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iii

Detecting Start and End Times of Object-Handlings on

Table By Integrating Camera and Load Information

Ryuta YASUOKA

Abstract

Recently, many systems have been proposed to support human activity in real

time by multimedia guidance such as sound, video, and so on. An intuitive

way of manipulating the systems is to use actions performed naturally in the

activity. Such intuitive manipulations help users do the tasks. As the natural

actions, we focus on putting and taking actions to objects on a working table.

We naturally handle the objects when doing the tasks at the table.

Detecting putting/taking action to each object helps predicting what task

the user intends to do next. Hence, the intuitive interface is realized if the sys-

tem is manipulated throuth these actions. Our goal is to detect putting/taking

action to each object on the table in real time through the observation.

There are two different traditional approaches to detect these actions: by

cameras and by load sensors. The approach by cameras observes the objects to

estimate their positions and to detect putting/taking action to each object. As

humans understand various events from visible infoemation, an image contains

rich information and is used for wide variety of applications. However, cameras

cannot track objects when the objects are occluded. In such case, this approach

cannot detect putting/taking actions until the finish of the occlusion. In this

sense, this approach cannot detect these actions in real time.

The other approach, by load sensors, uses variation of load. The load varia-

tion is caused by putting and taking objects on a table, and is a good evidence

to detect putting/taking actions. It is easy to observe the variation because

load signals are one dimensional. However, this approach cannot differentiate

putting/taking actions when two or more objects are put and/or taken at once.

In such case, the load change in load signals caused by the objects’ displace-

ments are all combined into one variation of load.

We overcome these difficulties of the sensors by integrating them on a statis-

tical model. Cameras can differentiate putting/taking action to each object as

long as they are not occluded, even through two or more objects are displaced

iv

at once. Load sensors can detect at least that any of objects are displaced, by

focusing on variation of load. This is done in realtime. Hence these two sensors

compensate each other by an integration. Moreover, our statistical model en-

ables to recover objects’ locations by using camera’s information after the finish

of an occlusion. This recovery is necessary when two objects are displaced at

once under the occlusion.

We evaluated our approach by three experiments; one contains the difficult

situations for the use of only the single sensor, and the other two observe real

activities at a working table. In the first experiment, our approach could detect

putting/taking action to each object correctly while the objects were occluded

and two or more objects are displaced at once. Our approach could also estimate

the objects’ locations rightly when the object is occluded.

In the second and third experiment, we applied our approach to two real

activities: paper craft and cooking tasks. As a result of the paper craft task,

for detection of put objects, the recall was 64.3%(9/14 times), and the precision

was 34.6%(9/26). For detection of taken objects, the recall was 30.0%(3/10),

and the precision was 14.3%(3/21). As a result of the cooking task, for detection

of put objects, the recall was 58.3%(7/12), and the precision was 29.2%(7/24).

For detection of taken objects, the recall was 56.3%(9/16), and the precision

was 47.4%(9/19). Load changes caused by disturbance were also successfully

rejected [At a rate of 63.0%(17/27)]. We need to improve the algorithm for

separating these disturbing vibrations of load in the future.

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5

2.2 YE;s5rQ$?OsIjs0+O&*;~oN!P

+aiGO\A*K$*NHM,\(7?lgH$BjJ/aE$?@1N

lgHNhL,q7$H$&dj,"k%3lKP7F$SchmidtiNj! [7]

Ke=5lkYEKpE$?j!GO$YE;s5r_V7?!PfrxQ7

F$*NH!PfHN\(Khj88?ON}:rYEKhj>\Q,9k%L

o$*NOM,OsIjs07J$Bj!jK0/3HOJ$%~O+i60

,"C?lgr|/H*N,hil?jV+l?j7?lgN_YEQ=,/

3k%hCF$*N,1lNlgOYE,:/9lPOsIjs0,+O7?$

^?$YE,}C9lPOsIjs0,*;7?H=j9k3H,G-k%

SchmidtiOYE;s5rQ$F$*NOlD7+1~K\07J$H$&

>jNbH$feG*N,V+l?3H$hil?3H$"k$O]l?3H

r!P9k3Hr\*H7?&frTC?%=N]$SchmidtiNj!GOP

]*NHM*HN\(G=j9keojK$fNMyKYE;s5r_V7F

YEN}:G*N,hil?jV+l?j7?3Hr=j7?%YEN}:r

Q$k3HG$*N,V+l?N+$hil?N+$"k$O]lkJIy+

i%l:K0$?N+rhrK=j9k3H,G-k%^?$3Nj!GO*

NH7DHN\(rYEN}:KhCF=G9kNG$*N,1lG"lPW

CN-5KX8J/j"k?$`G*NNOsIjs0N+O&*;r!P9

k3H,G-k%

*NNLVOMyK++kYENfrxQ7Faak%MyNYE;s5N

<m@ (*U;CH)r F offk (k = 1, . . . , 4)H7$*N,V+l?jhil?j

7?eKYE;s5K++CF$kYEr FkH9k%^?$F̃k = Fk −F offk H

7$FΣ =∑

k F̃kH9k%P]*NNLV (x, y) O$YENfrxQ7?J<N

0 (1),0 (2)KhCFW;G-k%?@7$xmaxO!PfN#}$ymaxO!P

fND}H9k%^ 1KYE;s5N^r(9%

x = xmax

F̃2 + F̃4

FΣ

(1)

y = ymax

F̃3 + F̃4

FΣ

(2)

^?$feG?+,/-?+I&+N=jO$YEN60Km\7FT&%"

37?YEG<? qlenDN8`P9 σqrW;7$σq,gM δbeforer6(lPf

K60,/3C?H=j7$feG?+,/3C?H9k%=Ne$σq,gM

6

����

���� ����

����

F1 ( 0 , 0 ) F2 ( 0 , xmax )

F3 (0 , ymax) F4 (xmax , ymax)

F∑ ( x , y )

^ 1: YE;s5N^

δafter$~KJlP$=N60,}^C?H=j7$60N0eNYENQ=+

i?,/3C?N+rW;9k%^?$60,}^C?eNYEG<?+i0

(1),0 (2)KhjE4LVrW;7$*NNLVrdj9k%

?@7YErQ$?j!GO$"k*N,V+l?jhil?j9k3HG

60,/87$=N60,}^k^GK!N*N,V+l?jhil?j7?

lg$=liO1~r,%7F!P9k3H,G-J$%J_$0Khil?

jV+l?j7?*NN60,}+9k0K!N*N,hil?jV+l?j

7?3HrV*N,1~K\07?WHFV%#tN*N,1~K\07?l

g$=liK~8?YEN}:,g;5lFQ,5lF7^&%=N?a$Y

EQ=+iV+l?*Ndhil?*NrCj9k3H,$qKJk%

Jehj$+airQ$?>hj!GO$;s5N-AH7F$P]*NK

WC,"C?lgKj"k?$`GOsIjs0N+O&*;r!P9k3H

,$qG"k%l}G$YE;s5rQ$?>hj!GO$*NNE5,{N

G"CFb$1~K#tN*N,\07?lg$=liNOsIjs0r,1

FjP9k3H,$qG"k%

\&fGO$+aiHYE;s5r,ZKH_go;k3HKhj$3li

Ndj@Nrhr^k%+airQ$F*Nrf+i%lF$kVbIW9k

3HG$YE;s51HhjhrKDNNhL,G-k%^?$YE;s5r

Q$k3HG$*NKWC,"C?lgGb?i+NQ=,"C?3Hrj"

7

k?$`G!P9k3H,G-k%\FGO$3liNx@rh+7?$+a

iHYE;s5r}g7?OsIjs0djbGkrsF7$j"k?$`G

#t*N1~NOsIjs0N+O&*;r!P9k%

h3O +aiHYE;s5N}gKhkOsIjs

0+O&*;~oN!P

+airQ$?j!GO$WCfK*NNOsIjs0rj"k?$`Gj

PG-J$3H,$YE;s5rQ$?>hj!GO#t1~K*N,\07

?lgKPhG-J$3H,dj@H7Fs2il?%l}G$=l>lNj

!N9jb8_9k%+airQ$?j!GO$P]*NKWC,51lP*

N,#tGb=l>lN*NNLVrdj9k3H,G-k%^?$YE;s

5rQ$?j!GO$*N,#t"CFbYEQ=Km\9k3HGWCKX

8J/j"k?$`K$/J/HblDJeN*N,hil?jV+l?j7

?3HO!PG-k%

3liNdj@d9jr'^(F$\&fGO+aiHYE;s5+i@i

lkpsr}g9k%+ai$YE;s5N=l>lNj!GOsIjs0j

P,TD=Ju7K$3li 2Dr}g9k3HKhCFPh9k%5iK$N

(*JbGkKhj}g9k3HG$*NLVKX9k>brN()Y^CW

H7F]}9k3H,G-kh&KJk%>br]}9k3HG$WCfKY

E;s5@1GO*NLVNCj,$qJlgb$eG+ai&Nps,@i

l?H-Kj+PjG-kh&K9k%

3.1aGdjrj0=9k3HKhj$\FGhj7&djrqN=9k%3.2

aGO+aiHYE;s5r}g7?N(bGkN5WKD$FRYk%3.3a

GOIWP]*NNi|P?nHKD$F$3.4aG+ai&NW;bGkN\

Y$3.5aGYE;s5&NW;bGkN\YrRYk%

3.1 djNj0=

*NNOsIjs0 ηr$J<NMKjA9k%

η = {o, toT , toP} (3)

33G$oO*NNDNiYk$toT O*N o,hil?~o (OsIjs0N

8

(0,ymax)

htm = true

(0,xmax)

(0,xmax)

(0,ymax)

(0 , 0)

(0 , 0)

htm = false

^ 2: Xmt NuVuV^

+O~o)$toP O*N o,V+l?~o (OsIjs0N*;~o)G"k%

Q,G<?fK*N,#t"ku7GOsIjs0 ηrjP9k?aKO$

hil?jV+l?j7?*N,P]*NN&AIlG"k+H$C?1l-

=jdj,88k%=3G\&fGO$*NIWKhCFP]*N,hilF

$k+V+lF$k+KC(FP]*NNLVbdj9k3HG$DNiYk

oNhLrT&%

~o tKD$FO+aiNUl<`l<HKgo;k$"k$O$YE;s

5N5sWjs0l<HKgo;k3H,M(ilk%\&fNQ,D-K*

1k+aiNUl<`l<HOs 15fpsG"k%3NUl<`l<HO\&f

,[j9k"Wj1<7gsKaailkj"k?$`-KYcOJ$HM(

?%>CF$#sOYEN5sWkGOJ/+aiNUl<`Vfr~o tH

ja?%

~o tGNQ,G<?fKM DN*N o1, . . . , om, . . . , oM ,8_9kH-$

*NNuVrXt = {X1

t , ..., Xmt , ..., XM

t }H9k%Xmt O*N omNuVr=9

QtG$*N om,OsIjs05lF$k+]+r=9 hmt = {true, false}

H$*N om NLVr=9 lmt = (x, y)+iJkJ^ 2K%3lirQ$kH$

Xmt = {hm

t , lmt }H=5lk%?@7$hm

t = trueO*N om,jK}?lF$k

3Hr$hmt = falseO*N om,V+lF$k3Hr$=l>l=9%

~o 0+i~o t^GNVK@il?Q,M+i=_NuVXtrdj9k%

D^j$~o tK*1kQ,MrZt$~o 0+i t^GNQ,MrZ0:tH7F$

F*N omKP7FN( P (Xmt |Z0:t)raak%P (Xm

t |Z0:t),a^lP$hmt N

Zj+oC?~o+i$=N*NNOsIjs0N+O&*;N~o tom

T $tom

P

9

,W;G-k%3liO$gM δhrxQ7?sM=h}rHCF$0 (4),(5)N

h&Kj0=5lk%

P (hmt−1

) < δh ∧ P (hmt ) ≥ δh ⇒ tmT = t (4)

P (hmt−1

) ≥ δh ∧ P (hmt ) < δh ⇒ tmP = t (5)

3Nh&K$F*NKP7FF~oGN(P (Xmt |Z0:t)raak3HKhj$

*NNOsIjs0rj"k?$`GjP9kh&Kdjrj0=7?%

\FGOh|HYErH_go;k&fNGiNJ,H7F$IWP]*N

KP7F$/D+N)sror_1k%^:$lYK/3k*NNOsIjs

0N+O&*;OsD^GH$&)sr_1k%\FGO$MV,nH9k~

K=NnHrYg9k79F`r[j7F$k%nHrT&?/Nlg$MV

NjOs\G"k?alYK}C?jV$?j9k*NOsD^GG"kHM

(ilk%>CF3N>jO$B]NnHK*$F5}NJ$)sH$(k%

^?$B]NyenHK*$FOnHKhCFC)5lk*NO+(dE5

NC',Q=9k%5iK$ZGnHKhCF*NNDtbQ=9k%7+7

\&fGO$*N,WC5l?]d#t1~K\09k]K88kdjr$+

airYE;s5N>}+i@il?psr}g9k3HGPh9k3HKg

cKV$F$k%3N?a$P]*NNDt$ZS$+(dE5NC'LNQ

=XNPhO#eN&f]jH7$P]*NNDtd=NC'LOQ=7J$

bNH9k%

3.2 +aiHYE;s5r}g7?N(W;bGk

3.1aGRY?N( P (Xmt |Z0:t)rW;9k?aK$+aiHYE;s5r}

g7?$OsIjs0rN(*Kdj9kbGkrsF9k%

N( P (Xmt |Z0:t)O>0NuVXt−1KhCF~U=7$+D$l!^k3U

-r>j9k3HG!0Nh&KQA9k3H,G-k%

P (Xmt |Z0:t) =

∫

P (Xmt |Zt,Xt−1)P (Xt−1|Z0:t−1)dXt−1 (6)

P (Xt−1|Z0:t−1)O>0N~o t− 1GNh}kLG"kNG$>0Nh}GW;

Q_G"k%hCF$i|uVP (Xm0)HN( P (Xm

t |Zt,Xt−1)raak3H,

G-lP$N( P (Xmt |Z0:t)rW;9k3H,G-k% i|uV P (Xm

0)O 3.3

10

aG\YrRYki|P?nHKhj@ilk%N(P (Xmt |Zt,Xt−1)OJ<N

MKW;9k%

sFj!GO+aiHYE;s5rQ$F*NrQ,7F$k?a$Q,M

ZtOh|ZIt HYE ZW

t HK,1k3H,G-k%=3G$ZIt HZW

t O_$K

H)G"kH>j7FP (Xmt |Zt,Xt−1)NW;rT&%D^j$

P (Xmt |Zt,Xt−1) = P (Xm

t |ZIt ,Xt−1)P (Xm

t |ZWt ,Xt−1) (7)

H7$+ai&GNW;P (Xmt |ZI

t ,Xt−1)HYE;s5&GNW;P (Xmt |Z

Wt ,Xt−1)

K,%7FM(k%

sFj!GOF*NKP7F$+ai&NW;bGk+iO*NN8_N(

^CW P (lmt )rPO7$YE;s5&NW;bGk+iO*NN8_N(^C

WP (lmt )HOsIjs0N-5NN( P (hmt )rPO9k%=l>lNW;bG

k+i@il?POr0 (7)Khj}g9k%=Ne$N( P (Xmt |Zt,Xt−1)+

i0 (4)$0 (5)KpE$F*NNOsIjs0 ηrjP9k%

3.3 *NNi|P?nH

\&fGOP]*NNtO{NG"j$^?$3liN*NN+(dE5N

C'LOTQG"kH$&)sr_1F$k%3N)sNbHGO$GiKQ

,7?C'LrQ,f:CHxQ731lPh$%>CFsFj!GO$Gi

KIWP]*NNC'LrP?9k%

qN*JP?}!H7FO$IWP]*NrlD:DYE;s5eKV/3H

rT&%=N]$+aiHYE;s5rQ$F*NomNC'L fm = {wm, sm}

rP?9k%wmO*NNE5r=9C'$smO*NNheG!P5l?C'@

N8gG"j$C'@NtO*NKhCF[Jk%YE;s5NN$:rM87

F$wmO?Q µm$8`P9 σmN5,,[NQia?H7?%smOGrabner

iNj!r2MK7?W;r0sK_W7F*j$smK^^lkFC'@OC

'LH*NNE4LV^GNjPB8r]}7F$k%smNFC'@,]}9

kC'LH*NNE4LV^GNjPB8O$3.4aG\YrRYk+ai&N

W;bGkGNC'@NP~U1HP]*NNLVj<KxQ9k%

^?$3Ni|P?nH,*;7?~or 0H7$~o 0GNF*NNi|

uV P (Xm0)rW;9k%P?~O*NO,:V+lk?a h0

mKD$FO$

P (hm0= true) = 0 (8)

11

P (hm0= false) = 1 (9)

H9k%^?$*NNE4LVrxQ9kH+aiHYE;s5=l>lKh

k*NLVdjkLN0g-,Hlk%>CF$*NN8_N(^CWP (lm0)

O+ai&$YE&NW;bGk&K$3.5aGRYkYE;s5NE4LVr

Q$?+<Mk)YdjKhCF@ilk8_N(^CWH9k%4FNP]

*NNP?nHr*(kH$P?7?P]*NNIWr+O9k%

3.4 +ai&NW;bGk

P (lmt |ZIt ,Xt−1)NW;OGrabneriNj! [6]r2MK7?%FP]*NNC

'@ smH=NE4^GNjPLVX8r 3.3aGRY?P]*NNi|P?~

KaaF*-$3lr*NbGkH7FJ_NUl<`GQ$?%+ai&N

W;bGkGO$J<Nh}rF*NbGkhKT&%

~o tK*1k+aiNQ,h| ZIt +ijP5l?C'@N8gr f tH9

k%DN omN$UNC'@ ∀s ∈ smKP7F$C'LNjX,gMJeHJ

k f tNWGN&A$GbjX,b$bNrP~U1k%sHP~U1il?h

|ZIt fNC'@r f H9k%3NH- f NB8K$i|P?nHG@? s+i

omNE4XNjPB8rC(?LVKP7F$,&9+<MkrQ$?j<h

}rT&%jX,gMr6(kh&J f tNWG,8_7J$$D^jP~U/

C'@,h|ZIt NfK8_7J$H=G5l?smNWGO$WCJIKhj

LV,T@KJCF$kHM(ilk%3NlgKOCjNB8XNj<OT

o:$8_N(^CWKlMJ,[rC(k%GeK 1/|sm|GdCF5,=r

T&%

\&fGO$P]*NOfeKV+lF$k+jKD}5lF$k+N$:

l+G"kNG$6\iNQCA?XJbGk [2]rpK$C'@NjPP]

OOrD}fN*Nr^`M*NhHyeKV+l?*NNhN_KBj7?%

J*$C'LKO91<kds>KTQJC'LG"kSIFTC' [8]rQ$?%

^?$C'!PoH7FOGrabneriNj!KoCFHarris!Po [9]rQ$?%

3.5 YE&NW;bGk

YE;s5&NW;bGkP (Xmt |ZW

t ,Xt−1)N\YrRYk%SchmidtiNj

! [7]rZfH7$=lr#tN*N,1~Khil?jV+l?j7FbP~

12

G-kh&KH%9k%sFj!GO$"khVK?/HbsDN*N,hil

?jV+l?j7?3HrRH^HaN$YsHH7FM($P (Xmt |ZW

t ,Xt−1)

r$YsHKm\7FW;9k%

*NNDNiYk$ZS$=N*N,hil?+V+l?+$"k$O?b5

lF$J$+NuVrM87?H_go;r$YsHe = {e1, . . . , em, . . . , eM}

H9k%emO*N omKP9kOsIjs0uVNQ=r=7${−1, 0, 1}NM

rHk%?@7$1OV+l?3H$-1Ohil?3H$0OuV,QoCF$

J$3Hr=9%

$YsH e4NN8grEH9kH-$W;bGk P (Xmt |ZW

t ,Xt−1)O$e

Khk~U=rQ$F!0Nh&KQAG-k%

P (Xmt |ZW

t ,Xt−1) =∑

e∈E

P (Xmt |ZW

t ,Xt−1, e)P (e|ZWt ,Xt−1) (10)

0 (10) rQ$F$F*NNuVKP9kN( P (Xmt |ZW

t ,Xt−1) rW;9k%

P (e|ZWt ,Xt−1)O$YsH e,/3kN($P (Xm

t |ZWt ,Xt−1, e)O$YsH e

4HNF*NNuVKP9kN(r=l>l=9%

J*$lYK/3kOsIjs0N+O&*;OsD^GH$&)sro,

"k?a$uVQ= e (∈ e) 6= 0HJk*NNDtOsD^GH9k%/3j@

k4FN$YsH eN8gEO$e 6= 0HJk*NNDt,sDG"k$Ys

HN8gE2 (⊂ E)$lDG"k$YsHN8gE1 (⊂ E)r4Fss7$5i

K4FNuVQ= e, 0G"k$YsHrC(k3HGaailk%^?$$

YsHN/8O$2.2aGRY?YEN60+i=j9k}!G!P9k%

3.5.1 F$YsH,/-kN(NW;

0 (10)N&A$YsH e,/3kN( P (e|ZWt ,Xt−1)rW;9k%=N]$

V+l?+hil?+N=jKD$FO>0NuVXt−1rQ$k3HG=j:

Y,e,kHM(ilk%7+7$Xt−1rINh&KbGkKH_~`+O+

@GOJ$%>CF$#sOW;NJ1=N?aXt−1rQ$:P (e|ZWt ,Xt−1)

NW;rTC?%3NW;}!GO hmt O hm

t−1HH)G"j$Q,M ZW

t N_

KM89k%3Nlg$P (e|ZWt ,Xt−1)O!0Nh&KQA5lk%

P (e|ZWt ,Xt−1) = P (e|ZW

t ) (11)

F$YsH e ∈ E,/-kN(P (e|ZWt )O$e,/3C?]K[j5lkY

EQ=∆e

W HQ,5l?YEQ=∆tW rQ$FW;9k%J*$∆t

W OYE;

13

s5NQ,MZWt rQ$FW;9k%YE;s5NN$:rM87?lg$*

N omNE5O5,,[N (µm, σm)K>&%5,,[K>&N(QtNBb^

?5,,[K>&?a$∆e

W OuVQ= e (∈ e)rM87?4P]*NNE5N

B+i@ilk,[NN(QtHJk%3N3H+i$N(Qt∆e

W r8.9

k3N,[rN (µe, σe)H9kH$3N5,,[N?Q µe,8`P9 σeO=l

>l$$YsH eGN*N omNuVQ= em = {1, 0,−1}rQ$F!0Khj

@ilk%

µe =M∑

m=1

emµm , σe =

√

√

√

√

M∑

m=1

|em|(σm)2 (12)

Q,5l?YEQ= ∆tW r N (µe, σe)KvFOaF@ilkN(r P (∆e

W =

∆tW )H9k%3NH-$$YsH e,/3C?N( P (e|ZW

t )O!0GW;5

lk%

P (e|ZWt ) =

P (∆e

W = ∆tW )

ΣZ

(13)

33G$ΣZ O5,=`G"j$∑

e′∈E P (∆e′

W = ∆tW )G"k%

3.5.2 $YsH4HN*NNuVN(NW;

!K$F$YsH,v0psH7F?(il?lgN*NomKP9kuVN

N( P (Xmt |ZW

t ,Xt−1, e)rW;9k%P (Xmt |ZW

t ,Xt−1, e)NW;}!r$=N

$YsHGN*N omNuVQ= emKhCF,1k%

em = 0Nlg$=N$YsHGO*N omKX7F?b/-F$J$?a$

P (Xmt ) = P (Xm

t−1)H9k%em = −1H$&uVQ=,/3C?lg$omO}

?l?HM(ilk?a$OsIjs0NN( P (hmt )OP (hm

t = false) = 1H

9k%*N,}?lF$klg$*NHfHO\(7F$J$?aKYE;s

5GO*NLVOdjG-J$%>CF$*NN8_N(^CWP (lmt )O$l

M,[H9k%

em = 1H$&uVQ=,/3C?lg$=N$YsHG*N omOV+l?

H=j7F$k%>CF$OsIjs0NN( P (hmt )O P (hm

t = true) = 1H

9k%*N omN8_N(^CWP (lmt )KD$FO$=N$YsHe,E1HE2

NIAiK09k+KhCFW;}!r,1k%=l>l$J<Nh&KW;

9k%

e ∈ E1Nlg

$YsH eGV+l?$^?Ohil?H5lk*N,lDG"lP$=N

*NLVOV+l?lgbhil?lgb0 (1),(2)GW;5lkE4LVKJ

14

k%>CF$0NuVXt−1HH)G"kH7Fb:Yh/LVraak3H,

G-k (0 (14))%

P (Xmt |ZW

t ,Xt−1, e ∈ E1) = P (Xmt |ZW

t , e ∈ E1) (14)

7+7$E4LVraak0 (1),(2)KOC;&|;N>},^^lk%F;s

5NN$:,[+i8.5lkptr=l>l nk(k = 1, . . . , 4)H7$F̃kN?

Mr F̂k(k = 1, . . . , 4)H9kH F̃k = F̂k+nkH=5lk%3lr$E4N xB8

raak0 (1)Ke~9kH$!0Nh&KQA5lk%?@7$F̂Σ =∑

k F̂k$

nΣ =∑

k nkH9k%

x = xmax

F̂2 + F̂4 + n2 + n4

F̂Σ + nΣ

(15)

0 (15)K+ilkh&K$3NW;0Opt nkN`,C;H|;N>}r

^`%3N?a$F;s5NN$:bGkr5K xKP9kN$:,[rrO

*K;P9k3H,q7$%=3G$YE;s5N5sWjs0l<H,+a

iNUl<`l<HHfYFb$3HrxQ7F$+<Mk)YdjKhj e

K^^lk*N omN8_N(^CW P (lmt |ZWt ,Xt−1, e ∈ E1)r@k%qN*

KO$0 (1)$0 (2)Khj@ilk~o tN>0 qlen5sWkNE4LVrx

Q7?%J*$+<MkKO,&9+<MkrQ$?%

e ∈ E2Nlg

$YsH eGV+l?$^?Ohil?H5lk*N,sDNlg$YE;

s5NQ,G<?ZWt N_+i=l>lN*NLVr>\dj9k3HOq7

$%=3G$~OsY$:U#k? [5]NM(rxQ7$>0NuVXt−1r5

K P (Xmt |ZW

t ,Xt−1, e ∈ E2)rW;9k%

$YsHe ∈ E2GV+l?$"k$Ohil?H5lksDN*NroA, oBH

7$=liN*NNuVrXABt = {XA

t , XBt }H9k%N(P (XAB

t |ZWt ,Xt−1, e)

O$~OsY$:U#k?NM(rQ$kH!0Nh&K8+G-k%

P (XABt |ZW

t ,Xt−1,e) =P (ZW

t |XABt ,Xt−1,e)P (XAB

t |Xt−1,e)

P (ZWt |Xt−1, e)

∝ P (ZWt |XAB

t , e)P (XABt |Xt−1, e) (16)

e0NQAO$XABt ,{NG"kH$&roN<G ZW

t HXt−1OH)G"k

3HrQ$F$k%

15

0 (16)N&A$^:$&Uhl`NP (ZWt |XAB

t , e)OJ<Nh&K7FW;

9k%uVQ= e 6= 0G"ksDN*N oA, oBNLVOv0psH7F?(i

lF$k%3liNLVr=l>l lAt = (xA, yA) , lBt = (xB, yB)H9kH$0

(1)$0 (2)+iW;7?E4LV g$*NNE5N?QµA, µBHNVKO!0

G=5lkONb<asHN`jg$,8_9k%

µA(lAt − g) = µB(g − lBt ) (17)

3NX80r)sH7FQ$F$P (XABt |Xt−1, e)GW;5l?*N oA, oBN

uVN>b+i$0 (17)r~?5J$>br~Q9k (0 (18))%

P (ZWt |XAB

t , e)=

1 if µA(lAt − g) = µB(g − lBt )

0 otherwise(18)

YE1H@H$OsIjs05lF$k*NOf+i%lF$k?a$LV

OT@G"k%>CF$~o t− 1K*1kLV,j^i:$~OsY$:U#

k?NM(rQ$k3H,G-J$%7+7$sFj!GO+airQ$F*

N,OsIjs05lF$kGfbLVrW;7F$k?a$OsIjs0f

N*NKP7Fb~o t− 1K*1k8_N(^CWP (lmt |Zt,Xt−1),aail

F$k%>CF$0 (17)N)srxQ9k3H,D=KJCF$k%

l} P (XABt |Xt−1, e)KD$FO$*NOMVNUWG*NO0+5lk?

a$*}*J?0bGkr>j7FW;9k3HOq7$%3N?a$*N,

,&9,[K>CFis@`K\09kH>j7$>0NuVr~V/85;

k3HG@k%

JeNh&J3PaxKpE$F$F*N omN=_NuVP (Xmt |ZW

t ,Xt−1)

rdj9k%

\FGO$$YsHKm\9k3HG#t1~K*N,\07?lgKP~

9k%+aiN_GOWC~Kj"k?$`GOsIjs0N+O&*;,!

PG-J$djr$YENQ=+ij"k?$`KOsIjs0N+O&*;

r!P9k3HGrC7F$k%^?$WCfK#tNOsIjs0,+O&

*;7?lg$YE;s5N_GOP]*NLVNCj,q7$lg,"k,$

N(*JbGk=Khj$eG+ai&Nps,@il?~Kj+Pj9k3

H,G-k%5iK$+ai&N*NNLVpsrQ$k3HG$#tN*N

,1~K\07?lgGbYE;s5&GLVNW;,D=KJCF$k%

16

h 4OG$+aiHYE;s5rH_go;?sFbGkKhj$+ai$Y

E;s51NGOPhG-J+C?dj,rh5lF$k3HrB3Khj(

7$\FNsFj!N-z-r(9%

h4O B3&M!

3OGO$+aiHYE;s5+i@ilkpsr}g7?N(*JW;b

GkrsF7?%\OGO3Nj!rH&?aNO<I&'"$^?$B3H

M!KD$FRYk%B3rT&K"?j$sFj!NN(W;bGkNQi

a?_j,,WHJk%=3G$=wB3H7FYE;s5N:YN>A$Z

S$*N,V+l?jhil?j7?3HG/3kYEQ=N~V*d\NQ

,rTC?%=wB3NkLKpE$F$2OGRY?YEN60!PKQ$

kgM δbefore, δafter$ZS$YEN8`P9 σqrW;9kG<?NDt qlenr_

j7?%

4.3.1aNB3 (B3A)GO$WCfKP]*Nr1~KV/u7KP7Fs

Fj!r,Q7$j"k?$`GP]*NrV$?3Hr!PG-F$k3H$

ZS$*NLV,djG-F$k3HrN'7?%^?$4.3.2aNB3 (B3

B)GO$H_)FnHXN,QcH7F!PfeGnHTKZ<Q</iUH

rn.7Fbi$$=NG<?;CHKP7FsFbGkr,Q7?%5iK$

4.3.3aNB3 (B3C)G$4}nHXN,QcH7F 4MNo3TrP]K!

PfeG)`Nim-dZGrTCFbi$$=NG<?;CHKP7FsF

bGkr,Q7?%

GiK$4.1aG\&fGNQ,D-HO<I&'"N\YrRYk%3$F$

4.2aGOsFj!NW;bGkNQia?$gMr_j9k?aN=wB3N

\YrRYk%GeK$4.3aGB3A,B,CN\YH=NkL&M!rRYk%

4.1 Q,D-HO<I&'"

^:$\&fGQ$?Q,D-HO<I&'"N\YrRYk%\&fGO$

+aiHYE;s5r^ 3Nh&K_V7$P]*NNOsIjs0jPr

TC?%YE,W,G-knHfr)n7$yNeKV$FxQ7?%^?$

+aiOM*NhKhkWC,Gb/J/Jkh&K$nHTH~+$gC?

LVNe}K_V7?%HQ7?O<I&'"O$YErW,9km<I;k

17

^ 3: \&fNQ,D-

^ 4: nHfHYENG<

?m,<

^ 5: nHfK_V7?

m<I;k

(HBM=C9B , GgYE 50N)$m<I;kNG<?m,< (HBM=Quamtum

X MX840A)(^ 4)$+ai (Logicool Webcam Pro 9000)+i=.5lF$k%

m<I;kOnHfNMyK_V7? (^ 5)%^?$+aiO 640_ 480N+

i<h|rh@9kh&_j7?%nHf7DtO"k_=G}$|T-$b

5O=l>l 750mm$500mm$8mmNbNrQ$?%

4.2 YE;s5\<INC->A

YEN60r!P9k?aNgM δbefore, δafter$ZS$YEN8`P9σqrW

;9kG<?NDt qlenJIr_j9k3Hr\*H7F$=wB3rTC?%

4.2.1 YE;s5:YN4:

YE;s5K++kYEN?MHB]KYE;s5,(9MH,oKlW9

k3H,}[G"k%7+7$B]KON$:KhkFAru1k?a$$Y

sH,5/HbYE;s5,(9MO?M+i:lk%=3G$YE;s5N

m<I;kNYEN,j:Yr!Z7?%3NB3kL+i$YE60!PN

?aNgM δbefore,δafterrhj7?%

*N,!PfeKV+lFBj7F$ku7G;s5+iYEG<?r,j

9k%=3+iis@`K 5005sWkN,jG<?r*r7$=liNG<?

N,6r,j7?%*NKOELrQ(k3H,G-k*bjrHQ7?%*

bjNE5N,jKO ISHIDA=VIM-7000WrQ$?%IM-7000Om9 1gJ

bGE5r,j9k3H,G-k%50g+i 500g^GN$/D+NE5N*

bjKP7FG<?r,j7?%

50g , 500gN*bjNlgG=l>lN,6rW;9kH$50gN*bjN

YEG<? 500DN8`P9O 4.16$500gN*bjNYEG<?N8`P9O

18

^ 6: 100gN*bjNYEQ= ^ 7: 300gN*bjNYEQ=

4.18HJC?%100gd 300gN*bjGb$18h&J8`P9r(7?%3

N=wB3kL+i$YEN8`P9O7DK++kYEKMiJ$3H,N

'5l?%>CF$YEN8`P9OljG"kH>j7$δbefore, δafterNMr

δbefore = δafter = 2σ ; 8K_j7?%

4.2.2 YEN~V*Q=N4:

*N,!PfK\O7?]NYEN60,}^k^GN~Vr4:9k3H

Khj$YEN8`P9 σqrW;9k?aKQ$kQ,MOsN95 qlenr_

j9k%

*N,!PfK\O7?]NYEG<?NQ=rQ,7$*N,V+l?~$

hil?~NYEN60NQ=r4:9k%*NKO0aH1MN*bjrH

Q7$4.1.1aN=wB3H1MK$/D+NE5N*bjKP7FYENQ=

r4:7?%J*$sFj!GOP3*KYEG<?r,j9k5sWjs0

l<Hr 125HzK_j7F$k,$3NB3GO$hj\7/4:9k?aK

5sWjs0l<Hr200HzK_j7?%3lhjb$5sWjs0l<HG

Q,9kHN$:NFAru1d9/Jk3H,N'5l??a$5sWjs

0l<HO 200HzK1ak3HH7?%

^ 6$^ 7K=l>l 100g$300gN*bjGQ,5l?YEG<?N~V*

Q=r(9%IAiN*bjGb$*N,_V7FYEKg-JQ=,88F+

is 0.6CGQ=,}^C?%>NE5N*bjGb$?/Nm9O"kbNN

s 0.5CAs 0.7CGQ=,}^kkLHJC?%3lhj$o:+K[Jk~

oNOsIjs0Gb$/3C?~oN9,s 0.6CJbG"lP1~K/3C

?H=j5lk3H,o+C?%^?$qlenO$60,}^k^GK++k*h

19

^ 8: *NNOsIjs0NMR

=N~VHsFj!NYEN5sWjs0l<HrM87$qlen = 0.6∗125 = 75

H7?%

4.3 }gbGkN>A

=wB3NkLKhj_j7?Qia?rQ$FB3A,B,CrTC?%^:

B3AGO$;s51NGOj"k?$`GOsIjs0N+O&*;r!P

9k3H,$qJu7KP7F$sFj!KhCFj"k?$`G!PG-k

3HrN'7?%!KB3 B,CG$BD-XN,Qr[j7?B3rTC?%

B3BGOZ<Q</iUHrn.9knH$B3CGOM2Nim-dZG

rT&nHKP7FsFbGkr,Q7$INxYN:YG*NNOsIjs

0N+O&*;,!PG-k+rN'7?%

4.3.1 }gbGkN-z->A (B3A)

WCfK*NNOsIjs0r1~K+O&*;9ku7 (^ 8)KP7F$s

FbGkr,Q7?%+ai1HNj!GO$04KWC5lF$k*NKX

7FOOsIjs0N+O&*;O/J/HbWC,5/Jk^G!PG-J

$%^?$YE;s51NN>hj!GO$OsIjs0N+O&*;N?$

_s0O!PG-k,$=lir,1F!P9k3H,q7/$5iK$P]

*NLVNdjb$qG"k%

sFbGkGO$YsHKm\9k3HG$YE;s5Nps+i=l>l

N*N,V+l?+hil?+rN(*KW;9k (0 (11))%̂ ?$)s0 (17)

rQ$k3HGWCfN*NKP7FbLVrdj9k%3Ns@rB3G!

20

$YsH /-?~o [s] !P7?~o [s] !P~om9 [s]

Nj:Taken 8.411 9.035 0.624

O5_:Taken 10.439 11.063 0.624

Nj,O5_:Put 14.791 16.117 1.326

= 1: $YsH!P~o

^ 9: B]N*NNLV ^ 10: NjN8_N(^CW

Z7$sFj!N-z-r(9%

P]*NNl"N0-r^ 8K(9%P]*NKO$O5_ (46.7g)HNj

(91.7g)NsDrQ$?%Gi$!PfKO?bV+lF$J$ (^ 88e)%^

:$P]*NrlD:DV$F$-$i|P?rT& (^ 8f{e)%i|P?,

*;7?>er~o 0H7$*NrlD:Dhk (^ 8&e,8<)%=Ne$N

jKWC,"kuVGO5_HNjr1~KV/ (^ 8f{<,&<)%3NG<

?;CHKP7F$sFbGkr,Q7?%

kLO$P]*N,V+l?3H$hil?3HOi|P?nHb^aF4

F57/!P5l?%WCfK#tN*Nr1~KV$?lg (^ 8f{<)G

b$=li,V+l?3H,57/!P5l?%^?$sDN*N,1~KV

+l?>eNNjN8_N(^CWNPOr^ 10K(9%WCfGbNjNL

V,djG-F$k3H,N'5l?%

$YsHr!P7?~oH$B]K$YsH,/3C?~or= 1K(9%1

lN*NKP7FN$YsH!P~oOs 0.6CNm9,N'5l$sDN*

NKP7FN$YsH!P~oOs 1.3CNm9,N'5l?%3NxYNm

9G"lP$j"k?$`GNYgKYcOJ$HM(F$k%J*$$Ys

H,/-?~oOj0GN'rTC?%

4.3.2 H_)FnHXN}gbGkN,Q (B3B)

3$F$sFj!rB]NH_)FnHKP7F,Q7$\FGsF7?b

Gk,=uGINxYN:YGB]NnHfNOsIjs0N+O&*;r!

PG-kN+r!Z7?%

21

;q !Pst/V+l?st [s] !Pst/hil?st [s]

Nj 3/4 3/3

O5_ 2/2 0/1

+C?< 2/4 0/3

j, 2/4 0/3

= 2: sFbGkN,QkL (B3B)

o3TK$Z<Q</iUHNnHrTCFbiC?%Z<Q</iUHK

O$CanonRNWebZ<8 [10]Gx+5lF$kG`N&A$V&5.WrQ$

?%;qO$+C?< (22.4g)$O5_ (46.7g)$Nj (91.7g)$j, (16.3g)$Z

S$Z<Q</iUHQN|frHQ7FbiC?%O5_O|frZk?a$

NjO|fr=jgo;k?a$^?$+C?<Hj,O|fN^j\rD1

Fbi&?aKHQ7FbiC?%3lKhj$sD1~KhC?jV$?j

9k3H$ZS$hC?jV$?j9kJ0NN$:,YEK~k%J*$|f

OsoKZ/YE;s5G!PG-J$?a$!PP]*NKO^aJ+C?%

= 2KB3kLN\Yr(9%*N,V+l?3H$hil?3HKP9k

sFj!NPOkLNF=(O=l>l 64.3%$30.0%HJC?%NjJIN

"kxYNYE,"k;qOh/!P5l?,$j,d+C?<JINE5,

Z$;qO&^/!P5lJ+C?%3lO$^j\rU1kH$C?!Pf

H\(7J,iT&nHGQ$k;qO$HQ7?e=N^^V+lk3H,

?$%=N?a$YEQ=r!P9k3H,G-J+C?HM(ilk%J*$

B]KV+l?st$ZS$hil?stOj0GN'rTC?%

l}$*N,V+l?3H$hil?3HKP9k,g(O=l>l 34.6%$

14.3%HJC?%nHTH!PfHN\($"k$O$|fH!PfHN\(

KhCFYENQ=,/3j$=N?aKm!P,+il?%*N,V+l?

3H$hil?3HKhCF/3kYEQ=H$=lJ0N>NWxKhCF

/3kYEQ=Hr,1kh&J"k4j:`,#e,WKJk3H,N'5

l?%

4.3.3 4}nHXNsFbGkN,QJB3CK

B]N4}nHNltKsFbGkr,Q7$sFbGk,INxYOsI

js0r!PG-kN+rN'7?%

nHfeK^JDrGj7?D-GT<i<rQ$FM2Nirm-$=N

22

^ 11: B3CGQ,5l?h|Nlc

o3T !PstJV/K !Pst (hk) 5~Q

a 2/3s 2/4s 4/4s

b 1/3s 2/4s 1/2s

c 3/3s 2/4s 5/10s

d 1/3s 3/4s 7/11s

gW 7/12s 9/16s 17/27s

= 3: B3CNkL

e$M2rqzG>nZjK9knHr4MNo3TKTCFbiC? (^ 11)%

3NnHKP7FsFbGkr,Q7$4}oqG"kT<i< (30.5g)$qz

(71.4g)$M2 (95.0g)NOsIjs0,!PG-F$k+r!Z7?%^?$3

NnHGOZG~JIK*NNOsIjs0J0N6xGYEK60,/89

k%sFbGk,=N60KP7F$*NNuV,QoCF$J$H=j7$~

QG-k+KD$Fb!Z7?%J*$M2O)`G"k?a+(dE5NC

'L,TQG"kH$&)sKgoJ$P]G"k,$#eN]jbM87F

P]*NK^a?%

kLO= 3Nh&KJC?%*N,V+l?3H$hil?3HKP9k

F=(O=l>l 58.3%(7/12s)$56.3%(9/16s)HJj$,g(O=l>l

29.2%(7/24s)$47.4%(9/19s)HJC?%$YsH,/3C?s0.6A1.3Ce

K*NNOsIjs0r!P9k3H,G-?%^?$*NN\0J0K/x

7F!P5l?YEQ=,N'5l?,$=N&AN 63.0%(17/27s)r57

/~QG-?%lcH7F$"ko3TN4}nHKP9k5rG<?HsF

bGkNPOkLr= 4$= 5K(9%J*$5rG<?OB]N4}nHrQ

,7Fj0Gn.7?%J<KM!rRYk%

(*1)KX7FO$T<i<,hil?jV+l?j7?3Hr$qzHM2,

1~Khil?jV+l?j7?3HHm!P7F7^C?%4}T,T<i<

rhk$YsH,/3C?]NsFbGkNPOO$M2,hilFqz,V

23

$YsH ~o [s] !P

T<i<:T 18.9 (*1)_

M2:T 20.2 {

M2:P 57.3 (*2)_

T<i<:P 59.0 (*1)_

M2,qz:T 60.1 {

qz:P 102.5 {

= 4: 5rG<? (TOhil?3H$P

OV+l?3Hr=9)

argmax(P(e)) ~o [s] 5m

M2:T,qz:P 19.6 (*1)_

M2:T 21.3 {

M2:T,qz:P 24.9 _

Nothing 31.8 {

Nothing 40.8 {

Nothing 56.1 {

qz:P 58.3 (*2)_

M2:P,qz:T 59.3 (*1)_

qz,M2:T 61.1 {

M2:Put 97.1 (*3){

Nothing 101.5 {

qz:Put 103.5 {

= 5: sFbGkNPO

+lk3H,1~K/3C?N(, 37.1% $T<i<,hil?N(, 32.0%

Go:+KtC?%3lO$YEQ=,`w7F7^C?3H,6xHM(i

lk%3NdjXNPhO$#eN]jH7?$%

(*2)KX7FO$M2Ni,m+l??aKZ/JCF7^$$qzNYE

H`w7F7^C?3H,6xHM(ilk%3Nh&J*NN+(dE5C

'NQ=K#ePh7F$/,W,"k%

(*3)KX7FO$ZGfO60,d(VJ//3CF$k?a$YsH,!

P5l:$M2NZG,*oC?eKM2,V+l?3H,!P5l?%M2

NZG,*oC?>eN~oO96.1CG"C?%M2OZG5lF$k,$g

WYEOQ=7J$?aM2H=j9k3H,G-?%3Nh&K$*NN+

(,Q=7FbV+l?3Hr!PG-?cb"C?%

h5O *ojK

\&fGO$Q,G<?KpE$FyNeKV+l?F*NKP7FNOs

Ijs0rj"k?$`GjP9k3Hr\*H7?%

3N\*KX"9k>hj!KO$+airQ$?j!HYE;s5rQ$

24

?j!,"k%+airQ$?>hj!GO*NKWC,"C?lgK$j"k

?$`G*NNOsIjs0rjP9k3H,6}*K$qHJk%^?$Y

E;s5rQ$?>hj!GO*N,#t1~K\07?lgK$=l>lN

*NNOsIjs0r,1FjP9k3H,6}*K$qHJk%

\FGO$+aiHYE;s5+i@ilkpsr}g7?N(bGkr,

Q9k3HG$;s51NGO$qG"C?WC$#t1~\0Nu7KPh

7?%+aiGO*NKWC,5$Bj$#tN*N,1~K\07Fb=l

irL9K!P9k3H,G-k%YE;s5GO*N,#t"C?H7Fb$

YEQ=Km\9k3HGWCKX8J/j"k?$`G$/J/Hbhil

?jV+l?jH$C??i+NQ=,/87?3HO!PG-k%>CF$3

liN;s5r}g9k3HG_$N;s5GOq7+C?u7KPhG-k

H|T5lk%^?$N(bGkrxQ9k3HG$?H($WCfK$+D$

#tN*N,1~K\07?lgGb$WC*;~Kmjrj+Pj9k3H

,G-k%

B3GO$1NN;s5GO!P,$qJu7$ZS$B]NnHKP7Fs

FbGkr,Q7?%0TNB3GO$WCfK#tN*N,1~K\07F

b$=lir,1F!PG-k3HrN'7?%^?$P]*NNLV,djG

-F$k3HrN'7?%eTNB3GO^:$Z<Q</iUHNn.nH

KP7FsFj!r,Q9k3HG$sFj!,B]NnHKP7F*N,h

il?jV+l?j7?3HrIl/i$57/!PG-k+r!Z7?%3

NkL$*N,V+l?3H$hil?3HKP9kF=(O=l>l 64.3%$

30.0%HJj$,g(O=l>l 34.6%$14.3%HJC?%

^?$o3TK4}nHrTCFbi$$=NnHKP7FsFj!r,Q

7?%3NkL$*N,V+l?3H$hil?3HKP9kF=(O=l>

l 58.3%(7/12s)$56.3%(9/16s)HJj$,g(O=l>l 29.2%(7/24s)$

47.4%(9/19s)HJC?%*NN\0J0K/x7F!P5l?YEQ=,N

'5l?,$=N&AN63.0%(17/27s)r57/~QG-?%*N,hil?

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