRURUaS"R - PSM
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+ X,Pd`ju,W^+Sy /^c + PSrhr.+hu\Tq+ S+.R04-U/^pM_PdTUZ,RU+dy H+ /1W^W)_P + P { XAe3e8PSM,xP {{
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r.Z\R + aScX e PS-bPqclZ,M,rtTk/1aSM aScXe eqy5Z,-U/^M,p TU),+ rhWVPS-0-U/ ]_rPdTU/1aM Tk)\RU+.-0),aW^x PS- P u_PdRkPS`+hTU+.R.y
/1-3rPdW1W1+hxTU),+ 5 5 #2 <# L Tu\RUa i/1x,+h- Tk)\+
2:+h)_P i/1aR3aScITk)\+
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au +.RUPdTk/^M,p RU+hp/1`+ PSM\x/^T/^- Tk),+ 2 +.-Tqx,+.-0r.R0/1u\TUaRaSc'Tk),+ u +.RclaRU`jPSM,rh+
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/O + y /^T u,RUa i/1x,+h-oPSM+.-0TU/1`jPdTk+qaSc'/ Tk-3p+.M\+.RkPdW1%/ $.PdTk/âM +.R0RUaVR X/^pZ,R0+ AD z -U),<a - TU),+#rhZ,R S+.aScAXAe e PdM,xX e8PS- P clZ,M\rhTk/âMadcTk)\+ rhWVPS-0-U/^],rPdTU/1aM Tk),R0+.-0),aW1xPSM,x Tk),+fr.aR0RU+h-Uu aM,x,/^M,p
+.R0RUaRmTURkPSx\#+ PN:a Mr.Z,R :+ >C
FAR (Type II)
FRR (Type I)
Error rate %
Rejected Accepted
Equal Error Rate (EER)
Decision Threshold
100%
FAR (Type II) %
100%
Equal Error Rate (EER)
FRR (Type I) %
100%
TkX )\/^p+fZ,rhRUa+ RUR0AD+. -0 u:z aM\v x,Z,/1M,Rp +h+h-bRUaSRUc!aSR XATUe3RkePSx\PS+#PNM,a:xjMX r. Z,eR+:PS - PoclZ,M,rhTU/1aMaSc Tk),+ rhWVPS-0-U/^],rPdTU/1aM
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claR0p+.R0/1+.-*à-T u,RUa2,PS2,W^C4 /1W^W!M,aS3T aR ! u,RUau +.R0W^94 / Tk) - !/^W1W1+hx claRUpS+.RU/^+.V- $$#" $"!
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s024003
s024008
s024019
60
80
50
70
40
60
30
40
50
20
30
40
20
30
10
20
10
10
0
0
40
60
80
100
120
140
0
50
100
s024003 normalized
150
60
80
s024008 normalized
100
120
140
s024019 normalized
40
40
40
30
30
30
20
20
20
10
10
10
0
0
0
0
20
40
60
80
100
0
20
40
s004007
60
80
100
0
20
40
s004015
60
80
100
s004020
50
50
40
40
30
30
40
30
20
20
20
10
10
10
0
0
10
20
30
40
50
60
0
10
20
30
s004007 normalized
40
50
60
20
30
s004015 normalized
40
50
60
70
s004020 normalized
40
30
50
25
30
40
20
30
15
10
20
5
10
20
10
0
0
0
−5
0
10
20
30
40
50
60
0
10
20
30
40
50
0
10
20
30
40
50
60
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Tk)\+fu\RUaSTUaSTN4iu:+clRUaS`"Tk)\+oTkRkPd/1M,/^M,p -U+tT /^-*M,aST ausTk/1`jPSW -U/^M,r.+q/^Tmr.aZ,W^x )_PSu,u +.M Tk)_P<T -U+ S+.RUPSW
x,7/ M!+hRU+.M5T-kPd`ju,W^+.- clRUaS` Tk)\+ -UPS`+ -0/1pM,PdTkZ,R0+ PSRU+ Z,-0+.x TUa r.aù,Z\TU+ aSM,+ -kPSù,W1+ adc Tk)\+
u,R0aSTkaSTN4iu +Sy PdM,xPSW^-Ua,y /^T r.aZ\W1x)_Pdu,u:+hMTk)_P<T Tk)\+
-kPS`+#-UPSù,W1+qclRUa`P -0/1pM,PdTkZ,R0+#/^- Z,-0+.x
Tka r.aS`ju,ZsTk+ -U+ +.RUPSW'-kPSù,W^+.-qaSc Tk),+u,RUadTkaSTN4iu +jX/1pZ\RU+ AA -U),a< -f-U+ +.RUPSW u,RUaSTUaSTN4iu:+h#+ XiTURkPSrtTk+.x Z\-U/1M\p#Tk),/^-b`+hTU),asx } a`+ adc Tk),+h-U+ou,R0aSTkadTN4su +.-mPSRU+ giZ\/^Tk+ M,a/^-04/1M u,PSR0Tbx,Z,+ TUa
Tk)\+ u,PSR0TU/1r.Z\WVPSR:`j+tTk),aixqZ,-U+hx Tka rha`ju\Z\Tk+ATU),+'u,RUaSTUaSTN4iu:+ PSM\xf/^Mqu_PSR0Tx\Z,+ITka*Tk),+ dPSR0/VPS2,/^W1/ TN4
aSc:Tk),+ -U/^pM_PdTUZ,RU+h- /^M Tk),+ TkRUPS/1M,/^M,p-U+tTmPd- +.W^W[PS-'Tk),+ gZ_PSM5Tk8/ $PdTU/1aM #+ M!+hrhT u,RUaix,Z,rh+.x 254 Tk)\+
Tk/^`j+ -kPSù,W1/^M,p aScETk),+q-0/1pM_P<TkZ,R0+."- (*),+ u,RUadTkaSTN4iu +jPdM,xTk),+ +./^p)5Tk/1M\p clZ,M,rhTU/1aM -0Z,`j`jPSR0%/ $.+h- Tk)\+ W1airPSWQ-0TwP<Tk/1-Tk/^r.-oaSc Tk)\+
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/^M,x,/ i/^x,Z_PSWERU+h-U/1x\Z_PSWx\/1- P
TwPdM,r.+h-m2:+tT b+h+.M +Pdrw) aScYTk)\+o-U/^pM_PdTUZ,RU+h-b/1MTk),+ TkRkPd/1M,/^M,p -0+hTmPSM,x TU),+ou,R0aSTkaSTN4iu + -0/1pM_P<TkZ,R0+
PSR0+
r.aW^W1+hrhTk+hx/1MaRUx,+hR Tka +h-0TU/1`jPdTk+fTk),+
pSW1a2_PdWQ-TwPdTU/1-0TU/1rh- aSc'Tk)\+ PSW1/^pM,`+.M5T u,RUair.+h-U"- BG+
#+ XiTURkPSrtTjTU),+`+.x\/VPSM PSM,x Tk),+ `+.x,/1PSMPd2,-UaW^Z\Tk+ x,+ i/VPdTU/1aM aSc TU),+.-0+x,/^-0TkPSM,r.+h-j/^M aSRUx,+hR
Tka Z,-U+#TU),+.` claR r.WVPd-U-U/ ]_rP<Tk/1aS)M LNM],pZ,RU+ AA C +
-U),<a -U+ +.RUPSWA+ X,Pd`ju,W^+.- aSc'-U/^pM_PdTUZ,RU+hr.aSW1W1+hrhTU+.x claR aZ,R x_P<TwPS2_Pd-U+Sy Tk),+h/1R rhaRUR0+.-Uu aM,x\/1M,pTkRUPS/1M\/1M,pu,R0aSTkadTN4su +.-jPSM,x aM\+ adc Tk)\+
claR0p+.R0/1+.V- "! $%
*( ),+j+.RUR0aRqRkPdTU+.-#PSRU++ dPSW^Z_PdTk+hx ],RU-0T.yQclaRq+.PSrw) /1M\x,/ i/1x\Z_PSWA-0Z,240+.rtT PSM,x!yQ-0+.r.aSM,xYyclaRqTk)\+
),aW^+qx_PdTwPd-U+hT" Pdrw)-UZ\240+.rtT - Tk+h-0T3-U+tToPdW1W1a< -*Z,-*TUarhaù,Z\Tk+TU),+fXAe eBG+frhaù,Z\Tk+hx
Tk)\+oX e Z,-U/^M,p#RUPSM,x,aS`"PdM,x ->!i/^W1W^+.x claRUp+hRU/^+.-J ),+.R0+ Tk)\+ -0/1pM_P<TkZ,R0+.- clR0a` PSW^W[aSTk),+hR adTk),+hR
-UZ\42 0+.rtTk6- +.R0+ Z\-U+.xPS- RkPdM,x,a` claSRUp+hRU/1+h"- +hW1-UaSM +hT'PSRW @s y @z u,RUaSu:a-0+.x P rhaù,W1+tTk+b-0+hT'aSc[pSW1a2_PdWs`+PS-0Z,RU+h`j+hM5Tk-TUa2:+mZ\-U+.x /^M
aR0x,+.RmTUa x,/1-0rPSR0x pSRUa-0-mclaRUp+hRU/^+.-m2 +hclaR0+u:+hR0claR0`j/^M,p PSM54 ` PdTUrw),/1M\p oM,W^4jTk/^`j+ x,Z,RkP<Tk/1aSM
/1- Z,-U+hx /^MaZ,Ro-4i-0Tk+h` /1MaRUx,+hRoTka x\a P -Ur.R0+.+hM,/1M,p aSc pR0a-U-oclaSRUp+hRU/1+h-oPSM\x -0u:+h+.x Z,uTk)\+
#+ Xsu +.R0/1`+.M5TkV- (*),+#TU/1`+ x\Z,RkPdTU/1aMaScATU),+
-U/^pM_PdTUZ,RU+h- /^MTk)\+#TkRUPS/1M,/^M,p-U+hT /1- -0TkaSRU+.xPSW1aM\p
/^TU)Tk),+#u,RUaSTUaSTN4iu::+ (*)\+
Tk/1`+#x\Z,RkPdTU/1aMaSc PSW1WE-U/^pM_PdTUZ,RU+h-Z,M,x,+hR Tk+h-0Tq/^-orw),+.r !d+.x Tka 2 +
/^TU),/1M TU),RU+h+-0TkPSM,x_PSR0x x,+ i/VP<Tk/1aSM,-maScETk),+`+PdM x,Z,RkP<Tk/1aSM claRbTk)\+frhaRUR0+.-0u:aM\x,/1M,p -0Z,42 0+hrhT
Signature from set s025
@
Reference signature for set s025
Forgery in set s025
50
50
80
40
60
30
40
20
20
10
40
30
20
10
0
0
90
100
110
120
130
140
0
0
Signature from set s027
20
40
60
80
100
Reference signature for set s027
120
140
160
180
Forgery in set s027
60
50
40
50
40
30
40
30
30
20
20
20
10
10
10
0
0
40
60
80
0
100
−20
Signature from set s037
0
20
40
80
100
Reference signature for set s037
120
140
160
Forgery in set s037
30
35
25
30
50
25
40
20
20
30
15
15
20
10
10
10
5
5
0
0
60
80
100
120
0
0
10
20
30
40
50
−5
120
140
160
180
}
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x,+ s/1PdTk/âM PSR0+oZ,-U+hx/^M,-0TU+PSx aScETk)\+`j+.PSM PSM,x Tk)\+-0TwPdM,x_PSR0x x\+ i/VPdTU/1aM } /^pM_PdTUZ,RU+h-mTk)_P<T
c PSW^WIaZ\Tk-0/1x,+ Tk)\/1-f2:aZ\M,x PSR0+jR0+ 0+.rtTk+hx PS- claR0p+.R0/1+hW- ),/^W1+ -U/^pM_PdTUZ,RU+h- / Tk),/^MG2 aZ,M,x\-
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r.aSM,-U/^x,+.R0/1M,pTk)\+.` TUa 2 + u,/^+.r.#+ /1-0+ W^/1M,+.PS"R GLNM aSRUx,+hR TUa -U),<a TU),+ u:+hR0claR0` PdM,r.+ aSc3Tk)\+
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+.R0RUaRTkRUPSx,#+ P a M r.Z,R +h"- (*),/^- M,aR0` PdW1%/ $.PdTk/âM -U+h+.`- TkaG2:+u:+hR0claR0`j+hx /1M Tk),+x\8/ M:+.RU+hM5T
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10
time param. − EER = 5.00%
9
Eucl. arc−len. − EER = 3.21%
aff. arc−len. − EER = 5.29%
8
FAR vs. FRR for set1 (random forgeries) no axis alig.
3
time param. − EER = 1.61%
Eucl. arc−len. − EER = 0.59%
aff. arc−len. − EER = 0.48%
2
6
FAR (%)
FAR (%)
7
5
4
1
3
2
1
0
0
1
2
3
4
5
6
FRR (%)
7
8
9
0
0
10
2
3
FRR (%)
FAR vs. FRR for set2 (skilled forgeries) no axis alig.
10
time param. − EER = 2.60%
9
Eucl. arc−len. − EER = 3.53%
aff. arc−len. − EER = 4.16%
8
FAR vs. FRR for set2 (random forgeries) no axis alig.
3
time param. − EER = 1.05%
Eucl. arc−len. − EER = 0.93%
aff. arc−len. − EER = 0.83%
7
2
6
FAR (%)
FAR (%)
1
5
4
1
3
2
1
0
0
1
2
3
4
5
6
FRR (%)
7
8
9
0
0
10
1
2
3
FRR (%)
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8
FAR vs. FRR for set1 (random forgeries) axis alig.
4
time param. − EER = 4.21%
Eucl. arc−len. − EER = 3.15%
aff. arc−len. − EER = 3.76%
7
3
5
FAR (%)
FAR (%)
6
time param. − EER = 2.00%
Eucl. arc−len. − EER = 0.77%
aff. arc−len. − EER = 0.43%
4
3
2
2
1
1
0
0
1
2
3
4
5
FRR (%)
6
7
0
0
8
FAR vs. FRR for set2 (skilled forgeries) axis alig.
8
6
3
4
time param. − EER = 0.87%
Eucl. arc−len. − EER = 0.73%
aff. arc−len. − EER = 0.58%
3
5
FAR (%)
FAR (%)
2
FRR (%)
FAR vs. FRR for set2 (random forgeries) axis alig.
4
time param. − EER = 2.71%
Eucl. arc−len. − EER = 2.29%
aff. arc−len. − EER = 3.02%
7
1
4
3
2
2
1
1
0
0
1
2
3
4
5
FRR (%)
6
7
0
0
8
1
2
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3
4
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FAR vs. FRR for set1 (skilled forgeries)
10
FAR vs. FRR for set1 (random forgeries)
5
time param. − EER = 5.16%
Eucl. arc−len. − EER = 4.54%
aff. arc−len. − EER = 4.52%
9
8
time param. − EER = 2.54%
Eucl. arc−len. − EER = 1.22%
aff. arc−len. − EER = 0.94%
4
6
FAR (%)
FAR (%)
7
5
4
3
2
3
2
1
1
0
0
1
2
3
4
5
6
FRR (%)
7
8
9
0
0
10
8
3
4
5
FAR vs. FRR for set2 (random forgeries)
5
time param. − EER = 3.36%
Eucl. arc−len. − EER = 3.28%
aff. arc−len. − EER = 3.81%
9
2
FRR (%)
FAR vs. FRR for set2 (skilled forgeries)
10
1
time param. − EER = 1.27%
Eucl. arc−len. − EER = 1.06%
aff. arc−len. − EER = 1.00%
4
6
FAR (%)
FAR (%)
7
5
4
3
2
3
2
1
1
0
0
1
2
3
4
5
6
FRR (%)
7
8
9
10
0
0
1
2
3
4
5
FRR (%)
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FAR vs. FRR for set1 (skilled forgeries)
5
FAR vs. FRR for set1 (random forgeries)
time param. − EER = 2.90%
Eucl. arc−len. − EER = 2.40%
aff. arc−len. − EER = 1.89%
4
time param. − EER = 0.88%
Eucl. arc−len. − EER = 0.28%
aff. arc−len. − EER = 0.12%
FAR (%)
FAR (%)
1
3
2
1
0
0
1
2
3
4
0
0
5
1
FRR (%)
FRR (%)
FAR vs. FRR for set2 (skilled forgeries)
FAR vs. FRR for set2 (random forgeries)
5
time param. − EER = 1.27%
Eucl. arc−len. − EER = 1.73%
aff. arc−len. − EER = 1.11%
4
time param. − EER = 0.28%
Eucl. arc−len. − EER = 0.35%
aff. arc−len. − EER = 0.22%
FAR (%)
FAR (%)
1
3
2
1
0
0
1
2
3
FRR (%)
4
5
0
0
1
FRR (%)
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Individual equal error rates for set1 (skilled forgeries)
30
time param.
Eucl. arc−len.
25
aff. arc−len.
Individual equal error rates for set1 (random forgeries)
15
time param.
Eucl. arc−len.
aff. arc−len.
20
10
EER (%)
EER (%)
A
15
5
10
5
0
0
10
20
30
Subject #
40
50
56
1
10
20
30
Subject #
40
50
56
Individual equal error rates for set2 (skilled forgeries)
30
time param.
Eucl. arc−len.
25
aff. arc−len.
Individual equal error rates for set2 (random forgeries)
15
time param.
Eucl. arc−len.
aff. arc−len.
20
10
EER (%)
EER (%)
1
15
5
10
5
0
0
1
10
20
30
Subject #
40
48
1
10
20
30
Subject #
40
48
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FAR vs. FRR for set1 (skilled forgeries)
8
harmonic mean − EER = 1.89%
DPM distance − EER = 4.52%
weighted correl. − EER = 2.96%
Procrustes dist. − EER = 3.60%
7
6
5
FAR (%)
FAR (%)
FAR vs. FRR for set1 (random forgeries)
2
4
3
harmonic mean − EER = 0.12%
DPM distance − EER = 0.94%
weighted correl. − EER = 0.20%
Procrustes dist. − EER = 0.51%
1
2
1
0
0
1
2
3
4
5
FRR (%)
6
7
0
0
8
FAR vs. FRR for set2 (skilled forgeries)
8
5
FAR (%)
FAR (%)
6
2
FAR vs. FRR for set2 (random forgeries)
2
harmonic mean − EER = 1.11%
DPM distance − EER = 3.81%
weighted correl. − EER = 1.50%
Procrustes dist. − EER = 1.96%
7
1
FRR (%)
4
3
harmonic mean − EER = 0.22%
DPM distance − EER = 1.00%
weighted correl. − EER = 0.43%
Procrustes dist. − EER = 0.31%
1
2
1
0
0
1
2
3
4
5
FRR (%)
6
7
8
0
0
1
FRR (%)
2
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Signature from set s019
Reference signature for set s019
False Reject in set s019
Forgery falsely accepted in set s019
30
40
50
40
30
25
40
20
30
15
20
10
30
20
20
10
10
5
10
0
0
0
40
50
60
70
80
90
100
0
0
10
Signature from set s025
20
30
40
50
60
Reference signature for set s025
70
80
90
100
−5
100
False Reject in set s025
50
110
120
130
140
150
Forgery falsely accepted in set s025
80
50
60
70
40
40
60
50
50
30
40
30
40
30
20
20
30
20
20
10
10
10
10
0
0
90
100
110
120
130
0
0
0
20
Signature from set s041
40
60
80
90
100
Reference signature for set s041
110
120
130
140
100
False Reject in set s041
120
140
160
180
Forgery falsely accepted in set s041
20
35
40
40
30
15
30
25
30
10
20
20
15
10
5
10
0
0
−5
20
5
10
0
60
80
100
120
140
−5
160
20
40
Signature from set s001
60
80
100
120
0
40
60
Reference signature for set s001
80
30
70
25
60
80
100
120
100
False Reject in set s001
20
50
120
140
160
Forgery falsely accepted in set s001
80
40
60
30
40
20
20
10
15
40
30
10
20
5
10
0
0
100
120
140
160
0
0
−5
0
Signature from set s027
20
40
60
80
80
100
Reference signature for set s027
120
140
160
80
False Reject in set s027
100
120
140
160
Forgery falsely accepted in set s027
100
100
40
40
80
80
30
30
60
60
20
20
40
40
10
10
20
20
0
0
80
100
120
140
160
180
200
0
0
20
40
Signature from set s035
60
80
100
120
140
100
Reference signature for set s035
120
140
160
180
80
False Reject in set s035
100
120
140
160
180
200
Forgery falsely accepted in set s035
30
60
60
25
50
40
50
20
30
40
40
15
30
20
30
10
20
20
10
5
10
10
0
0
0
0
100
120
140
160
−5
20
40
60
80
100
110
120
130
140
150
160
100
120
140
160
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X(3.5)
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60
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Signature from set s037
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CDPM Reference signature for set s037
120
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30
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15
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35
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5
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120
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Signature from set s025 subsampled by 4
80
80
80
60
60
60
40
40
40
20
20
20
0
0
90
100
110
120
130
140
0
90
Signature from set s027
100
110
120
130
140
90
Signature from set s027 subsampled by 2
100
110
120
130
Signature from set s027 subsampled by 4
60
50
50
50
40
40
40
30
30
30
20
20
20
10
10
10
0
0
40
60
80
100
0
40
Signature from set s037
60
80
100
40
Signature from set s037 subsampled by 2
50
50
50
40
40
40
30
30
30
20
20
20
10
10
10
0
0
60
80
100
120
60
80
100
Signature from set s037 subsampled by 4
0
60
80
100
120
60
80
100
120
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80
80
60
60
40
65
65
original signature
signature w/ noise
60
60
55
55
50
50
45
45
original signature
signature w/ noise
40
20
20
40
0
0
90
100
110
120
130
140
90
Signature from set s027
100
110
120
130
140
Signature from set s027 with noise added
60
60
50
50
40
35
105
110
35
115
115
55
original signature
signature w/ noise
50
25
45
40
40
30
30
20
20
10
10
40
60
80
130
original signature
signature w/ noise
20
35
30
15
25
20
100
40
Signature from set s037
125
40
0
0
120
30
60
80
55
100
Signature from set s037 with noise added
60
10
65
65
70
75
80
85
30
50
50
28
40
40
26
30
30
24
20
20
22
10
10
20
original signature
signature w/ noise
50
original signature
signature w/ noise
45
40
35
60
80
100
30
18
0
0
120
60
80
100
60
120
62
64
66
68
70
85
90
95
100
105
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8
7
6
6
5
5
4
3
4
3
2
2
1
1
0
0
1
2
3
4
5
FRR (%)
6
7
DPM − EER = 3.81%
CDPM − EER = 3.41%
7
FAR (%)
FAR (%)
FAR vs. FRR for set2 (classif. with matching dist.)
8
DPM − EER = 4.52%
CDPM − EER = 4.52%
0
0
8
1
2
3
4
5
FRR (%)
6
7
8
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FAR vs. FRR for set1 (classif. with mult. dist.)
4
FAR vs. FRR for set2 (classif. with mult. dist.)
4
DPM − EER = 1.89%
CDPM − EER = 2.12%
DPM − EER = 1.11%
CDPM − EER = 1.50%
3
FAR (%)
3
FAR (%)
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1
2
1
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0
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2
FRR (%)
3
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4
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FRR (%)
3
4
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FAR vs. FRR for set1 (classif. with matching dist.)
10
9
8
7
7
6
6
5
4
5
4
3
3
2
2
1
1
0
0
1
2
3
4
5
6
FRR (%)
7
8
9
DPM − EER = 4.39%
CDPM − EER = 3.86%
9
8
FAR (%)
FAR (%)
FAR vs. FRR for set2 (classif. with matching dist.)
10
DPM − EER = 5.40%
CDPM − EER = 4.86%
0
0
10
1
2
3
4
5
6
FRR (%)
7
8
9
10
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FAR vs. FRR for set1 (classif. with mult. dist.)
5
FAR vs. FRR for set2 (classif. with mult. dist.)
5
DPM − EER = 2.14%
CDPM − EER = 2.39%
4
4
3
3
FAR (%)
FAR (%)
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DPM − EER = 1.34%
CDPM − EER = 1.55%
2
1
0
0
1
2
3
4
0
0
5
1
FRR (%)
2
3
4
5
FRR (%)
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FAR vs. FRR for set1 (classif. with matching dist.)
14
FAR vs. FRR for set2 (classif. with matching dist.)
14
DPM − EER = 7.63%
CDPM − EER = 6.86%
12
10
FAR (%)
10
FAR (%)
DPM − EER = 6.38%
CDPM − EER = 5.22%
12
8
6
8
6
4
4
2
2
0
0
2
4
6
8
FRR (%)
10
12
0
0
14
2
4
6
8
FRR (%)
10
12
14
TS $.30
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FAR vs. FRR for set1 (classif. with mult. dist.)
7
FAR vs. FRR for set2 (classif. with mult. dist.)
7
DPM − EER = 3.09%
CDPM − EER = 3.68%
6
5
FAR (%)
FAR (%)
5
4
3
4
3
2
2
1
1
0
0
DPM − EER = 2.71%
CDPM − EER = 2.86%
6
1
2
3
4
FRR (%)
5
6
0
0
7
1
2
3
4
FRR (%)
5
6
7
TS $.30
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FAR vs. FRR for set1 (classif. with matching dist.)
9
8
7
7
6
6
5
4
5
4
3
3
2
2
1
1
0
0
1
2
3
4
5
FRR (%)
6
7
8
DPM − EER = 3.49%
CDPM − EER = 3.44%
8
FAR (%)
FAR (%)
FAR vs. FRR for set2 (classif. with matching dist.)
9
DPM − EER = 4.82%
CDPM − EER = 4.83%
0
0
9
1
2
3
4
5
FRR (%)
6
7
8
9
TS $.30
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FAR vs. FRR for set1 (classif. with mult. dist.)
FAR vs. FRR for set2 (classif. with mult. dist.)
5
DPM − EER = 2.16%
CDPM − EER = 2.43%
4
4
3
3
FAR (%)
FAR (%)
5
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2
1
DPM − EER = 1.11%
CDPM − EER = 1.35%
2
1
0
0
1
2
3
4
0
0
5
1
FRR (%)
2
3
4
5
FRR (%)
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EER vs. subsamp. fact.(classif. with matching dist.)
Equal Error Rate (%)
7
EER vs. subsamp. fact.(classif. with mult. dist.)
4
set1 − DPM
set2 − DPM
set1 − CDPM
set2 − CDPM
3.5
Equal Error Rate (%)
8
6
5
4
3
set1 − DPM
set2 − DPM
set1 − CDPM
set2 − CDPM
3
2.5
2
1.5
0
2
Subsampling factor
1
4
0
2
Subsampling factor
4
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EER vs. noise level(classif. with mult. dist.)
2.5
4.5
Equal Error Rate (%)
Equal Error Rate (%)
5
set1 − DPM
set2 − DPM
set1 − CDPM
set2 − CDPM
4
3.5
3
0
2
set1 − DPM
set2 − DPM
set1 − CDPM
set2 − CDPM
1.5
1
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