• 検索結果がありません。

JAIST Repository https://dspace.jaist.ac.jp/

N/A
N/A
Protected

Academic year: 2021

シェア "JAIST Repository https://dspace.jaist.ac.jp/"

Copied!
52
0
0

読み込み中.... (全文を見る)

全文

(1)

Japan Advanced Institute of Science and Technology

JAIST Repository

https://dspace.jaist.ac.jp/

Title

スリット回転型エッジ特徴抽出器を用いたコーナー検

出に関する研究

Author(s)

江藤, 康隆

Citation

Issue Date

2002‑03

Type

Thesis or Dissertation

Text version

author

URL

http://hdl.handle.net/10119/1577

Rights

Description

Supervisor:阿部 亨, 情報科学研究科, 修士

(2)

! #"$%"'&()#*+-,/.0

1325476 8:9 ; <=45>

?@ A%B

CDFEHGJILKNMPOLQHKHRJQHK

SHT

ILKNUPVHI

SHT:WFXZY\[

KN]H^

2002

_

2

`

(3)

! #"$%"'&()#*+-,/.0

1723456 aFbc <745>

d5e3f3g3hie aFbc <745>

d7e3fFg j:kml 47>

d7e3fFg nHopNq <745>

?@ A%B

CDFEHGJILKNMPOLQHKHRJQHK

SHT ILKNUPVHI SHT:WFXZY\[ KN]H^

2002

_

2

`

Copyright c

r

2002 by Yasutaka Etou

(4)

copyright c

r

2002 by Yasutaka Etou

Corner Detection using Slit Rotational Edge-feture Detector

Yasutaka Etou

School of Information Science,

Japan Advanced Institute of Science and Technology February 15th, 2002

Keyword : Corner detection, Edge detection, Slit rotational edge-feature detector

Edges in images include useful information and consequently they play an important role in com- puter vision (e.g., segmentation, feature-extraction). Particularly, corner points where some edges intersect include useful information, and therefore detecting the corner in images is a important role.

However, stable and accurate corner detection is di

s

cult, because edges break easily around a corner.

For this reason, many corner detection methods have been proposed. The existing methods can be divided into two approaches: one is region-based approach; and the other is edge-based approach.

In the region-based approach, an image is segmented into regions by using edge detection method and segmentation method, and corners are detected by extracting the pixels that have local maximum curvatures in region boundaries. However, because of the rounding e

t

ect of boundary, it is di

s

cult for the region-based approach to detect corners at the exact position (pixel). To avoid this problem, most of the recent attempts in corner detection use the edge-based approach, which works directly on the image. In the edge-based approach, edges in the image are extracted, and corners are detected by analyzing edge-connectivity on the basis of corner model. Nevertheless, it is di

s

cult for this ap- proach to detect corners stably, because a corner is composed of intersection of edges and extracted edges break easily around a corner. For these di

s

culties, a corner detection method using slit rota- tional edge-feature detector (SRED) has been proposed. By evaluating the certainties of edges for all directions at each pixel, this method can detect corners stably. However, in this method, the accuracy of corner detection varies with the directions of edges, and the corners in the region of low contrast cannot be detected. In this paper, I propose a new stable and accurate corner detection method by adjusting these two problems.

To solve the first type problem, we propose a new corner detection method using weighted and interpolated SRED (WI-SRED). To acquire the accurate edge-feature for all directions at each pixel, WI-SRED is modified from the original SRED in two points: the first one is to interpolate the pixels

I

(5)

in a slit, and the other is to weight the pixels in a slit. To compute the accurate edge-feature and prevent its accuracy from depending on the edge direction, it is necessary for every direction of a slit to complete the apparent number of pixels contained in the slit. For this purpose, in the proposed method, the pixels in the slit are interpolated with the neighboring pixels by the bilinear interpolation method. For acquiring accurate (i.e., high-resolution) directions of edges, it is profitable to use a long slit. Therefore, to extend the apparent length of the slit, the pixels in a slit are weighted by the weight function whose weight is made proportional to the distance from the center of slit rotation.

The next step is to determine the edge directions at each pixel, the direction-feature is computed from edge-feature by using . direction-feature detector (DFD). In original corner detection method using SRED, when edge directions are determined, the value of threshold for direction-feature is set to a large value to avoid the noise on images. However the accurate posion of edges cannot be decided, because the direction-features is few in the region of low contrast. As the result, the corners cannot be detected. In fact, there is own properties for the value of parameter in DFD: When the value of paramater of DFD is large, its detection accuracy is robust for noise on images, however its direction is lack of accuracy. Adversely, when the value of paramater of DFD is small, its direction accuracy is improved, however its detection accuracy depend on the noise on images. To avoid the second major problems from these properties, DFD is applied to edge-feature by changing the mask size of DFD.

Firstly, the parameter of DFD is set to a large value, then the edge directions are extracted. Secondly, the paramater of DFD is set the value of smaller than the value of the first step, then the edge directions are extracted. Then, the edge directions are extracted by combining these two values. The edge directions are improved by continuing this process.

However, these directions are determined on the basis of the derivatives of intensities, therefore, they include many false edge directions caused by the noise in images. In the proposed method, to reduce the false edge directions, the edge certainties based on region separabilities are used. This region separabilities are computed by using the pixels around such extracted edge. By detecting the directions whose the separability is greater than a threshold value, edge directions for each pixel can be determined.

After the deciding of the edge directions, when the following two conditions are satisfied, the respective pixels are regarded as detected corners. (these conditions are (1) let an angle between the adjacent edges, at least one angle is not equal to

u

, (2) for each edge at the pixels, the edge certainty is computed, the mean of the separability at the such pixel is greater than a threshold value. ) Finally, we carried out several corner detection experiments for synthetic images and real images. In these experiments, original corner detection method using SRED and corner detection method using SUSAN operator are used to compare with the proposed method. It was appear to be the proposed method using WI-SRED achieves stable corner detection compared to the corner detection results from the other methods. Futhermore, stable corner detections for the region of low contrast can be achieved.

II

(6)

copyright c

r

2002 by Yasutaka Etou

v w x y#z { | } x ~€  ‚ ƒ „ …† ‡ ˆ

‰ Š ‹ Š Œ ƒ  Ž  ’‘ “

?@ A%B

CD”EHGHILKNMPOLQJKHRHQHK SHT

ILKNUHVHI

2002

_

2

`

15

•

–F—L˜N—š™

:

›

—Zœ—5žŸ” (¡/¢”£=žŸ” 

X:¤

¢/¥§¦3¨H©¡/¢£«ªH¬H­/Ÿ5®

¯7°5±3²”³µ´5¶3·3¸¹7ºH»i¼7½5¾7¿3À3Á:ÂÄÃ7ÅÆÇ½7È7É3Ê3ËÍÌHΫÏÑÐ3ÒÈ3É5Ó7ÔµÕ7Ö5×PØ7Ï

ÙÚ

ūۧÜ5ÝNºÍÞ5²Lßáàãâ«äæåçØµè”éêÕ

ÙÚ

ÅêëN¼«Àêì”Àßáí7îäçËðï3±ÛêÕæ´HȧÜ3ÝZºÍñ3òóÂ

ô ë7õ÷öµßµéµøÇù3úè=ûFËÇå”ü=Ïçâ=ýiÕµÖ5×HØ«ÏN¼iÀµì”ÀßÿþH¹µäZËÍÛHȧÜ3ݺ

èçû3ËÑå §õ §º5ëáÕã¼7Àµì”Àè3Û

ÙHÚ

ÅÑÏFë᳔äFÓ3â«ýiՔõ3øÏ

Ó3¼iÀµìÀ§þã¹3Û ãÈ!" §ÓÇå

# $&% è”È('")§ÏN¼µÀÇìÀêþ¹ ô* ë+,-.FÔFÓçËÇë7ÕFü&êÛ/102)43ÿø”ȧ±HÊ3Ë

ë7è05ËÍå65 ø3Û§¯7°È.78 §â

ô*

Õié95ÄøçÛ

ÙZÚ

Å«È(78 â

ô *

è=û3ËÍåð¯7°PÈ(78

â ô * è3ÛæÕ

ٔÚ

Å þP¹ ô * ³Ñ¯7°7±=² ô * ß;:ZÓ=ËÍÈ4<Nö ÕðÖ7×LßêÓ2)áø7õ=Ïͯ=°È§±7²

Õµ¯5°=>ZÏ?@PÏ/A0=ºÇù7ú÷ß;BäÇÈ<ãöͼ7ÀêìÀNß þ¹7ä”ËÇå §õ& æºiëÿÕP¼iÀ

ì”À(”è3Û CD=½(EFµ½G÷Â

ÙHJIJKL

ëJæËiâ«ýµÕ.MJNZºO PZèN¼µÀÑì”À”ßáþ¹«äçË

ÛQ(!Nèçû”ËÍåR«ÏST÷ß;UHÊ=Ë=â=ýFÈêÕVZÏN¼iÀµì”Àêþã¹7è3ÛXWY3Ö7×HØiè¼µÀµìNÀiÏÑþ

¹ß[Z69

ÙHÚ

ŵÈ7"8 Íâ

ô*

ëih \è=ûFËÇå

ÙHÚ

Å7È(7"8 êâ

ô*

ÛµÕ¼7ÀÇìÀX] E^çõ&

ÙHÚ

Å X-Fß[_`ä”Ë4ÇÈ<ãö Õ

ÙãÚ

ÅÑÏÇ´5¶ß ¸¹iäZË4ðè¼7ÀÇìÀ”ß þã¹7ä”Ëêå6

õ º=ë Õ¼iÀµìÀ”ßÿí3îäçËæù3úHÈ7É5Ó7Ô3ÛµÕabZÏ

ÙãÚ

Åêë cdeêԔÓ3Ë5â«ýiÕ

ÙPÚ

Å

ÏÇ´7¶N뵸H¹µè40 f”È3¼iÀµìÀµëge7â(OPèêþH¹4-”Ë4Íë'HÓÇå.6§ÏSTßh_iNä

Ë5â7ý5ÈµÕ jkêÛl5ÖmÈno §Ôprq

ÚL

ßst-vuJË4ÑÈ<ãöÄÕ

ÙãÚ

ÅÑÏNNõ -Fß

wxyiè zçý”Ëpq

ÚL st{

ÙHÚ

Å ´3¶7¸H¹(|

(SR ED)

ßh}:”äZË§è §ÔN¼µÀµì”À

ß þã¹µäZË

ô*

ß[+,o §Ô3ÓçËÑå ðõr ÿÕµÏ

ô *

È5É3Ó7Ô3ÛEHÅ3Á^µÖ3×PÏ~ HÈ<Pö ÕXl

x1yµè

ÙHÚ

Å ´5¶PÏǸ¹ë€º”ËÇå

%

âµÕ¼3½

L

CXp

L

ρÓêù5úè3۔¼iÀµì”ÀßÿþP¹iè

0=º5ÓSXT3·”ë3û”ËÇå3üAµèX‚ ƒ4„”è”ÛµÏ ô * ÏSXT7·è3û”ËEHÅ5Á^µÖ3×Ï~ …†J¼5½

L

CXp

L

ÏÇþ¹5È7ø”ÓµÔ‡ˆ" áÕ<ãö‰ o êâ3¼7ÀÇìÀ§þH¹ ô* ß;+,ß§äZËÑå

I

(7)

SRED

ÚL

ÙÚ

Å ´5¶7¸P¹(|

(WI-SRED)

È<ö‘n’ZäçËÑå4ÑÏ

WI-SRED

SRED

πPº3Ëð·HÛXpq

ÚL

ß;“7îNäZËÍÖ mãȔ•\ßv:ÓçËðÕ % âÇÕpq

Ú&L

ÏÍÖmãÈn §ÔÇÜ2Nß;–äçËiä”Ë

èçû3ËÑå

ÙHÚ

ÅÑÏx1y7ȗ˜" ºçÓ

ÙHÚ

Åð´3¶\ß(z”ý”Ëiâ=ýçÈ3ÛêÕp&q

ÚL

ßh“3î”äZËæÖmÏ

bß[wNÔçÏxAyµèX™šãȵäZ˛5ݔëçû”ËÑå1 ßhœ

#

äZË=â=ý5ȵÕ+,

ô*

è”Û(

1

ž

”.•÷ß

:Ó5â§Ö3×Pϟ1 ß;Z69 êÈ<ãö Õ1µÏNÁX¡¢7ÏSXTãÈ(näZË._i\ߣ”ËÇå % â

ÙHÚ ÅÇÏJx

y=ϝß;¤ZýFË5â=ý5ÈÇÕpq

Ú&L

Ï¥-Fß;¥…)ðä”Ëx

*

ë‡2‹R¦NËÇå §õ& Õpq

ÚL

Ï

ا”õ&[¨FâOPHÈ/A0=ºÇܐPß;–”ä”Ë4Íèn’”è03Ë5â«ýiÕ4pq

ÚL

Ï¥-”ßh©A‹FË

§º&)ªZϤHÓ

ÙÚ

Å«ÏxyNß(zZý3Ëðë3è40çËÍå ‚ ô* è”Ûpq

ÚL

Ï¥-7È«¬o

âêܐPß Ü2­b…4 Ôpq

ÚL

È®:3ä”ËÇå

ž È ÙÚ

ÅÍÏxyNß[i”ä”Ë7â«ý5ÈêÕJzçý5â

ÙÚ

Å ´5¶Zõ[x1y§´7¶7¸¹|

(DFD)

ß[®: áÕ

x1y§´5¶

(

ÙãÚ

Å ´3¶Ènäç˯7±°

)

ßvzZý3ËÇåXŒZÏ

ô*

È3É7Ó7ÔiÕ1Çϱ²”賡 ´çÏ~

ß[UãÊçË5â«ýçÈXx1y§´5¶HÈn”ä”˵X¶7Ð5ÒPÏ·1C¸3À3Á«Ï¶ß;¹7±4/102) Íâ7ëµÕ ºãÈç¼5½

L

Cp

L

ρãÓêù7úèFÛXxAyæ´5¶ë»-)§ºLö Õ

ÙHÚ

Å3ßÿþH¹7è40Xf”ȵռ3པÈF¼7ÀÇìZÀNß

þH¹µè40=ºFÓêåR«ÏNÁ¡4¢=ÏST÷ß;_i”ä”Ë5â«ýFÈÇÕÑÏ·AC¸7À”ÁµÏ/0-iÈn”äZËæ´¾Nõ

Ղ ô * è”Û¿^ ÀpXÁNÀ^Fèn’ êâxyê´7¶ß;z”ýçËÇÈ<ãö‘_ iß(£ZËÍå

DFD

Ï·

C4¸3ÀNÁ/R0-iÈn" ÍÔ7Õ·1C4¸5ÀNÁ«ÏJ¶ë/A03Ó0iÕr³¡´NÈn ðÔRÃÄp

L

è”û”Ë=ëiÕ

ÙÚ

Å«Ïxyiëf ”ËÇåºãÈÑÕ

DFD

ÏJ·C¸7À”ÁÑ϶”ëX»-iÓA07ÛµÕ

ÙÚ

Å«ÏJxy7Ï͸H¹(

HÛNÓ¼3à\ßhÅJË4æë3è0=Ë«ë7Õ³(¡´çÏ~÷ß(ƔÊçËæ´¾”ëçûFËÇå

üÇè«Õ

DFD

ÏJ·1C ¸3À3Á«Ï¶÷ߦ/A02)ðäçË4ÇÈ<Pö ՔÉ7É

%

õçº

ÙÚ

ÅxAyZßÿ¸¹ §â

ÇNÕX»6-7º¶ßhÈãø ·RC4¸3ÀNÁÇèNéeµÔx1yÇ´F¶÷ßzZý=Õ3ü…7ßvÉ1JÊAd u\Ë1ÇÈ1<Jö Õ

ÙHÚ

Å(x1y=ÏyË\ߣZËÇå ðõ ÕµÖ5×HØ7È3Û'Ì) ÏR³¡´7ëXÍ

%

”Ë5â7ýiÕ zZýçâxAy

È7Û(g2eæÔ긹-Fâxy”ß[ÍΫå.g2eæÔêþ¹1 §â

ÙÚ

ÅÑÏxy”ß†Ï ö[ÐÑ)ðâ«ý5ÈêÕz5ý5â

ÙZÚ

Åxy7ÏÒÓ7¯5°”êïZÏѱ¨z”ý”Ë4æè7ÕXo §Ôê¯3°Nëµ± ¨-Ëx1y7ϐNß

ÙãÚ ÅÑÏ

x1y §ÔXi NäZËÇå

-ÍÈÑՔ¼7ÀêìÀ”ß þ¹iäFË=â«ý3È

ÙZÚ

ÅÑÏJxyNß[i êâ(Ç3ÕѸH¹4-.”â

ÙZÚ

Å7È5É=ÓiÔµÕ

ԝöÕÊ9

ÙHÚ

ÅÑÏ3º5äÖ PÏ

1

øFÛ

u

èçº) Õ %

âµÕÔ÷ö‰Ê9

ÙãÚ

Å 3è“3î-NËͯ5°NÏѱ

¨”ë¤HÓ205È7"8‰×÷ß7¼7ÀêìNÀׅ ðÔµþ¹7ä”ËÇå

Ø ÇãÈµÕ + ,o êâ ô* ÏÙÚ¾\ß;ÛäFâ«ýFȵÕÜ Ý3Ö3× # œPÏÑÖ3×ZÏ

2

Þßàáâ ßãä

åXæ ç6è;éêXëì íîïRð

âñÑòó(ôõö1ß

SRED

èv÷1ø ëùú

ò

SUSAN

û4üý;þà

è†ÿ4÷

ó

ë(ùúè÷

óò í î

ó(ô

ùú

ó;ô2ß ø

þ1þ

çå

ò

è!

ó

ëXì

II

(8)

i

" # $ %

&'(*)+,-./

021ð*34

þà65879:

ð<;=*>*@?A

ßCBD

;=ø

ô.ã ä2EJßGFIH

9JLKM 0N

)

è!OëGPì

E

åQ

FHG9

þ1þ

è!RSIPTVU

(

J , ;

KM 0WX

5 ù

Y[ZèQ

Þ\]

åì

ß ë^

ã ä_Eß

þ1þ

è;ç_P

òJC`a

;

KM 0T

ò å

ì

ó Y ó 0*

þ1þCbc

å

JF_H9ßdeT f6g

+

Pøë*^

IY

ÞAß

ø

þ1þ çI

J`a

;Lh

ó

øì

ijlk

å;Cmon

ß þ1þ

çIùúI

[pV4ô ø

*lJqIr ns

Þ ; (

>

ò

å

r

ì6t

ÞJ

&'

;Vu 8 ó

ë(ùú

Qvt

ÞJFTH9

;Cu 8 ó

ë(ù úå*ì

&'

;Cu 8 ó

ë(ù úå

JVFH<9

ç2(ù ú

+<&'(*)

ù úè;÷ø*

ò

;wxZ

vã ä

èø2n

Þ Y ß

&*'

;

()

ó

&'yz

ß{|2ßqxr

0

\]

è}IP

ò

;w_ZL

þ1þ

è;çIPì

ó Y ó 0G

~ þ

þCb*c

å

J€

ðCT‚Xð*ƒ

5„F…†‡[ˆ

f[gVë^

V‰Š

0L‹Œåx

þ<þ

è[çIP

ò

J

hAåì_

ߎ

è>*ë*^;

Gc‘ß

þþ ç_ å

J’G“ã äE åI

þAþß

ç

1è[é6v

FHG9

;u 8 ó

ëùúG”•1å*ì

FHG9

;Cu 8 ó

ë(ùú

J

þ1þ–

 ñ Y

FHG9óp

è!—˜IP

ò

;w_Z

F_H9ß ,-

è /

GPT

ò

åI

þ1þ

è;ç_Pì

ó

Y ó 0*

þ1þ

è~RSIP

\]

;=ø

ôJG™šßF_H9

›œê

ô

øë^

F2HG9

ß

,-

/ Xå

r

;

þ1þ

žê ëC‹Œ1åç

p<

ò

møì

6(ߎ

è~—*ŸxP

ë^;

 ¡¢J£ã¤

;¥

ó(ô¦¨§GH[ˆ

詪

p@«

ò

;Tw_Z

F_H9ߊ

Y

ó<p

è

¬­®

å¯^

¦[§GHˆ

©ª°

FHG9 ,-/

C±

(SR ED)

è~²÷PT

ò

å

ó(ô

þþ

è;ç_PTùúè

oó(ô øì

ó Y ó~

ß

ù ú;=ø

ôJ



9àñXãä2ß<³´

;Tw2Z

£

­I®

å

FH9 ,-

ß /

µI0ì k ë

ð

ˆ!¦¶ˆ‰ß·

ø

\]

å J

þþ

èhç2å

r

0ø

Ž

.

ì

X帹ºå

J ß ù ú

ß*Ž

.

åL

9àñXãä1ß³´…ò»·

ð

ˆ!¦¼ˆ ß çI;

Þ ø

ô½¾"ó!

w_Z¿

ó

ë

þ1þ

çùúè èCPTì

k

<



9à(ñ ãä2ßÀTÁ

³´

;C¥

óvôJõöß

SRED

;LÂTÃ[n

KTÄÞr¦[§Hˆ

©ª°

FIH9 ,-/

C±

(WI-SRED)

;wIZÅ¥ÆTPì

ß

WI-SRED

ò

SRED

ß

µ20

.

J¦§<Hˆ

èÇSxPT

ã¤

;ÈÉèv÷1ø

ò@

k ë

¦§Hlˆ ßã¤

;¥

ó(ôK2Ä

è

bÊ

PGP

ò

åì

FHG9ß

­I®

;LËÌ

ó

0ø

FH9 ,-

èC¯^ë*^;

J¦l§Hˆ

è~ÇSPT

ã*¤1ß

š è ¬ ôß

­x®

åÍÎ_;PTLÏ

M

ìI

èhæ

i

PTë*^;

G ùúAå

JCÐ

1

Ñ

ÈVÉ6è

÷1øë

ãä2ß<ÒIÓ

è;é6v

ò

;w_Z

ßAàXáâ ߎ

;C¥IPTV—ŸèÔì k ë

FHG9ß

­

®

ßL

èÕT^ë*^;

¦[§Hlˆ ßÖp

è Ö n@P

­

úI

½2Á_×

ì

ó Y

ó¦[§GH[ˆ ß

EØ

Y

!ÙT

ëL‹Œ;

qxr

0

KTÄ

è

bÊ P

ò

奯å

r

ë^

¦[§H[ˆ‰ßÖp è~Ú

Á

0ln Õø

­®

èC¯T^ å ì¸ùúå ;í*Û

(9)

ii

ë

KTÄ

è

K2ÄGܚ…ò4ó;ô¦[§Hˆ

;÷Pì

Ñ ;

FIH9ß

­T®

è!Ÿ*P ë^;

¯^ë

FIH9 ,-

Y

­I®C,-/

±

(DFD)

è!÷

ó!

­I®C,-

(

F_H9

,-

;L¥IPLÝ (Þ

)

è@¯T^ì

õöß

ùúI;= ø

ôG

ß<ßà åá

áâßL³

´

è!_>ë^;

­I®C,-

;¥PGãä

BD2ßåIæþàJß äèç

(

qIr n ó

ë

è

;ð

ˆ!G¦oˆ ß·

ø

\]

å J

­x®V,-

é

p

nC0Z

FH9

èhç å

r

;

Gê

Oë;

þþ

è

çXå

r

04øì_

ßAàá4âߎ

藟Pë^;

ßGåxæ þàXßGqrp

;¥PT ,*ì

Y

¸ù úå

Jíñî¦ïAþñ 奯

ó ë

­®,-

è¯^

ò

;w_ZŗŸèCÔTì

DFD

ßå

æþAàLq_rp

;¥

óôåIæþAàJß äI

qxr

ø

ò<rG

á

áâ

;¥

óvô_ðñ¦òˆ

å*

FIH9Jß

­®

 ì

è ;

DFD

ßåTæ þàß

äé

p ø

ò<rJ*FIH9Jß

­T®

ß /

J ø ê

Oè~ó¨

ò

å

r

á

áâßL³´

èCô>

,ì

ì

å

DFD

ßåIæþàJß

ä6è

qxr

n@P

ò

;w2Z

==

k

Y0

FIH9

­x®

è / ó ë

õ é p

0äoè~ö

Þå_æþAà åxQê

ô

­I®,-

èL¯T^

÷ è@ø

Äù

œ «

ò

;Iw¨Z

FHG9

­I®

ßL

®ú

èLÔTì

ó Y

óXãäE

; J mûn

ß á áâ

ü k

ë^

¯T^ë

­x®

; J

ž2ê

ô / p

ë

­®

è!üýJìVž2ê

ô

çI

ó ë

FIH<9ß

­®

è»þoZ!ÿnvë^;

¯^ë

FTH

9

­®

ß

&'

ÈU

ß ( Ù

¯^

ò å

ó(ô

&'

(

Ù[p

­I®

ßÄ

è

F_H9ß

­I®

òó(ô

ŸxPTì

p

;

þ1þ

è;çIGPë^;

FTH9ß

­T®

è!Ÿ

ó ë õ / pV

ë

FTH9

;=ø

ô

Z ù v

FHG9ß 0P

2ß

1

ÞJ

å0n

k ë Z ù v

F_H9Ó åÇS

p<

&'

ß (

Ù Õø

òLr

;u 8¿.

è

þAþ

.

òóvô

çIPì

õ

;

oó ëùú

ß

ì

è IP4ë^;

ãäò i æ

ßãäß

2

Þßàáâ ßãä

åXæ ç6è;éêXëì íîïRð

âñÑòó(ôõö1ß

SRED

èv÷1ø ëùú

ò

SUSAN

û4üý;þà

è†ÿ4÷

ó

ë(ùúè÷

óò í î

ó(ô

ùú

ó;ô2ß ø

þ1þ

çå

è! ëXì

(10)

iii

i

1

1

2

4

2.1

!"!#!"!"!$!#!"!#!"!#!"!#!"!#!"!$!"!#!"!#!"!#!"!#!"!#!$!"!"!#!"!#!"!#!"!#!"!$!#!"!#!"!

4 2.2

þ1þ

çIùú

!"!#!"!#!"!#!"!$!"!#!"!#!"!#!"!#!"!#!$!"!#!"!"!#!"!#!"!#!"!$!#!"!#!"!

4 2.2.1 (1)

&'

WX_;ÂIèn ùú

!"!#!"!"!#!"!#!"!#!$!"!#!"!#!"!#!"!#!"!"!$!#!"!#!"!

5 2.2.2 (2)

FH9

WX;ÂÃ[nªùú

!#!"!#!"!#!"!#!"!$!"!#!"!#!"!#!"!#!"!#!%!#!"!#!"!

5 2.2.3 (3)

ß&ß

ùú

!"!#!"!"!$!#!"!#!"!#!"!#!"!#!"!$!"!#!"!#!"!#!"!#!"!#!$!"!"!#!"!

7 2.2.4

þþ

; Ü

PVWX

ß½¾ !"!#!"!#!"!#!"!$!"!#!"!#!"!#!"!#!"!#!$!"!#!"!"!

8 2.3

ê !"!#!"!"!$!#!"!#!"!#!"!#!"!#!"!$!"!#!"!#!"!#!"!#!"!#!$!"!"!#!"!#!"!#!"!#!"!$!#!"!#!"!

10

3

')(+*-,/.102435*687:979;=<?>A@?BDC8EGFIHJ:H8KD<ML:N

12 3.1

!"!#!"!"!$!#!"!#!"!#!"!#!"!#!"!$!"!#!"!#!"!#!"!#!"!#!$!"!"!#!"!#!"!#!"!#!"!$!#!"!#!"!

12 3.2

¸Ië0

½TÁ

­

!#!"!#!"!#!"!#!"!$!"!#!"!#!"!#!"!#!"!#!%!#!"!#!"!#!"!#!"!#!"!$!#!"!"!#!

12 3.3

¦§H[ˆ

©ª°

F_H9 ,-/

±èv÷øë

FIHG9 ,-/

!#!"!#!"!#!"!$!#!"!#!"!

13 3.4

­®,-/

±èv÷øë

­x®C,-/

!"!#!"!#!"!#!"!$!"!#!"!#!"!#!"!#!"!#!$!"!#!"!"!

13 3.5

¦§H[ˆ ©ª° F_H9

,-/

±èv÷øë

þ1þ

çIùú

ßGŽ

.

!$!"!#!"!#!

15 3.6

ê !"!#!"!"!$!#!"!#!"!#!"!#!"!#!"!$!"!#!"!#!"!#!"!#!"!#!$!"!"!#!"!#!"!#!"!#!"!$!#!"!#!"!

16

4

WI-SRED -

O5PQRM'S(?*T,U.0:2V35*16M79V;=<?>

17

4.1

!"!#!"!"!$!#!"!#!"!#!"!#!"!#!"!$!"!#!"!#!"!#!"!#!"!#!$!"!"!#!"!#!"!#!"!#!"!$!#!"!#!"!

17 4.2

þ1þ ß W

!#!"!#!"!#!"!#!"!$!"!#!"!#!"!#!"!#!"!#!%!#!"!#!"!#!"!#!"!#!"!$!#!"!"!#!

17 4.3

¸Ië0

½TÁ

­

!#!"!#!"!#!"!#!"!$!"!#!"!#!"!#!"!#!"!#!%!#!"!#!"!#!"!#!"!#!"!$!#!"!"!#!

17 4.4



9àñã ä

Y

MXð

ƒ

ã äVYß<cZ !"!#!"!#!"!$!#!"!#!"!#!"!#!"!"!#!$!"!#!"!#!

18 4.4.1

ãä1ß\[:]^

(resampling)

!"!#!"!#!"!#!"!#!"!$!"!#!"!#!"!#!"!#!"!#!$!"!#!"!"!

20 4.4.2

ãä



þ4àJß ÈVÉ

(interpolation)

!"!#!"!#!"!"!$!#!"!#!"!#!"!#!"!#!"!$!"!#!"!#!

20 4.5

KTÄbrG¦§H[ˆ

©ª°

F_H9 ,-/

±

!"!#!"!"!$!#!"!#!"!#!"!#!"!#!"!$!"!#!"!#!

21

4.6

ê !"!#!"!"!$!#!"!#!"!#!"!#!"!#!"!$!"!#!"!#!"!#!"!#!"!#!$!"!"!#!"!#!"!#!"!#!"!$!#!"!#!"!

22

(11)

iv

5

35*168_A`ba\cd)e:FHJ:HMKA<

24

5.1

!"!#!"!"!$!#!"!#!"!#!"!#!"!#!"!$!"!#!"!#!"!#!"!#!"!#!$!"!"!#!"!#!"!#!"!#!"!$!#!"!#!"!

24 5.2

FIH9

­x®

ß

Ÿú

ò þþ

ç

!#!"!#!"!#!"!#!"!$!"!#!"!#!"!#!"!#!"!#!%!#!"!#!"!

24 5.2.1

&'

ß\f (:g

;LÂIÃ[n

þAþ . ß /

ú

!"!#!"!#!"!#!"!#!"!#!$!"!#!"!"!

25 5.2.2

&'

ÓßT‡G¦*Ó (g

;VÂxÃn<

þ1þ . ß /

(ú

!#!"!#!"!#!"!$!#!"!#!"!

27 5.3

þ1þ

çIæç

ê O

!"!#!"!#!"!$!#!"!#!"!#!"!#!"!"!#!$!"!#!"!#!"!#!"!#!"!#!%!#!"!#!"!

29 5.3.1

FHG9ß

­I®

Y4ß ËÌ_;

Ü

PT.æç

!"!#!"!"!$!#!"!#!"!#!"!#!"!#!"!$!"!#!"!#!

30 5.3.2

hi1ß³´

0ø

ãä

;=>

þ1þ ß çI;

Ü

Pæç

!"!#!"!

30 5.3.3

i æ

ßãä

;=*>

þ<Aþ ç_*;

Ü

Pæç

!#!"!#!"!#!"!#!"!$!"!#!"!#!

31 5.4

ê !"!#!"!"!$!#!"!#!"!#!"!#!"!#!"!$!"!#!"!#!"!#!"!#!"!#!$!"!"!#!"!#!"!#!"!#!"!$!#!"!#!"!

33

6

j

36

k:l

38

m5nM4o

39

qp%r

41

(12)

1

s

1

t u

"

ij

vw (x

è J

g×^Iyz5{

+|

8}:~;C¥S8€1‚±„ƒ²÷…M†WX

BDJ1‡

Y « 0ø

Qb{‰ˆL04Š1€ø‹

p

;

1‚±5{

ìŒ_®ú

5ÅðH[ˆŽ:

{M‘’_;TwxZ“‚±Gƒ²”DM†

•

¦1–—ð1THˆ!JMÓ

;˜ˆ\Š1€Ï

Mb™š‡

0M›œDˆ:?€1÷n

M ¯ p

wv;*0Š\€

r

†\‹

Pž;

vw[ðHˆ81Ÿ‰ ¡

'

ð1IH[ˆ8¢V£

4

§+–

‚ 5 •

¦–—

͉ž¤U¥¦

p

€V§*I‹

¨õ

pT

;

Õb©ªyzI;=>*?«

¬­

+1®V¯\°

0I1<;*=§1€

M¬­ð\THˆ88±

¥³²

ð\IH

ˆ

0I1:ˆ\§Š1†

w_ZÅÕ

0x³ˆbƒµ´6v\†*^{

ð1THlˆ

{LÏ

M ì Jqxr

n0Š\€V§n+žV¶v·‹

+€

l

{

ð1IHlˆ¸Ž

{I¹º;?»§

Ið1_H[ˆ

;

xÓ

\´GŠ€V§*wv<0

w2Z Õ

ž1¼”ë0½¾¿

Œ‰À

Ï M

;*0Š€nM‹

ÓJ\Á

•1Âà ƒÅÄÇÆMȉˆ%É

B

;?É ÀbÊË

Y‰ƒµÌÍVž

r Ë

‹³ÎI{ ÄÇÆ

Ë

È4ˆM§Tv“¿

Œ ;

J

ÊË

•ÂVà ƒ0ÏÑÐY{ÂÒI;w_Z ()

P Ë ¿ Œ

ˆMÓb{

()

pÔ

†L¥Õ

À

É4ž

ÊË

Y=ˆ“Ì:Í

P Ë ¿ Œ {6s“Ö

ÊVË

‹1רI;

Á1xÓJ

1?{xwvV0 ,-Þ

žQŠ1€Ó

Ô

Ð{M¿

Œ

ƒ+×

i

8€³§

Ë

YAˆI§vȈ

J?Ù=Ú\Û4Ü

žÝbÞ³§

À Á Î Ô

Ð?{

2

Ö{¿

Œ

{Iß5àáGˆ:?€

1

Öâã

Áä4å {Iæ

ç

ãVè Ë:é

{bž

ʄê$ëìê"í‰î

ÎVˆMݞVïÞ:§

é

{ˆðߘà

Ë

Ȉ

Á

é4ñ

1

Ö=ˆ8€

ÁòGó ÀIô:õ

?€¿

Œ

?€§

Ë ˆ é

ߘà

Ë

ÎVˆ?{

2

ÖVãMö5÷

Ë ÷ Ë1À

žVï

Ë

‹Ó‰Îž

ÁvwÑøIùGúüûŸ4 

¡\ýÑø\=ùGúÿþ

À

ä‰å

ˆ

þ

{I¿

Œ

ƒ4Ö1á ˆ³+€

Á

° {

2

Ö³{I¿

Œ4À

ó

ã?¿

Œ  €§

Ë ˆ ߉à Ë ˆ Á

ÊË

•Âà ƒ VÖ

Üý ã\ö

î˜Ë

á é

Ö

ˆµß4à

Ë

Έ

À

ž³ï Ë ‹

Î

Ô

ž

ý

ö‰žÝVã

2

Ö Ò

é

ã\´"!

Ô"#

ï$%

1

ÖVÝ

:ý

¤&'ã

(

î³Ë

'*)

Á

é4ñ+

ÖÝ-,

ù.

ã ( î˜Ë

'")*/

ÊVË

%

ý10

&'=ã

(

î³Ë

'") 2

# Ý Á Ê

Ë"3

ÂÃ 45

À 0 é6287

Ý:9;/<

ûÜ

Þ=>

2

#*?

Ë@A

ãMö î˜Ë

Î

CBD6E

Ð Ô

Ë %

$F*,

ù-.

ã ( îVË

'*)VãÖ

?#

ÝF45 BG

9;*F éH27

ÝIJ‰ã="!HK

#*?

ËL

Î

M /\ö î˜Ë

Î

BDE

Ð Ô Ë

%-NOã:ÝPQ

á*/Ý45R

TSU úVW-XûYZ"[

45

\ å

ã]:÷8^

ISODATA

5Þ6_

L`WU6aTbcV ã˜è-^

‰ÞH_

Bd

^1%

Q

á*/ÝF*,

ù

.

ef

2

#gih

$

ý :jk

î

^-,

ù.

ef5Þ6_

Bd

^%

Y 7 ý

ö

‰Ýl4ãmPQ

')i:n

?

^%Ho

piq "2

# F Q , ù.

ý

öã]

?#

n ?

^rs=Ý Gt

Û / d

^

vu

à*^

ÜHw / d

^%

î

Þ-!*xF

ý

ö=ã]

?-#

Ý:yz{

-g+hC#*?

^

:ý ã?ö

î

^m|

} Bd

^

vu

à8^%,

ù-.

Ý~bހ

Ü+wƒ‚H„…†

F‡~*³Þ€

Bˆ

^o :B

/ïÞ

? %

‰

$â-F

d

^mŠö/‹Œ

BŽ

…?

rs"F ‰

Š:ö/

ý yz{

B‘2

# 2

? F8’“

2

#"?

^

ý

”Vݕs

…†#

2 ñ

%o

$â1F*,

ù-.

ã˜è^

ý

öÝyz

g+h

$

:ý

j-k

$bâã

S–—bCU˜H™"ù`

ã,

ù.

›šHœ

î | } B8d

^% ‰ ñ Ý u…ñ1é

FPQ

ýL10

&'+Cl‰ãn

?

^rs‰ã

鏝*Bd

^%

‰ †

݇~T³Þ€:n

?

^$bâF~LÞ

€:ž

Ÿ 82 î 7

FH¡

B¤

j 2 $ ê

FH¥ o M

/VÝ:¨•s

(13)

1

ª «¬

2

ãbÞ

ê û î ? %

ý

ö/ÝF45R

‡~*ހ

û , ù.

Þ6_

@A­®¯

ã]÷^~bހ ›°

ô

/±"n

î

^Crs*F

ý

ñ 7

ö/ïÞ

? è 7 rs

B8d

^%NOTVãÝF‡~*³Þ

bý

€

n

?

$:rs*F8¥

—²*—³´

/VÝ

Rounding

µ¶

B·

ï # 2 ñ %

$F~bÞ-,

ù.

€

:n

?

$rs"FH¥

—²T—³´

/ ,

ù.



¸

7

%o

$bâ1F

ä‰å

B¹ºVî

^è ñ Þ

:ý

ãÝ?ö/VïÞ

? %

äVå»*¼½¾

¿À

î

^1Þ

w

œF

@A­®¯

ã]÷^‡-~bހ ~

bހ

Áå

³ÞÂÃÄV÷ Þ*^"¥

—²—

Ÿ

?

K$:45



ÝÅ

}

ÞÆ‘Ç-

¶ $ î o ã

Þ*^%

¥

—²—

 Ý

ý

ö=ã-È

wCÉ F¥

cʖ—aÌËÎÍ.*Ïc ã]

?-# # é Å } Þ }Ð

ÒÑ

/ d

^%1Ӊà"œF

@A

ÂÃ

d

!Ô

[1]

FÕÖ×O

ØÙ

[2]

Þ6_ã é Å }

ހ

"2

#

±*n

…

†

^% ‰

$bâF45

 / d

^8¥

—²T—



Ú

„ î

^"o Ý # é Å }

Þ"o / d ^ vu

à"^%

o è ñ ÞT¥

—²—

 | } '

Üiw FÛ

/Ü

Y 7 ¥

—²T—

Ú

„

BÝÞ

…†#

ï$%

‰

2 # F ‰

†w:

=݇Vï

7

2

Ñ

ã\ö÷8^o mB

/ïF ‰

† w Ý ‰

†8ß-†

‡~T:Þ

ý

€ã

Ä 7é

[3][4]

~*³Þ-,

ù.

€5ã*Ä 78é

[5][6][7][8]

?

ñ

ý ö

2

Ñ

à

ãà

h ^ é / d

^%

2 Ü 2

FÛ

/ ÝÞ

…†

$*¥

—²*—

Ú

„

=Ý

ý

öã]÷8^



á à

#8?

Þ ?

%CP1Q

‡1~*bÞ

ý

€‰ã:*Ä 7Câã

ø—ä 2

#

ÝF

É

F

@1A Ñ

Ü

ý

ã?ö

2 # F ‰

F

äHåæ*c

¥

—‘ç

ݏ*n 2 #

=>

‡4ïbÞ o M

¥

—²—

Ÿ 82

# Ú

„ î

^%

2 Ü 2

Fo

âã

ø-—ä /VÝ

:ý ö

ï :&*F6¥

—²—:³´

/

Rounding E

é

ect

B·

ï # 2

-?

F¥

—²—

Ýêë6›ìLí

# 2 ñ %

é‰ñHÒÑ

âã

ø—ä /VÝ¥

—²—-î1ïð

ñò

2

#î-ïðÜHw

,

ù.w 2 …

óô 2 # ¥

—²*—

Ú

„ î ^ ? ñ1é

/ d

^%

2 Ü 2 F

o âã

ø—ä /VÝ*¥

—²—³´

/,

ù.

B

‚„

/ï

É

ã,

ù.õ-öVÜHw

¥

—²*—

›Ú

„ î

^$â1FH¥

—²T—

ÂÃ

B

Ɇ#

2 ñ %

o

† wC-÷ø óù

î

^-$â:ãF

SRED

ún

?

$8¥

—²L—

Ú

„

[9]

BÝÞ

…†8#?

^%8o

†

ÝF

ý

€ ,

ù-.

€›ûës8!-Ôü^8o ã˜è

ê

F¥

—²T—

Ú

„ î ^ T/

d

^%-N

OãÝF

ò @ Ð /,

ù.

"2

#8ý˜Üiw 2 …

þVáTÿã

Ñ

?-#

â^8o ãVè

ê

FH¥

—²T—

Ú

„

Œ Ë t ò'

ÿ ¯ TK

#"?

^ T/

d

^%6o

ã˜è ê F

:ý

ö=ãVè^

bý

y

z ¯ @ Ð ã!

†É ãF

$F,

ù-.1



ã

é ‘2

$*¥

—²L—

Ú „ B

…†

^%

2 Ü

2

F6o

=ã:݇4ï

7

2

Ñ

ø B

…†"#*?

^%

1

Ñ Ç 82

#

F",

ù-.1

áTÿãVè ê ¥ —

²*—1‚„

Œ

B

ÞK

# 2 ñ o F

2

Ñ Ç 2

#

F8¥

cGú¦WUSú §?

 ¥

—²—

Ý:Ú

„

/ïÞ

? o / d

^%

ïH.a:ð

@A

ã]:÷8^{Ý

.—

ìí

# 2

? F{

áLÿ:ã

èK

#*.—1

Œs

? B

=>

î

^%

2 Ü 2

F¥

—²*—

Ú

„1 è ñ

Þ45



ë

Ñ

÷^F

.

—1Vû ÈVÝ

»

/VïbÞ

? é Bd

^%

¬ /Ýo

è ñ

Þ ! #"

à # F Œ Ë t

ò'+Å

» 2

$¥

—²*—

Ú

„:

+ Vî

^

$bâ:ã

SRED

n ? $¥ —²*— Ú „ ÷ø



ã$

ê7

ë1F5è êÎt

ò 2

$"¥

—²—

Ú

„

Ýޘî

^%

î&%

!*xF

.1—:µ¶

('&) 2 #

F,

ù.*

ÿ

,+-

…

ÔF

$F,

ù

.1./

@A

0

Œ1ã˜è^324

ý

t

ò'ã˜è^24=ã:=65"^"o /-FH¥

c…úvW1Uìú

=ã]

é ‘2

$¥ Ú

/ #8

7 %

(14)

1

ª «¬

3

¬98

©

2

ª /:F;=<*

% ¥

—²*—

Ú

„:

‰ã

Ñ

?-#>?

î

^%

©

3

ª /:F

SRED

n

?

$"¥

—²—

Ú

„

=ã

Ñ

?#@BA

î

^%

©

4

ª

/:F

SRED

n

?

$"¥

—²—

Ú

„:

÷

ø  ã 2 #

WI-SRED

:ýCD

Œ:n

?#EF

L^8¥

—²—

Ú

„

ÝÞ4î

^%

©

5

ª

/G:F

@AH

p

ã]

?#-0I %

÷ø "2

#

D6E

wú†

^J

‡‰ï

… ã Ñ

?#

') 2 #

FKJ

‡Vï

…

ã˜è^

„LM¶N.

'O+-

î

^"¥

—²T—

Ú

„

=ã

Ñ

?-#8 ')

Ë

âã

ø-—ä

ã

Ñ

?#P9Q

^%KR

ã ©

6

ª

/ST

L

âT(U î %

(15)

4

V

2

W X Y Z [

2.1

\^]

@A

:_‡

%

ï*—a

K

#?

^%

/

F8¥

cʖ—8aË Í.8Ïc ã]

?#

_8‡

%

ï—a

þ

# H p

` Mî

^o :/ï

%

? /-FP

H p "2

# ‰

"Áa+w 45*

%6

o M

‚„

2

# H p Ob

ñ o CB

YH?

%m45*

%H

o M

;<

%:é

2

#

:,

ù.

(

cd

)

û

FL¥

—²*—

F

BDE

w †

^%,

ù.

:

2

1>

è ñ ã

`

3 ð , ù‰úÒ

ë-/

%H7

F ‰

e

k

}Ð émº

^o

B

/ï^%o

H p :F3f

L

@A

{

@

ã:=g

2 $ ë

%î

o

CB

/ï^% ‰ 2 # Fo

{ @ ã

=g 2 # é

F3h9i

d

^C€+

d êkj

! % ? % ‰ † él

!

wÉ

FC€R6:m-*/ï^-$âF¥

cʖ—8a

ã K # { @ :n

?1û

î

?ïL—"a / d

^%

2 $ B K # ,

ù.

::Ú

„

[10][11][12][13]

:P H p

82

# Å }

%H

p

2

#

DE

^o :B

/ï8^%L¥

—²T—

:-,

ù.

€#os

2 # ] ê F

@AH

p

ã]

?#

Å } %

€

Ýp4î

^% ‰ 2 # FH¥

—²—

ݏ*n

î

^o ãVè

ê

FNOL

%

@A

óô Bq

¾

%

^%-Ó65"œF

@A

Á1ý

ö"F×O

‚6„

Fr

Z"[s[

%

_(tnuBv:w

?

vu

5*^%

…Twxy*?

o x

F-€Rz:-,|{

. Ú

„

,}

Q#…Twx

m-T/9~^B5FKh

i d

^€+

d

|€

j ! % ?

%6o

$=1FH¥

—²T—

Ú

„‚

P H p 82

#

:Å } %H

p

2

#

DHE

^8o B

/G~8^%

,9{

. ¥

—²—1ƒ0„

45 "2

#A

^ … B IJ

x

=>B…"^CrL/

d

^o

CBD6E

wú†

^%

A ^ … IJ

x

=z5^

‚=„Gx

:F=†‡

„

=>"F×O<

®

„ˆ‰&Šz„

=>F×O‹

£6xŒ

^:=>F



õxŒ

^:=>

%

_vÜ

Y 7 „ }Ð

B

'B5

wݠ

^%

2 a 2

F¥

—²*—

/:o

†iwŽ„

}Ð

„=

4

x9‘

…

?’

o † :¥

—²*—=„

ÂÃ

x ]

?“”

Ü „ ,•{

. B 0 

/–—LK

“?

^K˜K

x

F™6š

}Ð

B

”›|xœOž•Ÿ

2md

K

“"?

^˜=/

d ^ ’ ‰ „

˜&L¥

—²—Bœ

Ú „

…*^"o :-,6{

.

œ Ú „

…L^"o 

Œ¡€‚¢£

/ d ^ ’ 2 a 2 FH¥

—²T—

45

„ | } ' aiw

FÛ¥¤/Ü

Y 7 „ ¥ —

²—

Ú

„¦§

BÝÞ

…m†“

~˜

’

oo/:FÛ|¤/

ÝÞ

…†“

~˜*¥

—²*—

Ú

„¦§|x

Ñ

?K“

¨©

…*^

’

2.2

ª¬«®­¯«±° ²´³¶µ

/

¤/

ÝÞ

…†G“?

^"¥

—²T—

Ú

„¦§6„

âãG·

—ä :"¥

—²—6w

2

…=„

ò¸

x¹ Ä~‡

~

7º›Ñ

„¦§

F&…

%

—*xF»¼€½

x¹ Ä¥¾

¦§

F&¿z{À:€½

x¹ ÄÁ¾

¦&§

F ‰

„Âz„¦§

F

xÃz

^"o• 

BÄ

~8^

’

(1)

Å9ÆÇ9È|ÉÊzËÍÌÏÎÐ

(16)

2

ª ÑÒ

ST

5 - Deriche-Faugeras[3]

(2)

Ó6ÔÕÇGÈÁÉOÊ|ËÖÌ×ÎKÐ

- Kitchen-Rosenfeld[5], Chen[6]

- Beaudet[7]

- Harris[8]

(2)

ØÙÚ¡Ù=ÎÐ

- Smith-Brady[14]

-

ÛÜ

[9]

»¼Ý½|Þßáàâ˜

¦§

Ä9ãäåæçè

œOé9êëì

»¼|Þ

Ãí âîï

äð|ñòzóôõáöŽ÷(ø

ù

âOú

ôõû9õ

Ú|üýþÿ Ä

þ9¿

÷#ø ù

âîÿ

Ä9ãôõûzõ

ë

â

÷

ýþÞ

ôõûBõz÷

ÚzüKý•þ3ÿ!

þ#"î

ä

%$

Žì

ôKõû9õ

Ú¡ü

ì&

ò('

ã%)

Þ

ä+*,

Ý-.

/OÝ-

ì10 Ý-

÷3241567

î

SRED

÷ ù8

î

ôõû9õ

Ú|ü%9

ä

:;<=

Þþ

<>÷3?@

GâBA

8

SUSAN

CEDGF

õ &

÷H ù

âî

ôõû9õ

Ú|üI

þ

ìKJ

ãä|ôKõû9õ

Ú¡üÿ

÷MLN

ì

3

ê

ä/*,

Ý-|Þ%O!PRQ1S

'ETõðä

OÝ-¡Þ

OPGQUS

'(TKõð

Þ%VW â3úXGY

ì S

'(TKõðäZ

ìK[•ì

S

'ETõð

ì1\]

Þ ê 8 ú N^

ì ÿ

ìéBêë

÷3_`

Þ%abáâú

ä J

2.2.4

ÞE"E1cúdeBý•þK

2.2.1 (1)

fghGikj/lnmpoBqr

ås!t

Þ

ä*,

Ý-zÞ1OP.Q ÿ

ã

"u

÷

Úzü|âîï ä(vxw

î

*,Í÷yz

ý9þ%

ê

"

ä

éBêë&ì

*,

Þ

ç&èÍ÷

V í âOú

äEZ

ì ï ä

Ú|ü|âî

KÞ{ âúE|%}

ì ~!

AK€

÷

ôõû9õ

Gâ3úÚ¡üý•þ

ì‚

ås!t

þK

*,

Ý-¡ÞOP

8

îÿ

[3][4]

ã

ézêë%ƒ„

%$

ú 8 þ ‚

% ã%*,

Ý-|ÞO(P

8



t

Aÿ

숇kê þ

Deriche

[3]

ì

ôKõû9õ

Ú|ü

ÿzÞ

ê 8 ú _`

Þ%‰Šzþ

Deriche

ãä

"Ku ä

:Úzü

÷3‹

8

äZ

ì ï

÷MŒ

âŽú vxw

î

*,

ì

÷

Ú|ü

ýþ11$GÞ!

ä

K%Ž/

N

ސ‘•ýþ

ôõû•õ9÷#ç蒓

땔

+%–(

‚  þ1

Z

ì ï ä vw

$Gî

% N ì

ç—

Þ+{âOú

K

ì˜(™

ä ê

"

äUš›`œ(žGŸ |÷M¡

c

ä/Z

ì

|}

÷¢£

â3ú

ä

|}

ì ~

8

€

÷ôKõû9õ

âúÚ|üKý•þ1|1}

ì~

8

€

÷U¡

cGþ

˜

ãä

x

¤¥

y

¤¥

Þ%{ â3ú

I(x

¦

y)

ìK§¨

V ÷ ù8

ú

š›`œ!ž©Ÿª¥÷«E¬

ý9þE+

‹G­

î%

2.2.2 (2)

®°¯±h.i²j/lnmpoUq#r

Ý-zÞ1OP.Q ÿ

ãäKçèN

³

š|ôõûzõ9÷

Ú¡üýþS

'(Tõð

þ ´µ!

ãä

S

'TKõð

%A

­ ú 8

þ1 ås(t

ÞE S

'ETõð ãäZ

$¸$

ôKõûBõ

(17)

2

º »¼½¾

6

ëG Þ

ê 8 ú ì

Í÷M‹ 8 ôKõû9õ

â

÷M¿À

âOú

ôKõû9õz÷U¡

cþ LÁ

ã

Ý-zÞ1OP.Q ÿ

ì#Â%ÃÄ QÆÅ

$Bî

3

êì

ÿ

÷M_`

Þ1ÇÈýþK

Kitchen

Rosenfeld

ã9ôKõû9õ

â

÷ÊÉ

 t A1Ë

æÌÍ

BÎ

N

ÞÏÐþUË

æ

옙

ÑÒÓ

ìÔ †

7

þ(âî

ôKõûzõÕ

ü ã Ë æÌÍ

ì ~!

÷Oø ù

âî%Ö×

~Ø

EÙ

ÿ

÷MH

Â

Þ(#

ä|ôKõûBõ

ì/ÚÛ]

1A9þ

Ø

Þ1{ âúE|}

÷MÜ

Ð

5(67

ú

äÉ

 t Þ1×

~

A9þ

Ø

÷+Ý

ê

ÐüýÞ

ä•ôKõû9õ

ì Õ ü

÷‹

Â

"î

ä•ôKõûzõ

â%#Þ

kitchen

ã%ßà

ì Â Þ

¿À

â3ú

8

þ1

Þ

kitchen

á

I xx I 2 y

â

2I xy I x I y

ã

I yy I 2 x

I 2 x

ã

I y 2 (2.1)

Beaudet

ãGôõûzõ

â%

÷

Gauss

|1} †äáâú

äçè

†å|ÞÏÐ&þ

2

ß ì

Taylors’s

æ!ç

÷Mè

à 8

úé%ê¡Þ%ë

§ A

DET

C(DGF

õ & ÷

ƒ„

âî

DET

á

I xx I yy

â

I 2 xy (2.2)

ôõûBõ%Õ

üÞ ã

ìCED°F

õ

&ì

×ì

DET

ìí

{ì¡ÞKþîìïð|Þ(#

‹  ä

2

ß(ñ

»òBì X Ø

ÞÏÐþ |

‚

ªó 5¥÷

†9ý%ô

æ

âŽú

ä

|1}

÷

†äzýþî/c

ì»%òzì

2

ß ¨ V ä

ê

"

ä

Hessian

‹õ

‚ þ

Hessian

‹õzã

ýA 6 Ã

ä ö

2.1

ì

 Þ

çèÖ÷3¹

1

ßñä1¹

2

ß

ñä

Ë æ

ì ~!

÷M¹

3

ß(ñ

Þýþ

ôõûzõ1÷

´(

ì

|%å

‚Køù

Þ

ÑÒ

ý•þ

\ú

÷Oø

ù

âî

I ì

H

á

I xx I xy I xy I yy

(2.3)

%†1$9þ1

Hessian

‹/õ

ì

‹õàüû

H

û ã

|+å

ì X Ø

ÞÏÐ&þ|}

÷

†9ýI

ì

âOú ù(8

$9þK

"î

ä

|%å

ì X Ø

ÞÏÐþ1ý

~

|1}þýÿ#|%}

ìÔ Gâú

¿À

K$9þ|1}

ã

á û

H

û

(1

ã

I 2 x

ã

I y 2 ) 2 (2.4)

¢£

K$9þ1

ì

=ì

ߝàOýŠ



ãä

V

ã

þKîc|}þ

DET

ãå

ì

÷Mè

ê

(ÞAþ1

þ‰ŠGú

8

þ

Harris

ã

æ(ç

(analytic expansion)

÷ ‹x­

ú

Plessey

ôõû9õÕ

ü

÷

ƒ„

âî%

ž

ò Gã

W

á

(n

n)

â3ú

ä

"u

§¨

V¡Þ#

I x , I y

÷¡

c

ä(Z

ì ï ä

I 2 x , I y 2 , I xy

÷

XGY

¡

c9þK

Þ ä

I 2 x , I y 2 , I xy

Þ

Gauss

»ò

÷MÜ

Ð

5E67

ú

I ˆ 2 x

á

I 2 x Gauss I ˆ 2 y

á

I y 2 Gauss I y ˆ I x

á

(I x ˙I y ) Gauss (2.5)

;4

ê&ì

<=

ì

ˆ I 2 x , ˆ I 2 y , ˆ I y I x

÷B¡

c

ä ‹õ

A

ì

ì

1

2

÷«¬

â

ä

Þ

~

Aì

÷

þ



÷Kôõû9õ

Ø

Gâî

A

á

I ˆ 2 x I y ˆ I x

I y ˆ I x I ˆ y 2 (2.6)

(18)

2

º »¼½¾

7

0 2 4 6 8 10 12 14 16 18 20

2 0 6 4 10 8 14 12 18 16 20 0

50 100 150 200 250 300

ö

2.1:

ôõûzõz÷"!

–#

çè

(

$

)

äçèÍ÷M¹

1

¹

2

ì

ß(ñ

âú äçè

ì

ȕþ

÷¹

3

ßEñ

GâOú%

“t

Þ Ý î&

5 ì

ôõûBõ

Ø

(

'

)

()

Þ ã

Plessey

ì

ôKõû9õ%Õ

üÿ

ãôKõûBõ

â

ì*

}þâŽú

C p

÷

C p

á

T raceC DetC

á

I ˆ 2 x

ã

I ˆ 2 y I ˆ 2 x I ˆ 2 x

â

I y ˆ I x

á

1

ã

2

1

2

(2.7)

«¬

â ä

C p

‚

ÿG 8

&ì

4GôõûBõ

Ø

Gâ3ú

Õ

ü|â3ú

8

þ

2.2.3 (3)

+-, ./,!q#r

K

ãôõû•õ9÷3Õ

üýGþ )ä

K#Ý-.

*,

Ý-

ì10 Ý-

÷"0 ù

âîÿ9

ä

"î ä ¶

Þ

ôõûzõ

â

÷

|}! †ä9ý9þÿ.

ã%’

Q21A9þ3ÿ¡Þ

ê 8 ú _`

Þ%abzýþ

Smith

ã&ôõû9õ

â%Þ{ÖâOú|}

ì

a3

÷54

56

8

î7Öâ

8 /|÷

d „ â,ú

ä

SUSAN

CDGF õ & ÷

ƒ„

âî%

SUSAN

CDGF

õ &

ã+:;<=

Þþ

<>Ò

‚ ë @ Aî/c

ä%Õ

ü

œ 8

‚

u$EA 8

SUSAN

CED°F

õ &

ã9:

;

žG÷<0

ù â ä-=>

ì

ç—

ì Ë æ Ê´

8 Ë æ÷

I ê

ž?@

ì

ç—

ìò

N(r 0 )

÷÷

òBA þ

N(r 0 )

á

r

C

M

D

1

âFE

(

ûû

I(r)

â

I(r 0 )

ûû â

t)

G

(2.8)

r

ã

Øz줥

ä

r 0

ã

ž ì

=>

줥

ä

M

ã

ž

ìIHKJ

I

ã-LžT3çè

ì &

5|ã Z

ìIM

N ì

ä OPõç&è

ì &

5zã

R, G, B

ì

XRY

ì ì

÷%(ž©Ÿ

Þ/A

Š9îI

ì ä

t

ã

î%ì

þK

L

ò

ÞKþË æ ì

ÑÒ

‚

t

# ÿÐ/$KQ

äR S

ÞT U ã A 8

îc

<>Ò

ì

?@

]!‚

A 8 =

> ‚

ô=õûBõ

ÞVzî

 Þ ä

N

‚

I ­

IÿQMAþ1 Z

ëR

ã

u$9þ(

N

ì

ì

ãW:

ýþ1

ê

"#

ä

N

ì

×ÿì

ìIX Y Þ

ôõû9õz÷MÕ

üý•þÍâ

ë â

ä(çè

Þ

ãLò

‚Z Q ! –

(19)

2

º »¼½¾

8

a b

c

d e

Resion1

ö

2.2: SUSAN

CDGF

õ &

I[

ž ì

=>

‚ K

N Þ

$;Q

ä ž ì

=>

w

Ë æ ì ÷ I

ê

ç—

ìò‚

;

ž å

Ô!‚

1

\

2(b)

ä

ëR2]

$ú

‹

QÊå

Ô

ãW:

ý9þ

(c)(d)(e).

"Kî ôKõ

ûzõ^

ž ì

=>

‚

î

 ã

ž å

Ô6ì

1

\

2

_ `

^

Aþ

îc

ä

a õ

ób÷‹G­

î ä

N

÷B¡

cú

ôõû9õB÷MÕ

üKý•þ1

ö

??

c

SUSAN

CD°F

õ

&=ì

0 ùd ÷<egf

îI

ì

þ

ö

??

^ Ï 8 ú 9h:

ž ì

=>

‚

(a)

c

ôKõûBõ

ì

œ 8

;

Axji

(b)

c

N ; A ­

îI

ì

þ

SUSAN

CED°F

õ

&c

=>

w

Ë k

ìl

—

ò ÷ òA

þ ì ö

??

^ Ï 8

ú

ž ì å Ô ^ { f ú

(a)

c

1

\

4

i

(b)

c

1

\

2

%Aþ

mn

c X l

—o^

Ï 8 ú ’ ú

ì/˜™

ìpBqG f

÷¡

ci Z ì

ïi

ì/˜™

÷

¡

cKú

r

ì

Aýsk

÷ôõûzõ

f

¿Àgf

î%X

˜™ ì

ìK\ú

÷

f (x

¦

y

¦ut

)

á

1 k

k

r

v

0

I(x

ã

r cos

t ¦

y

ã

r sin

t

) (2.9)

¡

cGþ%(%

I(u

¦

v)

cl

—

P(u

¦

v)

^

ÏÐþÈ9þ

þ1 Zwf

úi

/

ìpq f c

g(x

¦

y

¦utyx

)

á

max

z

û

f (x

¦

y

¦ut

)

â

f (x

¦

y

¦ut ã"{

)

û

(2.10)

| ¡

c[}~o}i€o‚ƒ

˜™c

f

q…„

h(x

¦

y

¦†t

)

á

R

n

v

0

f (x

¦

y

¦

theta

ã

n)

â

R

n

v

0

f (x

¦

y

¦ut â

n) (2.11)

|

«¬gf

}~‡‡|

R(0

ˆ

R

‰ {

)

cŠ[‹BŒ Ž 

|[ ‘~;’

f“

i”•;}€‚r–ƒ —–˜sk

™

{<š›

|–‘skœ<žŸ[ƒ–| B¡i’ ƒ¢£œ¤¥¦¥¢§

f¨“©oª

˜K‘I~‡ ‡|

c

”K•

„

 ‘€-‚ƒ«B¬

c

€‚ƒ

pq…„ f­™

€o‚IƒI® ¯[ 

™°£±"²

˜;³¤¥¦B¥´µ

^¶

³ “

·¸

kƒ¹K‘

­ºK»

„<¼

º

”K• ‘[‡K§

™

|;½[‘}–•i¾¿

fh“

¤¥¦B¥œ

©oª

|½–‘~

2.2.4

À Á…ÂÃÁÅÄoÆoÇÅÈÉwÊËoÌ[Í

¤¥¦¥

©ªº ¶

³

“ÎÏ Ð

—K‡K§Ñ ¤¥¦¥

„Ò

­

œ[Ӄ

»Ôº

¿ Õ

Ò Î

¤¥¦¥ƒÖ×

œ<ØwœFÙwÚ

“

Ӄ

»;Ôº “©ª

˜K‘Û| ‘~

(20)

2

Ý Þßà á

9

âã

Ö × ºäBå

³ } ¤¥¦¥

©-ªæ ç

|;р‚;œ

©ª

Ò

“Î

’[ƒIè

ÎéêBë

—Ö × ºìäBå

½€‚œ

ßígÒ

“ îo±ïâ ãðñ

œ

°ò

˜K‘ó’

Ò

“Î

’ ô

âã ðñ õº

¤¥¦¥

™ö–÷

˜

‘§ùø¿

Ò

Îâã ð ñõú ûü

ôýþ

ú · Ú “

¤¥¦B¥oÿ

Ò ­

œ<¿ ÕB˜[‘óŸ

Î

¤¥I¦B¥

ÿ Ò ­ Ñ

â ãðñ

ô

ûüBú

¿ Õ

­

 ‘ó

Ò Û Ò Î

ô ¥ ú Ñ

â ãð ñ

œ

©Ãªº

»

©Ãª

˜[‘

§ º[»

Îéêë ºìâã

ϯ

ë ë º

‘

§Ñ

º

— ‘

™Î

ô

ºÎÏ Ð

—ô[Ѥ¥¦B¥œ!

ò

˜K‘

âãð ñ™

Óô

»Ôº©oª ­

  “

;œ

ßí/Ò

“

³ ‘

Û ú

 ‘óo¤¥¦¥´µ

ú

Ñ#"$Ãô%

™'&)(+*-,

Ú “

³–‘

ï

•'".

º

—BÚ

“ ¶

Î Ò ¡ Ò

¡ Î /

™

®¯K ‘

ï

•'0 þKô1³ 2œ

©oªú

½—;³ó’ 

º43

Ò

“Î25-6ºî…±ìïâ

ã ðñ

œ

°ò

Ò “ ·

¤¥¦¥´µô27¥-8Ñ

©ª­

  ï

2œ

äoºéêë

—7¥-8K§

Ò

“'9

,

 B‘

ï • Î

¤¥¦¥´ µ

ú

Ñ40 þô

» ³

âã ðñ

œh”K•‘

§

™ ú

½ ¼ Î :<;

œ>=?‘

§

· Ò ¡ Ò

¡–;‘ó ’[ô ï •

Î @A

—K¤¥¦¥ô'B C

ú ™©oª­

  ¼ Î ¼   ï B-C

ú

¤¥

¦¥

™©oª­

  “ Ò Ô

í D

œ2FE

( ó ô

§ìÛwÿ

Îâã ð ñ-ºäå

³ ï

¤¥¦B¥

©-ªìæç

Ñ

ê GBë

Ö ×

™'5-Hw­

  “ Ò

³

Î éêë

Ö × º-I',

 ‘ §

™ JKBú

 ‘ § ™

³%L;‘ MN

Ô ó Ò Û Ò

Ωoª;­

  ï

/ ;œ

éêë

—Ö×§

Ò

“-

—–˜

§IÑPOQ[ô HRS

º T

‘VU Ÿ

ô'W XYÃô2Z

ú

 ‘

§ÑP[L —;³ó

2Ö × ºäå

³ ï

¤¥¦¥

©oªæç

ô ¥ ú Ñ

Îâã

Ö×Ãô äå

³ ï

¤¥¦K¥

©

ª

ô¥£§\o—]

Î2^-_;õ

ô

êG-ë

—Ö×oô

;[ú` a

¤¥¦¥-œ>b;¿˜‘ó;’ô ï • Î

éêBë

Ö×

ºI,

  ¼ ºc-“

ô

^-d-º3

Ò “

¤¥¦¥…ÿ

Ò ­

œh”K•B‘

§

™ú

½‘ó

Kitchen- Rosenfeld

ô

æçú¶

³ “ Ñ ¸

þ e-fKô

é ½ ­ § ¸

þKô4g-h ºPiwÔ

«B¬ôg h YÃô4j

ú

¤¥¦¥

ÿ Ò ­

œ<¿ Õ

Ò “

³[‘ó

Ò Û Ò Î

¤¥¦¥

º

µ³k Gml

Ó Î ¸

þKô'gh-Y

™no

˜[‘4p-¬

™ 

‘ ï • Î ¸

þô4g-hÃô

é

½³k

G

ôFq%rœ

Ô'sìÎ

¤¥¦B¥´ µ

ú

ô Ñ :<;

œ>=?

“ Ò

³ Î

¤¥¦¥ÿ

Ò ­

ôýþoÑ

@ A

—B¤¥¦B¥–ô4B-C

úê Gë;ºt éº

—‘

§IÑ

o

—;³ó

íD

ë ºÎ

¼   ï B%C

ú

¤¥¦¥

™©ª ­

  “ Ò

ÔPJK

œ<žŸó

Beaudet

ô

æçº¶

³ “ Ñ Î

¤¥

¦¥-ÿ

Ò ­ œ

Gauss

ûü

§4uvôý þ£§

Ò

ï™Î

Gauss

ûìü

ô

t;é

¢

™'w

¼…Ò

·

¤¥¦¥–ôFB

C§Ñ'x y

Ò

—[³ó

ôIý þoÑ ¤¥¦¥ô

-ºzö

˜[‘

ï • Î

¤¥¦¥

™ g ,

 ;¡

©-ª[­

 

‘{B C

· g , ‘ JK™

[‘ó|

ïIÎ

Harris

ô

æçº¶

³ “ Ñ

Š‹Œ}P~

œ

x

«¬B§

y

«K¬ô4 €

 v º2‚ƒ

‹Þ

$£œ!„

s“



,…B“

³[‘ó

Ò Û Ò Î/

ô'†

΂ƒ

‹ Þ

$oÑP‡

ψ-‰ºK»

‘

ˆŠ

h§

Ò

“‹Œ-­

 ‘ ï •

΁-

ô é

½–³4k

G

ô'q r£œ{Ž

sìΏ-Bë º

¤¥¦¥K§Ñ4\×;‘PBC

ú‘4’

v

™é

½ (

—“

Δ

Ú ï B-C

ú

¤¥¦¥

™©oª;­

  “ Ò Ô ó

 Åÿìô'•–Û…ÿ

Î

/

Ö×

ºäå—(

¤¥¦K¥

©-ª

ô|¥'

º

ђ |˜ 

º43

Ò “ ô JFK

¢ ™

;‘

§

™

Û[‘ó

Ò Û Ò Î

 Åÿ¨ô JK

¢ º

љš ¢

™

“

Îõ ›

ô

æ çú

Ñ

éêB뜝 ™'5

³ ï • º BC

¼  

™°w±

‘§>ž<L;‘ó˜–—

,ŸÎéêë

—Ö×

²â ã

ô

  

Z—oÓôÖ×£œ

‹Œ2…

¼

ºêGKë

—

<#Iô é ½

­¨²

¬½ôÖ×;ô

;ú

¤¥I¦ ¥Kœ¢¡ £˜[‘

ï •

ÎhéêKë ºP^ _

œ

ï

† º

¤I¥¦¥

ô'B C

™ ¼

 ‘Ió

Ò Û Ò Î

¤¥¦B¥´ µ ú ô

ê Gë

— hÖ ×Ѥ¥¦¥

©-ª º¶

³ “

¤¥

¦¥ôFB-C£œ¢b¿˜K‘4†

º ¤

§ì˜

§ô

ú

½—;³Ö ×

ú

;‘ó

SUSAN

¥¦—§

¥8ÑP‡

Ï-ˆ ‰-ºK»

‘

ˆŠ

h

™¨Ð

— ï

•4B-C

™ ¼

 —[³1³

©ª4©ú

 ‘Ió

^-_õ

ô

^-d

œ

â ã

}4~

ô

^-d;Î

'ª«

õ-^d Î

¤¥¦¥œ!

ò

˜[‘

^d

§

3

¬

8¥|­

º

参照

関連したドキュメント

Causation and effectuation processes: A validation study , Journal of Business Venturing, 26, pp.375-390. [4] McKelvie, Alexander &amp; Chandler, Gaylen &amp; Detienne, Dawn

Previous studies have reported phase separation of phospholipid membranes containing charged lipids by the addition of metal ions and phase separation induced by osmotic application

It is separated into several subsections, including introduction, research and development, open innovation, international R&amp;D management, cross-cultural collaboration,

UBICOMM2008 BEST PAPER AWARD 丹   康 雄 情報科学研究科 教 授 平成20年11月. マルチメディア・仮想環境基礎研究会MVE賞

To investigate the synthesizability, we have performed electronic structure simulations based on density functional theory (DFT) and phonon simulations combined with DFT for the

During the implementation stage, we explored appropriate creative pedagogy in foreign language classrooms We conducted practical lectures using the creative teaching method

講演 1 「多様性の尊重とわたしたちにできること:LGBTQ+と無意識の 偏見」 (北陸先端科学技術大学院大学グローバルコミュニケーションセンター 講師 元山

Come with considering two features of collaboration, unstructured collaboration (information collaboration) and structured collaboration (process collaboration); we