画像検索 (特定物体認識) — 古典手法、マッチング、深層学習、Kaggle

ը૾ݕࡧ ಛఆ෺ମೝࣝ

ݹయख๏ɺϚονϯάɺਂ૚ֶशɺ,BHHMF
େࡕେֶେֶӃ৘ใՊֶݚڀՊϏοάσʔλղੳ ήετ࿮ߨٛ

খቌߞฏ !TNMZ

גࣜձࣾϦΫϧʔτςΫϊϩδʔζ "5-

1/125

View Slide

ࣗݾ঺հ
ϦΫϧʔτςΫϊϩδʔζͷϥϘͰ%"3ͷݚڀ։ൃΛ͍ͯ͠·͢ɻ
ݚڀ։ൃ΍ٕज़ΞυόΠβʔͷձࣾΛܦӦ͍ͯ͠·͢ɻ
⾣ ,BHHMFྺ೥ (SBOENBTUFS )JHIFTUSBOLUI $VSSFOUUI

⾣ ,BHHMF 5PQpOJTIFTY 1SJ[FY
˞ࠓ೥5PQ͸ճ ୯ಠճ

⾣ 5PQ$PEFS.BSBUIPO.BUDI 8*/4

⾣ "$.,%% ,%%$VQTUQSJ[FXJOOFS
2/125

View Slide

3FDSVJU5FDIOPMPHJFT"%7"/$&%5&$)/0-0(:-"#

View Slide

"HFOEB
ʹ͍ͭͯ঺հ͠·͢ɻ
⾣ 0WFSWJFX$MBTTJDBM"QQSPBDI

⾣ -PDBM%FTDSJQUPS
⾣ *OEFY4FBSDI
⾣ .BUDIJOH
⾣ %FFQ-FBSOJOH5SFOET

⾣ $//CBTFE-PDBM%FTDSJQUPS
⾣ $//CBTFE(MPCBM%FTDSJQUPS
⾣ $713`84PG-BSHFTDBMF-BOENBSL3FUSJFWBM$IBMMFOHF
4/125
全体的に基礎的な話題。 
後半に少しだけコンテストと 
発展的な話題。

View Slide


⾣ -PDBM%FTDSJQUPS
⾣ *OEFY4FBSDI
⾣ .BUDIJOH

"HFOEB
5/125

View Slide

ը૾ݕࡧʢಛఆ෺ମೝࣝʣ
⾣ ྨࣅը૾ݕࡧ
⾣ ͍ࣸͬͯΔ෺ମ͕ඞͣ͠΋ಉ͡zݻ༗ͷ෺ମzͰͳͯ͘΋ྑ͍
⾣ ಉ͡৭ௐɾಉ͡ܗঢ়ͳͲ
⾣ ಛఆ෺ମೝࣝ
⾣ ಉ͡lݻ༗ͷ෺ମzΛೝࣝ͢ΔλεΫ
⾣ ࣸਅ͔Β؍ޫ஋ͷ໊લΛಛఆ͢Δ
⾣ إΛೝࣝ͢Δ
6/125

View Slide

Ԡ༻ྫɿ(PPHMF*NBHF4FBSDI
Ξοϓϩʔυͨࣸ͠ਅ͔Β
ύϧςΦϯਆ఼ͱೝࣝɻ 
ؔ࿈৘ใΛදࣔ
$SFEJUIUUQTJNBHFTHPPHMFDPN
ͪ͜Β͸ྨࣅը૾
7/125

View Slide

Ԡ༻ྫɿ.FSDBSJ঎඼ը૾ݕࡧ
Ξοϓϩʔυͨࣸ͠ਅ͔Β 
طग़ͷಉҰ঎඼Λݕࡧɻ 
঎඼໊΍ΧςΰϦΛࣗಈೖྗ
$SFEJUIUUQTUFDINFSDBSJDPNFOUSZ
8/125

View Slide

ಛఆ෺ମೝࣝͷ೉͍͠ͱ͜Ζ
εέʔϧʜࡱӨ͞ΕͨಉҰͷ෺ମͷॖई͕ҟͳΔ৔߹͕͋Δ
▶ スケール

▶ 視点

▶ オクルージョン

▶ 照明

▶ 時間変化

▶ 阻害

9/125

View Slide

ࢹ఺ʜಉ͡෺ମͰ͋ͬͯ΋ࢹ఺ͷҧ͍ʹΑͬͯݟ͑ํ͕มԽ͢Δ
The Cube Houses in Rotterdam
▶ スケール

▶ 視点


▶ 照明

▶ 時間変化

▶ 阻害

10/125

View Slide

ΦΫϧʔδϣϯʜલํʹผͷ෺ମ͕ࣸΓࠐΜͰର৅ͱͳΔ෺ମ͕Ӆ
ΕΔ
▶ スケール

▶ 視点


▶ 照明

▶ 時間変化

▶ 阻害
11/125

View Slide

র໌ʜ໷ʹࡱӨ͞ΕͨɺனʹࡱӨ͞ΕͨɺேʹࡱӨ͞Εͨ
▶ スケール

▶ 視点


▶ 照明

▶ 時間変化

▶ 阻害
12/125

View Slide

࣌ؒมԽʜ࣌ؒతͳҧ͍ʹΑͬͯੜ͡Δࠩ
▶ スケール

▶ 視点


▶ 照明

▶ 時間変化

▶ 阻害
13/125

View Slide

્֐෺ʜं΍໦ͳͲಛఆ෺ମͷೝࣝʹؔ܎ͳ͍ීวతʹग़ݱ͢Δύ
λʔϯɻਖ਼͍͠ೝࣝΛ๦֐͠GBMTFQPTJUJWFΛ૿Ճͤ͞Δɻ
GBMTFQPTJUJWF
ෆਖ਼ղ͕ͩγεςϜ͕ਖ਼͍͠ͱޡճ౴͢Δࣄྫ
▶ スケール

▶ 視点


▶ 照明

▶ 時間変化

▶ 阻害
14/125

View Slide

ݹయతͳಛఆ෺ମೝࣝͷΞϓϩʔν
⾣
ը૾ू߹͔Βہॴಛ௃ -PDBMEFTDSJQUPS
Λநग़
⾣
ہॴಛ௃͔ΒݕࡧΠϯσοΫεΛ࡞੒
⾣
ΫΤϦը૾͔Βہॴಛ௃Λநग़ͯ͠ΠϯσοΫε͔ΒީิΛऔಘ
⾣
ہॴతͳಛ௃ͷ഑ஔʹزԿతͳ੔߹ੑ͕ͱΕ͍ͯΔ͜ͱΛ֬ೝ
DB DB
ը૾ू߹ ΫΤϦը૾
ݕࡧ 
ΠϯσοΫε
ఏࣔީิ
ݕࡧ 
ΠϯσοΫε

ہॴతͳಛ௃Λநग़ͯ͠ݕࡧΠϯσοΫεߏஙɻ<4JWJD -PXF +ÉHPV ʜ>
15/125

View Slide

⾣
Λநग़
⾣
⾣
⾣
DB DB
ݕࡧ 
ΠϯσοΫε
ఏࣔީิ
ݕࡧ 
ΠϯσοΫε

16/125

View Slide

-PDBM%FTDSJQUPSͷݕग़ͱهड़
ը૾͔Βہॴతͳؔ৺ྖҬͷ࠲ඪʢΩʔϙΠϯτʣΛݕग़͠ɺ 
ؔ৺ྖҬͷύλʔϯɾಛ௃Λهड़͢Δɻ
x0 = (72 9 73 57 79 4 38 11 69 57 . . . )
x1 = (21 15 42 3 99 97 64 16 97 88 . . . )
x2 = (11 87 80 12 30 15 92 91 28 1 . . . )
x3 = (38 77 67 98 43 2 9 16 17 32 . . . )
ݕग़͞Εͨؔ৺ྖҬɾ࠲ඪ ؔ৺ྖҬͷهड़
キーポイント Key point
記述・特徴量量 Descriptor
17/125

View Slide

Ԡ༻ྫɿը૾ͷ๓͍߹Θͤ *NBHF4UJUDIJOH

ࢹ఺Λগͣͭͣ͠Βͨ͠࿈ଓࣸਅ͔ΒɺύϊϥϚࣸਅΛ࡞੒͢Δɻ
$SFEJUIUUQBJTUBOGPSEFEVdTZZFVOHDWXFCUVUPSJBMIUNM
18/125

View Slide

Ԡ༻ྫɿίϯςφͷҠಈΛՄࢹԽ
ҟͳΔ࣌ؒʹࡱӨͨ͠ߤۭࣸਅΛ-PDBMEFTDSJQUPSΛ࢖ͬͯϚονϯ
άͯ͠ɺࣹӨม׵ߦྻΛٻΊΔɻॏͶ߹Θͤͯࠩ෼ΛՄࢹԽ͢Δɻ
$SFEJUIUUQTXXXLBHHMFDPNDESBQFSTBUFMMJUFJNBHFDISPOPMPHZEJTDVTTJPO 
%BUB%SBQFS4BUFMMJUF*NBHF$ISPOPMPHZIUUQTXXXLBHHMFDPNDESBQFSTBUFMMJUFJNBHFDISPOPMPHZEBUB
19/125

View Slide

ͲͷΑ͏ͳੑ࣭Λ͍࣋ͬͯΔ͜ͱ͕๬·͍͠ʁ
-PDBMEFTDSJQUPS͸ͲͷΑ͏ͳੑ࣭Λ͍࣋ͬͯΔ͜ͱ͕๬·͍͔͠ʁ 
ΧϝϥͷҐஔ΍޲͖ͷҧ͍ʹରͯ͠ؤ݈ͳੑ࣭͕๬·͍͠ɻ
⾣ εέʔϧෆม
⾣ ճసෆม
⾣ র໌มԽෆม
⾣ ΞϑΟϯม׵ෆม
20/125

View Slide

εέʔϧෆมTDBMFJOWBSJBODF
ہॴతͳؔ৺ྖҬαΠζʢεέʔϧʣʹରͯ͠ϩόετͳੑ࣭ɻ
⾣ ͦΕͧΕͷը૾ʹಠཱͯ͠ɺಉؔ͡৺ྖҬ͕ݕग़Ͱ͖Δඞཁ͕͋Δ
⾣ ղ૾౓΍ΧϝϥͷҐஔ͕ҟͳΔͱɺಉ͡෺ମΛࡱӨͯ͠΋ը૾಺ͷαΠ
ζ͸มԽ͢Δɻը૾ͷεέʔϧ͕มԽͯ͠΋ɺ%FTDSJQUPS͸มԽ͠ͳ͍
͜ͱ͕๬·͍͠
⾣ ʮہॴతͳؔ৺ྖҬͷαΠζʯΛࣗಈతʹܾఆ͍ͨ͠
QY
QY
21/125

View Slide

局所領域のスケールを⾃自動で検出する関数の例例。
スケールをパラメータとして変化させ、関数の極⼤大値を局所領域のスケールとする。
$SFEJU5JOOF5VZUFMBBSTWJBIUUQTBHTDTVOJLMEFpMFBENJOJOG@BHTEJQTT%*1@44@MFD@$PSOFST@#MPCTQEG 
22/125
scale
f(I, )

View Slide

scale
f(I, )
23/125

View Slide

scale
f(I, )
24/125

View Slide

scale
f(I, )
25/125

View Slide

scale
f(I, )
26/125

View Slide

scale
f(I, )
27/125

View Slide

scale
f(I, )
28/125

View Slide

正規化：固定⻑⾧長サイズに Rescale する
29/125

View Slide

ͲͷΑ͏ͳؔ਺GΛ༻͍Δ͔ʁ
εέʔϧෆมͳؔ਺͸࣍ͷੑ࣭͕͋Δͱ๬·͍͠ɿ
⾣ ࡱӨ৚݅ͷมԽʹରͯ͠ɺؔ਺͕҆ఆతͰ͋Δ
⾣ ୯ҰͷӶ͍ϐʔΫͷ͋ΔࢁͷܗΛͨؔ͠਺ ୯ๆੑ

⾣ ಉ͡ہॴྖҬͰಉ͡εέʔϧ͕ಘΒΕΔ
<4DINJE>Ͱ͸ݕग़ثͱͯ͠-BQMBDJBOPG(BVTTJBO -P(
ɺ͢ͳΘͪ
Ψ΢γΞϯͷϥϓϥγΞϯͷ৞ࠐΈॲཧ͕ྑ͍ͱධՁݚڀ͕͞Ε͍ͯΔɻ
$4DINJE 3.PIS BOE$#BVDLIBHF &WBMVBUJPOPG*OUFSFTU1PJOU%FUFDUPST
*OUFSOBUJPOBM+PVSOBMPG$PNQVUFS7JTJPO
QQ
30/125

View Slide

-BQMBDJBOPG(BVTTJBO -P(

Ψ΢γΞϯʹରͯ͠ϥϓϥε࡞༻ૉͰྠֲΛڧௐͨ͠΋ͷɻ
Ψ΢γΞϯ %

ೖྗʹରͯ͠৞ΈࠐΈԋࢉΛ༻͍Δɻ
Ψ΢γΞϯΛͰภඍ෼ͯ͠ɺ
֊ภඍ෼͢Δͱ
ʹରͯ͠΋ಉ༷ʹ֊ภඍ෼ͯ͠·ͱΊΔͱɺ
*ೖྗը૾ 
͸৞ΈࠐΈԋࢉ
ʢೋ֊ภඍ෼͢Δ͜ͱͰɺ໌҉ͷ͕ࠩɺࢁͱ୩ʹͳΔʣ
[G ]
LoG ⌘ [G (x, y)] =
@2
@x2
G (x, y) +
@2
@y2
G (x, y) =
x2 + y2 2 2
4
e (x2+y2)
2 2
G (x, y) =
1
p
2⇡ 2
e( x2+y2
2 2
)
導出
@
@x
G (x, y) =
@
@x
e (x2+y2)
2 2 =
x
2
e (x2+y2)2 2
@2
@2x
G (x, y) =
x2
4
e (x2+y2)
2 2
1
2
e (x2+y2)
2 2 =
x2 2
4
e (x2+y2)
2 2
x
y
[G (x, y) ⇤ I] = [ G (x, y)] ⇤ I = LoG ⇤ I
31/125

View Slide

-BQMBDJBOPG(BVTTJBO -P(
[G ]
*NBHF$SFEJU3VZF8BOHIUUQGPVSJFSFOHINDFEVFMFDUVSFTHSBEJFOUOPEFIUNM
LoG ⌘ [G (x, y)] =
x2 + y2 2 2
4
e (x2+y2)
2 2
32/125

View Slide

ิ଍ɿը૾ %σʔλ
ͷ৞ΈࠐΈԋࢉ
-P(͸৞ΈࠐΈԋࢉʢίϯϘϦϡʔγϣϯʣΛߦ͏͜ͱͰը૾શମʹ
ద༻͢Δɻؔ਺,Λ࠲ඪҠಈ͠ͳ͕Βؔ਺*ͱॏͶ଍͠߹ΘͤΔ̈ɻ
৞ΈࠐΈΛߦ͏ؔ਺, Y Z
ೖྗը૾* Y Z

ରԠ͢Δཁૉ͝ͱʹੵΛͱΓɺ 
݁ՌΛ଍͠߹ΘͤΔɻ
[G ]
͢΂ͯͷ஫໨ըૉ 
Y Z
Ͱܭࢉ
I22
I23
I24
I32
I33
I34
I42
I43
I44
K11
K12
K13
K21
K22
K23
K31
K32
K33
݁Ռ4 Y Z

৞ΈࠐΈԋࢉʢίϯϘϦϡʔγϣϯʣ

ʢ̈৞ΈࠐΈԋࢉ͸ɺ্Լࠨӈ͕qJQͨ͠ΧʔωϧͱͷॏͶ߹Θͤɻֶश͢Δ্Ͱ͸ͲͪΒ΋ҧ͍ͳ͍ͨΊɺ؆ུԽͷͨΊʹqJQ͠ͳ͍DSPTTDPSSFMBUJPOͰ࣮૷͞ΕΔ͜ͱ͕ଟ͍ʣ
S33 = I22K33 + I32K23 + I42K13 + . . .
S(x, y) = (I ⇤ K)(x, y) =
X
m
X
n
I(x m, y n)K(m, n)
33/125

View Slide

-P(ʹΑͬͯݕग़͞ΕΔ#MPC
-P(͸#MPC ਅԁͷൗ఺ʣʹ࠷େͷ൓ԠΛฦ͢ɻ
-P(ͷ൓Ԡ͕ۃେͱͳΔεέʔϧΛݻ༗εέʔϧDIBSBDUFSJTUJDTDBMF
ͱݺͿɻݻ༗εέʔϧͷ#MPCͷ൒ܘ͸ɺεέʔϧ܎਺͔Βٻ·Δɻ
2D→1D 断⾯面図 ϥϓϥγΞϯ͕θϩͱͳΔΑ͏ͳ 
Y Z࠲ඪ͕#MPCͷڥքઢͱͳΔɻ
G = 0 (1
x2 + y2
2 2
) = 0
= r/
p
2
ϐλΰϥεͷఆཧ͔Β
͔Β
*NBHF$SFEJU%JEJFS4USJDLFSIUUQTBHTDTVOJLMEFpMFBENJOJOG@BHTEJQTT%*1@44@MFD@$PSOFST@#MPCTQEG
34/125

View Slide

-P(Λ࢖ͬͨ#MPCͷݕग़खଓ͖
εέʔϧۭؒ಺ͷ#MPCݕग़Λ࣍ͷखଓ͖Ͱߦ͏ɻ
εέʔϧۭؒͷ࡞੒ 
༷ʑͳεέʔϧͰ-P(Λը૾ʹ৞ΈࠐΈॲཧͨ݁͠ՌΛ࡞੒
εέʔϧۭؒ಺ͷہॴ࠷େ஋Λݟ͚ͭΔ 
஫໨࠲ඪͷۙ๣ɺྡΓ߹ͬͨεέʔϧͷ-P(͔Β࠷େ஋Λ୳͢
஫໨࠲ඪͷۙ๣
஫໨࠲ඪ
✗
{
ྡΓ߹ͬͨεέʔϧͷ 
-P(΋ۙ๣ͱ͢Δ
35/125

View Slide

4UFQεέʔϧۭؒͷ࡞੒
LoG
LoG で畳み込み
36/125

View Slide

LoG
LoG で畳み込み
37/125

View Slide

LoG
LoG で畳み込み
38/125

View Slide

LoG
LoG で畳み込み
39/125

View Slide

LoG
LoG で畳み込み
40/125

View Slide

LoG
LoG で畳み込み
41/125

View Slide

= 1.00
42/125

View Slide

= 3.11
スケール係数を変えて LoG 適⽤用。
スケール空間を作る。
43/125

View Slide

= 7.33
44/125

View Slide

= 11.5
45/125

View Slide

= 15.7
46/125

View Slide

= 20.0
47/125

View Slide

Input image
= 1.00
= 20.0
= 15.7
= 3.11
= 7.33
= 11.5
48/125

View Slide

4UFQہॴ࠷େ஋Λݟ͚ͭΔ
Input image
Foot-print
近傍ピクセル、近傍スケールからピーク値を探す
= 1.00
= 20.0
= 15.7
= 3.11
= 7.33
= 11.5
49/125

View Slide

Input image
Foot-print
= 1.00
= 20.0
= 15.7
= 3.11
= 7.33
= 11.5
1FBL Y Z М
1FBL

50/125

View Slide

Input image
Foot-print
= 1.00
= 20.0
= 15.7
= 3.11
= 7.33
= 11.5
1FBL Y Z М
1FBL

51/125

View Slide

Input image
Foot-print
= 1.00
= 20.0
= 15.7
= 3.11
= 7.33
= 11.5
1FBL Y Z М
1FBL

52/125

View Slide

Input image
Foot-print
= 1.00
= 20.0
= 15.7
= 3.11
= 7.33
= 11.5
1FBL Y Z М
1FBL

54/125

View Slide

Input image
Foot-print
= 1.00
= 20.0
= 15.7
= 3.11
= 7.33
= 11.5
1FBL Y Z М
1FBL

55/125

View Slide

Input image
Foot-print
1FBL Y Z М
 
1FBL Y Z М
 
1FBL Y Z М
 
1FBL Y Z М
 
1FBL Y Z М
 
1FBL Y Z М
 
ʜ
しきい値以上の「座標、スケール」を選択
Results
= 1.00
= 20.0
= 15.7
= 3.11
= 7.33
= 11.5

View Slide

⾣ Y Z М
ͷϦετͷ͏͖͍ͪ͠஋Ҏ্ͷݕग़݁ՌΛऔΓग़͢ɻ
-P(ʹΑΔ#MPCͷݕग़݁Ռ
57/125

View Slide

<ԋश՝୊>-P(CMPCEFUFDUPSΛ࣮૷ͤΑ
-P(ʹΑΔ#MPCEFUFDUPSΛ࣮૷ͤΑɻ
⾣ TDJQZOEJNBHFpMUFSTHBVTTJBO@MBQMBDF
⾣ TDJQZOEJNBHFNBYJNVN@pMUFSͷ̎ͭΛ࢖͑͹؆ܿʹॻ͚Δ
58/125

View Slide

ͲͷΑ͏ͳہॴతͳؔ৺ྖҬɾϙΠϯτΛݕग़͢Δʁ
⾣ ΧϝϥͷҐஔ΍޲͖ͷҧ͍ʹରͯ͠ؤ݈ͳੑ࣭͕๬·͍͠
⾣ εέʔϧෆม
⾣ ճసෆม
59/125

View Slide

ճసෆมɿΦϦΤϯςʔγϣϯͷݕग़
ΦϦΤϯςʔγϣϯͷݕग़ɿྡ઀ϐΫηϧͷً౓มԽ͔Βɺ 
࠷΋ً౓มԽ͕େ͖͍޲͖ʢճసํ޲ʣΛௐ΂Δ
⾣ ΩʔϙΠϯτ͕ݕग़͞Εͨฏ׈Խը૾-ʹରͯ͠ɺޯ഑ڧ౓ʢً౓มԽͷେ͖
͞ʣͱޯ഑ํ޲Λࢉग़ɻʮޯ഑ڧ౓ˎΨ΢γΞϯॏΈʯͰޯ഑ํ޲ͷώετά
ϥϜΛٻΊɺϐʔΫ஋ΛΩʔϙΠϯτͷճసํ޲ͱ͢Δɻ
⾣ ΦϦΤϯςʔγϣϯͷ޲͖ʹਖ਼نԽΛߦ͏͜ͱͰճసʹෆมͳಛ௃ྔΛࢉग़͢
Δ͜ͱ͕Ͱ͖Δɻ
ฏ׈Խը૾
ΦϦΤϯςʔγϣϯ
✓(u, v) = tan 1

L(u, v + 1) L(u, v 1)
L(u + 1, v) L(u 1, v)
L(x, y, ) = G(x, y, ) ⇤ I(x, y)
60/125

View Slide

4*'5 -PDBMEFTDSJQUPS
<-PXF>
⾣ -P(ͷۙࣅͱͳΔ%P(ͱμ΢ϯαϯϓϦϯάΛซ༻ͨ͠Ξϓϩʔν
Ͱܭࢉޮ཰ԽΛߦ͍εέʔϧͱؔ৺ྖҬΛݕग़ɻ
⾣ ΦϦΤϯςʔγϣϯͷݕग़ͱྖҬΛϒϩοΫʹ෼ׂͯ͠ɺ֤ϒϩο
Ϋ͝ͱʹํ޲ͷޯ഑Λܭࢉ͢Δ͜ͱͰEJNͷ-PDBM
EFTDSJQUPSΛ࡞੒͢Δɻ
⾣ EJNΛ૯࿨ʹΑͬͯਖ਼نԽ͢Δ͜ͱͰɺর໌มԽʢେҬతͳ໌Δ
͞ͷมԽʣʹରͯ͠ؤ݈ͳੑ࣭ΛಘΔɻ

View Slide

ͲͷΑ͏ͳہॴతͳؔ৺ྖҬɾϙΠϯτΛݕग़͢Δʁ
⾣ ΧϝϥͷҐஔ΍޲͖ͷҧ͍ʹରͯ͠ؤ݈ͳੑ࣭͕๬·͍͠
⾣ εέʔϧෆม
⾣ ճసෆม
62/125

View Slide

ΞϑΟϯม׵ %

ϕΫτϧۭؒͰఆٛ͞ΕΔฏߦҠಈΛ൐͏ઢܗม׵ɻ
ઢܗม׵ʢ֦େॖখTDBMJOHɺႩஅTIFBSɺճసSPUBUJPOʣɺ 
ͱฏߦҠಈUSBOTMBUJPOͷ૊Έ߹ΘͤʹΑΔɻ
ม׵ޙͷ࠲ඪ ม׵લͷ࠲ඪ
ฏߦҠಈΛઢܗม׵Ͱදݱ͢Δ 
ͨΊʹ࣍ݩͷ࠲ඪΛಋೖ
ม׵ߦྻɿͦΕͧΕͷม׵ม׵ͷੵ
2
4
1 0 tx
0 1 ty
0 0 1
3
5
2
4
sx 0 0
0 sy 0
0 0 1
3
5
2
4
1 shx 0
shy 1 0
0 0 1
3
5
2
4
cos(q) sin(q) 0
sin(q) cos(q) 0
0 0 1
3
5
63/125

View Slide

4*'5͸ΞϑΟϯෆมͰ͸ͳ͍
4*'5͸ࣹӨมԽͨ͠ը૾ʹϩόετͰ͸ͳ͍ɻ
ΞϑΟϯྖҬΛݕग़ͯ͠ɺݕग़ͨ͠ΩʔϙΠϯτͷྖҬΛਅԁʹਖ਼ن
Խͯ͠ಛ௃Λهड़͢Δ͜ͱͰΞϑΟϯෆมͷੑ࣭ΛಘΔ͜ͱ͕Ͱ͖Δɻ
ݩը૾ʹͯΞϑΟϯྖҬ 
Λݕग़ͯ͠ਅԁʹਖ਼نԽ
ճస ಛ௃Λهड़
⾣ ,.JLPMBKD[ZLBOE$4DINJE  
l4DBMFBOE"⒏OFJOWBSJBOUJOUFSFTUQPJOUEFUFDUPSTz*O*+$7

⾣ 1FSEPDI .BOE$IVN 0BOE.BUBT + 
l&⒏DJFOU3FQSFTFOUBUJPOPG-PDBM(FPNFUSZGPS-BSHF4DBMF0CKFDU3FUSJFWBM*OQSPDPG$713`
⾣ 4PGUXBSFl)FTTJBO"⒏OFEFUFDUPSXJUI4*'5EFTDSJQUPSz 
IUUQDNQGFMLDWVUD[dQFSEPNDPEFJOEFYIUNM
64/125

View Slide

ͦͷଞͷ޻෉ɿ3PPU4*'5<"SBOEKFMPWJD>
3FMKB"SBOEKFMPWJ㶛"OESFX;JTTFSNBO  
z5ISFFUIJOHTFWFSZPOFTIPVMELOPXUPJNQSPWFPCKFDUSFUSJFWBMz $713`
⾣ ςΫενϟ෼ྨͳͲͰɺώετάϥϜͷهड़Λൺֱ͢ΔࡍʹϢʔΫϦουڑ཭
ΑΓРೋ৐ )FMMJOHFSͳͲͷڑ཭ؔ਺ͷ΄͏͕༏Ε͍ͯΔ͜ͱ͕஌ΒΕͯΔɻ
⾣ 4*'5ʹ୯७ͳม׵ΛՃ͑Δ͜ͱͰɺʮม׵ޙͷϢʔΫϦουڑ཭ʯ͕ 
ʮม׵લͷϔϦϯΨʔڑ཭ʯͱ౳Ձɻہॴಛ௃ͷϚονϯάਫ਼౓΋޲্͢Δɻ
xroot-sift =
q
xsift/
X
xsift
65/125

View Slide

ͦͷଞͷ޻෉ɿ)FTTJBO"⒏OF3PPU4*'5
࠷ۙͷը૾ݕࡧϕϯνϚʔΫͰ͸-PDBMGFBUVSFΛ༻͍ͨΞϓϩʔνͷ
405"ͱͯ͠ɺ)FTTJBO"⒏OF3PPU4*'5͕ൺֱର৅ͱͯ͠༻͍ΒΕͯ
͍Δ<3BEFOPWJ㶛C>
ΞϑΟϯม׵Ͱਖ਼نԽ্ͨ͠Ͱɺ4*'5ͱ3PPU4*'5Λൺֱɻ 
̎ը૾Ͱநग़ͨ͠-PDBMEFTDSJQUPSͷϚονϯάͷਫ਼౓Λ޲্͍ͤͯ͞Δɻ
$SFEJU3FMKB"SBOEKFMPWJ㶛IUUQTXXXSPCPUTPYBDVLdWHHQVCMJDBUJPOT"SBOEKFMPWJDQSFTFOUBUJPOQEG
66/125

View Slide

༨ஊɿ4*'5ΞϧΰϦζϜͷಛڐ
⾣ ΞϧΰϦζϜ͸ߟҊऀ%BWJE-PXFʹΑͬͯถࠃಛڐ641BUFOU
͕ग़ئ͞Ε͓ͯΓɺಛڐݖʹकΒΕ͍Δɻ
⾣ ೥݄ʹग़ئ͞Ε͍ͯΔͨΊɺಛڐݖͷଘଓظؒΛԆ௕͢Δਃ
੥ͳͲ͕ͳ͚Ε͹དྷ೥೥݄ʹࣦޮΛܴ͑Δɻ
⾣ Πϯλʔωοτ࿝ਓͱͯ͠͸ɺ-;8ѹॖ (*'ը૾Ͱ࢖ΘΕΔ

೥݄ࣦޮ ถࠃ͸೥
Ͱͷ੝Γ্͕ΓΛኲኵͱͤ͞Δ࿩ɻ
67/125

View Slide

ࢀߟࢿྉ
.*36νϡʔτϦΞϧɿ4*'5ͱͦΕҎ߱ͷΞϓϩʔν 
౻٢߂࿱ઌੜ 
IUUQTXXXTMJEFTIBSFOFUIJSPOPCVGVKJZPTIJNJSVTJGU
$4"ߨٛࢿྉ
-FDUVSF%FUFDUPSTBOE%FTDSJQUPST 
'FJ'FJ-Jઌੜ
IUUQWJTJPOTUBOGPSEFEVUFBDIJOHDTB@BVUVNOMFDUVSF 
MFDUVSF@EFUFDUPST@EFTDSJQUPST@DTBQEG
68/125

View Slide

⾣
Λநग़
⾣
⾣
⾣
DB DB
ݕࡧ 
ΠϯσοΫε
ఏࣔީิ
ݕࡧ 
ΠϯσοΫε

69/125

View Slide

-PDBM%FTDSJQUPSͷ#BHPGXPSET
ςΩετݕࡧͷݹయख๏Ͱ͸ɺର৅ͱͳΔهࣄͷ୯ޠͷҐஔ΍จߏ଄ͳ
Ͳͷ৘ใΛࣺͯͯɺग़ݱ୯ޠΛା٧Ί CBHPGXPSET
ͱͯ͠දݱ͢Δɻ
ը૾ݕࡧͰ΋ಉ༷ʹɺώετάϥϜهड़ͷू߹ͱͯ͠ը૾Λදݱ͢Δɻ
ہॴྖҬͷ࠲ඪɺεέʔϧɺ 
ΦϦΤϯςʔγϣϯɺώετάϥϜهड़
ώετάϥϜهड़ͷू·Γͱͯ͠ 
ը૾Λදݱ\Y@ Y@ Y@ ʜ^
70/125

View Slide

#BHPG7JTVBM8PSET
ը૾ݕࡧʹ͓͚Δ4*'5ͳͲͷώετάϥϜهड़͸࣍ͷ࣮਺ϕ
ΫτϧɻݕࡧΠϯσοΫεͱͯ͠ొ࿥͢Δʹ͸େ͖͗͢Δɻ
visual word: ID=1
͋Β͔͡Ί,NFBOT ֊૚,NFBOTͳͲͰΫϥελϦϯάͯ͠ɺ 
֤Ϋϥελͷத৺ΛWJTVBMXPSEͱͯ͠ఆٛ͢Δɻ 
ώετάϥϜهड़͸࠷ۙ๣ͷWJTVBMXPSEʹׂΓ౰ͯΔʢϕΫτϧྔࢠԽʣ
࠷ۙ๣Ϋϥελͷத৺఺
visual word: ID=2
x0 = (72 9 73 57 79 4 38 11 69 57 . . . )
x1 = (21 15 42 3 99 97 64 16 97 88 . . . )
x2 = (11 87 80 12 30 15 92 91 28 1 . . . ) ࠷ۙ๣Ϋϥελͷத৺఺
࠷ۙ๣Ϋϥελͷத৺఺
71/125

View Slide

సஔΠϯσοΫε ௥Ճ

visual word
visual word
visual word
λςɿWJTVBMXPSE*%ɺϤίɿJNBHF*%
72/125
4MJEFDSFEJU:BOOJT"WSJUIJTzIUUQTTJGEMWHJUIVCJPTMJEFTJOEFYQEG

View Slide

సஔΠϯσοΫε ݕࡧ

visual word
visual word
visual word
73/125

View Slide


visual word
visual word
visual word
74/125

View Slide


visual word
visual word
visual word
75/125

View Slide


visual word
visual word
visual word
ランキングされた 
検索候補
76/125

View Slide

)BNNJOH&NCFEEJOH
#BHPGWJTVBMXPSETͰ͸7JTVBMXPSETͱ͍͏ߥཻ͍౓Ͱͷස౓
ͰείΞϦϯά͢Δɻ
ಉҰͷWJTVBMXPSETʹׂΓ౰ͯΒΕΔώετάϥϜͷൺֱΛΑΓࡉ
͔͘ѻ͏ͨΊʹɺϕΫτϧΛόΠφϦԽͯ͠ϋϛϯάڑ཭Λ࢖ͬͯε
ίΞϦϯά͢ΔͳͲͷ޻෉͕<+ÉHPV>ʹΑͬͯͳ͞Ε͍ͯΔɻ
ϘϩϊΠਤͷηϧʹΫϥελ 
ʢ୯ҰͷWJTVBMXPSEͷۙ๣ʣ
ʹόΠφϦԽ
b(x) 2 {0, 1}d
ηϧ಺ͷϖΞ͸ϋϛϯάڑ཭Ͱൺֱ
77/125

View Slide

େن໛σʔλͷۙࣅ࠷ۙ๣୳ࡧɿ௚ੵྔࢠԽ
େن໛σʔλʹରͯ͠͸ɺΤϥʔΛڐ༰͢Δ୅ΘΓʹڑ཭্ۭؒͷΫ
ΤϦʹ͍ۙ఺Λߴ଎ʹ୳ࡧ͢Δ͜ͱ͕ඞཁͳ৔߹͕͋Δɻ
ྫɿEJN 99CJUqPBUCJU
ͷೖྗϕΫτϧΛͷ 
෦෼ϕΫτϧʹ෼ׂͯ͠ϏοτͰྔࢠԽͨ͠৔߹ˠCJUʹѹॖͰ͖Δɻ
௚ੵྔࢠԽ<+ÉHPV>Λ༻͍ͯೖྗϕΫτϧΛѹॖ͢Δ͜ͱͰɺϝϞ
Ϧޮ཰ͱߴ଎ͳۙࣅڑ཭ͷܭࢉ͕ՄೳͱͳΔɻ
x = ( x1
| x2
| . . . | xm )
10111101
00110101 11101110
直積量量⼦子化
(2^8=256 通りの割当)
78/125

View Slide

ࢀߟࢿྉ
ߨٛࢿྉ
lMFDUVSFNBUDIJOHBOEJOEFYJOH EFFQ
MFBSOJOHGPSWJTJPOz %FFQ-FBSOJOHGPS7JTJPO 
:BOOJT"WSJUIJTઌੜ 
IUUQTTJGEMWHJUIVCJPTMJEFTJOEFYQEG
lCJMMJPOTDBMFͷۙࣅ࠷ۙ๣୳ࡧz 
দҪ༐༎ઌੜ 
IUUQZVTVLFNBUTVJNFQSPKFDUTVSWFZ@QREPDBOO@CJMMJPO@QEG
ॻ੶
lίϯϐϡʔλϏδϣϯ޿͕Δཁૉٕज़ͱԠ༻z 
ୈষɿۙࣅ࠷ۙ๣୳ࡧ
79/125

View Slide

⾣
Λநग़
⾣
⾣
⾣
DB DB
ݕࡧ 
ΠϯσοΫε
ఏࣔީิ
ݕࡧ 
ΠϯσοΫε

80/125

View Slide

4QBUJBM7FSJpDBUJPO (FPTQBUJBM7FSJpDBUJPO

ઌఔͷۙ๣୳ࡧʹΑΔݕࡧީิ͸ɺώετάϥϜهड़͚ͩΛ࢖ͬͯಘ
ͨ݁Ռɻ
زԿతͳม׵Ϟσϧ ྫΞϑΟϯม׵
Λ 
Ծఆͯ͠ɺύϥϝʔλΛਪఆ͢Δ
زԿతͳม׵Ϟσϧͷݕূʹ͸PVUMJFSʹϩόετͳख๏͕ඞཁɻ
ΩʔϙΠϯτͷزԿతͳ഑ஔΛݕূ͢Δ͜ͱͰɺ'BMTFQPTJUJWFΛߴ
͍ਫ਼౓ͰऔΓআ͘͜ͱ͕Ͱ͖Δɻ
inliers
outliers
Image1 Image2

View Slide

Ϟσϧݕূͷखଓ͖ɿ3"/4"$<'JTDIMFS>
PVUMJFSTΛؚΉ؍ଌσʔλ͔Βɺ਺ཧϞσϧͷύϥϝʔλΛ 
ਪఆ͢Δ൓෮ܭࢉ๏ɻPVUMJFSTʹରͯ͠ϩόετͳख๏ɻ
ϥϯμϜʹϞσϧύϥϝʔλΛܾఆ͢ΔͨΊʹඞཁͳ 
࠷খͷ؍ଌσʔλ IZQPUIFUJDBMJOMJFST
Λબ୒͢Δ
IZQPUIFUJDBMJOMJFST͔ΒɺϞσϧͷύϥϝʔλΛࢉग़͢Δ 
શͯͷ؍ଌσʔλΛϞσϧʹద༻ͯ͠ɺڐ༰ޡࠩ಺ͷ؍ଌσʔλ਺Λࢉग़ʢJOMJFSTʣ
*OMJFSTͷׂ߹͕ᮢ஋Λ௒͍͑ͯΕ͹ɺ 
͢΂ͯͷJOMJFSTΛ࢖ͬͯϞσϧͷύϥϝʔλΛࢉग़ͯ͠ऴྃ
ͦ͏Ͱͳ͚Ε͹ɺΛ܁Γฦ͢ ࠷େ/ճ·Ͱ

82/125

View Slide

http://www.cse.psu.edu/~rtc12/CSE486/lecture15.pdf
ྫɿઢܗճؼϞσϧ
Ϟσϧɿઢܗճؼ ZBYC
ɺύϥϝʔλɿB Cɺαϯϓϧ਺ɿ̎
y = ax + b
$SFEJU3PCFSU$PMMJOTIUUQXXXDTFQTVFEVdSUD$4&MFDUVSFQEG
࠷খೋ৐๏ʹΑΓࢉग़
83/125

View Slide

y = ax + b
)ZQPUIFUJDBMJOMJFST
84/125

View Slide

y = ax + b
)ZQPUIFUJDBMJOMJFST
*OMJFST
ڐ༰ޡࠩ
85/125

View Slide

y = ax + b
)ZQPUIFUJDBMJOMJFST
*OMJFST
ڐ༰ޡࠩ
86/125

View Slide

y = ax + b
)ZQPUIFUJDBMJOMJFST
*OMJFST
ڐ༰ޡࠩ
87/125

View Slide

y = ax + b
)ZQPUIFUJDBMJOMJFST
*OMJFST
ڐ༰ޡࠩ
88/125

View Slide

y = ax + b
)ZQPUIFUJDBMJOMJFST
*OMJFST
ڐ༰ޡࠩ
89/125

View Slide

y = ax + b
)ZQPUIFUJDBMJOMJFST
*OMJFST
ڐ༰ޡࠩ
90/125

View Slide

y = ax + b
)ZQPUIFUJDBMJOMJFST
*OMJFST
ڐ༰ޡࠩ
91/125

View Slide

y = ax + b
92/125

View Slide

⾣ ϞσϧύϥϝʔλΛܭࢉ͢ΔͨΊͷσʔλΛαϯϓϦϯά
⾣ Ϟσϧύϥϝʔλͷਪఆ
⾣ Ϟσϧͱ੔߹ੑͷ͋͏αϯϓϧΛJOMJFSTͱͯ͠Χ΢ϯτ͢Δ
⾣ ܁Γฦ͠ɻJOMJFST͕࠷େͱͳΔϞσϧύϥϝʔλΛճ౴͢Δ
x0 = Ax
ϞσϧɿΞϑΟϯม׵ 
ύϥϝʔλɿΞϑΟϯࣸ૾ߦྻ" 
αϯϓϧ਺ɿ
93/125

View Slide

x0 = Ax
αϯϓϧ਺ɿ
94/125

View Slide

3"/4"$ͷྫ ⾣ ϞσϧύϥϝʔλΛܭࢉ͢ΔͨΊͷσʔλΛαϯϓϦϯά
४උɿ͋Β͔͡Ί̎ը૾ͷରԠ఺Λ࠷ۙ๣୳ࡧʹΑΓٻΊ͓ͯ͘
͢΂ͯͷ*NBHFͷ%FTDSJQUPS͔Βɺ*NBHFʹ͓͚Δ%FTDSJQUPS
ʹରͯ͠࠷ۙ๣Λ୳ࡧɻڑ཭͕͖͍͠஋ҎԼͷϙΠϯτͷΈ࢒͢ɻ
95/125

View Slide

Hypothetical inliers
x0 = Ax
αϯϓϧ਺ɿ
96/125

View Slide

x0 = Ax
αϯϓϧ਺ɿ
97/125

View Slide

inliers count = 20
x0 = Ax
αϯϓϧ਺ɿ
98/125

View Slide

x0 = Ax
αϯϓϧ਺ɿ
99/125

View Slide

x0 = Ax
αϯϓϧ਺ɿ
100/125

View Slide

inliers count = 63
x0 = Ax
αϯϓϧ਺ɿ
101/125

View Slide

inliers count = 110
x0 = Ax
αϯϓϧ਺ɿ
102/125

View Slide

inliers count = 162
x0 = Ax
αϯϓϧ਺ɿ
103/125
あらかじめ決めた繰り返し回数に
到達するまで繰り返す

View Slide

ީิू߹͔ΒJOMJFSTDPVOUͰSFTDPSJOH
ΠϯσοΫε͔Β 
ಘͨީิը૾
*OMJFSTDPVOUॱͷ 
߱ॱʹฒͼସ͑
2VFSZ
)PXSBI#SJEHF *OEJB

4UPSZ#SJEHF "VTUSBMJB

7JDLTCVSH#SJEHF 64

104/125

View Slide

ͦͷଞͷ޻෉ɿΫΤϦ֦ு2VFSZ&YQBOTJPO
ΫΤϦը૾ʹΑΔݕࡧ݁Ռ͔Βɺ৽ͨʹݕࡧΫΤϦΛ࡞੒͢Δɻ
ը૾ؒͰʮ෦෼తʹϚον͢Δؔ܎ʯ͕ଟ͍৔߹͸ಛʹ༗ޮɻ
52& 5SBOTJUJWF2VFSZ&YQBOTJPO
<$IVN>ɺ 
"2& "WFSBHF2VFSZ&YQBOTJPO
<$IVN>ɺ 
%2& %JTDSJNJOBUJWFRVFSZFYQBOTJPO
<"SBOEKFMPWJD>ɺ 
Ћ2& ЋXFJHIUFERVFSZFYQBOTJPO
<3BEFOPWJ㶛B>ɺ 
%'4 HSBQICBTFERVFSZFYQBOTJPOEJ⒎VTJPO
<*TDFO>ͳͲ
ݕࡧ ݕࡧ ݕࡧ
105/125

View Slide

ΞδΣϯμ
106/125

⾣ -PDBM%FTDSJQUPS
⾣ *OEFY4FBSDI
⾣ .BUDIJOH


View Slide

ਂ૚ֶशʹΑΔ໠Җ
*-473$͸೥͔Β࢝·ͬͨେن໛zը૾ೝࣝzͷίϯςετɻ
〜深層学習⼀一般の話題と画像認識（多クラス分類類）の⽂文脈での話〜

2010 2011 2012 2013 2014 2015
Classiﬁcation error (%)
0
10
20
30
CNN for ImageNet
Krizhevsky et al.
೥ʹେن໛ը૾ೝࣝʹ͓͚Δ
$//ʹΑΔϒϨΠΫεϧʔͷಥഁ
Ͱେ͖͘஫໨ΛूΊͨɻ
ͷେ෯ͳվળ
107/125

View Slide

$POWPMVUJPOBM/FUXPSLT $//

ϊʔυ͕ؒີ݁߹ͱͳΔ఻౷తͳ/FVSBM/FUXPSLTͱҟͳΓɺ
$POWPMVUJPOMBZFSΛ༻͍Δ͜ͱͰεύʔεͳ݁߹ʹΑͬͯߏ੒͞ΕΔɻ
͜ΕʹΑͬͯύϥϝʔλΛେ෯ʹ࡟ݮ͍ͯ͠Δɻ
୯Ұͷ-BZFSʹ͓͚Δೖྗͱग़ྗͷؔ܎Λ 
໛ࣜతʹදͨ͠΋ͷɻ
$SFEJU(PPEGFMMPXFUBM%FFQ-FBSOJOH CPPL

108/125
ˢʹ఻౷తͳ//
ˢʹ$// $//ͷೖྗ͸Ұ෦ͷύϥϝʔλʹରͯ͠ͷΈӨڹɻ 
ؔ਺ͷදݱྗ͸૚Λ૿΍͢͜ͱͰΧόʔɻ

View Slide

$//Ͱ&OEUP&OEʹֶश͞ΕΔΧʔωϧ
$//Ͱֶशͨ͠$POWPMVUJPOͷ,FSOFMΛՄࢹԽͨ͠΋ͷɻ
*NBHFGSPN<,SJ[IFWTLZ>
Τοδ΍#MPCʹ൓Ԡͦ͠͏ͳΧʔωϧ͔Βɺෳࡶͳ΋ͷ·Ͱଟ༷ɻ 
#MPCݕग़ثͰ༻͍ͨ-P(ͷΑ͏ͳΧʔωϧΛσʔλ͔ΒࣗಈͰशಘ͢Δɻ
109/125

View Slide

$//ͷશ݁߹૚ͷग़ྗΛ࢖͏<3B[BWJBO>
Ϋϥε෼ྨͷͨΊͷ$//Ϟσϧ 0WFS'FBU
ͷ'$MBZFS EJN
Λ 
XIJUFOJOHͯ͠༻͍ΔɻϢʔΫϦουڑ཭Ͱൺֱɻ
ྨࣅυϝΠϯͷը૾σʔληοτͰpOFUVOJOH͢Δͱɺ4*'5ΑΓྑ͍݁Ռʹɻ
*NBHFDSFEJU"MFY,SJ[IFWTLZIUUQXXXDTUPSPOUPFEVdGSJU[BCTQTJNBHFOFUQEG
110/125
Conv Conv MP
FC FC
େҬతͳهड़ʢ(MPCBMEFTDSJQUPSʣʹΑΔಛఆ෺ମೝࣝͷΞϓϩʔνɿ 
ը૾ΛͭͷϕΫτϧͱͯ͠දݱͯ͠ϢʔΫϦουڑ཭Ͱݕࡧ͢Δɻ

View Slide

1Z5PSDI࣮૷ɿ
7((
YY
1PPMJOHͷࣜɿ

*OQVU͸࠷ޙͷ$POWPMVUJPOMBZFSͷ 
0VUQVUͰYY
41P$<#BCFOLP>
F.avg_pool2d(x, (x.size(-2), x.size(-1)))
˞આ໌ͷศ্ٓɺ7((Λ༻͍͍ͯΔ

LFSOFMTJ[F ݸʑͷ,FSOFMͷશମ

Y
$POWPMVUJPOMBZFSʹΑͬͯಘͨہॴతͳಛ௃Λ·ͱΊΔɻ 
ˠLݸͷ,FSOFMͷ൓ԠΛผʑʹ%ʹQPPMJOH͢Δ 4QBUJBMlTVNzQPPMJOH

ʢTVNQPPMJOHͳͷͰɺͦΕͧΕͷʹΑΔ,FSOFMʹΑΔ൓Ԡͷස౓ͷΑ͏ͳදݱʣ
111/125
*NBHF$SFEJU:BOOJT"WSJUIJTzIUUQTTJGEMWHJUIVCJPTMJEFTJOEFYQEG

View Slide

."$<5PMJBT>
1Z5PSDI࣮૷ɿ
7((
YY
F.max_pool2d(x, (x.size(-2), x.size(-1)))
1PPMJOHͷࣜɿ

*OQVU͸࠷ޙͷ$POWPMVUJPOMBZFSͷ 
0VUQVUͰYY
Y
$POWPMVUJPOMBZFSʹΑͬͯಘͨہॴతͳಛ௃Λ·ͱΊΔɻ 
ˠLݸͷ,FSOFMͷ൓ԠΛผʑʹ%ʹQPPMJOH͢Δ 4QBUJBMNBYQPPMJOH

ʢNBYQPPMJOHͳͷͰɺͦΕͧΕͷʹΑΔ,FSOFMʹΑΔ൓Ԡͷ༗ແͷΑ͏ͳදݱʣ
LFSOFMTJ[F ݸʑͷ,FSOFMͷશମ


112/125

View Slide

1Z5PSDI࣮૷ɿ
1PPMJOHͷࣜɿ
࠷ޙͷ$POWPMVUJPOMBZFSͷPVUQVUʹରͯ͠ɺ 
4QBUJBMHFOFSBMJ[FENFBOQPPMJOHɻ-QOPSNͷΑ͏ͳQΛύϥϝʔλͱͨ͠ҰൠԽɻ
(F.<3BEFOPWJ㶛>
F.avg_pool2d( 
x.clamp(min=eps).pow(p), 
(x.size(-2), x.size(-1)) 
).pow(1./p)

gem
7((
YY
Q@L͸ֶशՄೳͳϞσϧύϥϝʔλ

113/125

View Slide

%&-' $//CBTFE-PDBMEFTDSJQUPS

࠷ۙͷϕϯνϚʔΫ<3BEFOPWJ㶛C>Ͱ͸$//CBTFE-PDBM
EFTDSJQUPSͷதͰͷ405"ɻΫϥε෼ྨͷ*NBHFMFWFMBOOPUBUJPOT͔
Β$POWPMVUJPOMBZFSͱ"UUFOUJPOMBZFSΛֶश͢Δɻ
"UUFOUJPOTDPSFΛ࢖ͬͯ-PDBMEFTDSJQUPSΛநग़͢Δɻ
-BOENBSL%BUBTFUͰֶशɻ 
-BOENBSLͰ͸ͳ͍ਓͷإͳͲ 
͕ഉআͰ͖͍ͯΔ
*NBHFDSFEJU)ZFPOXPP/PIIUUQTBSYJWPSHQEGQEG
114/125

View Slide

2010 2011 2012 2013 2014 2015
CNN for ImageNet
Krizhevsky et al.
2016 2017 2018
2004 2005 2006 2007 2008 2009
2003
Video Google
Sivic and Zisserman
2002
Hamming Embedding 
Jegou et al.
CNN off-the-shelf 
Razavian et al.
DELF
Noh et al.
GeM
Radenović et al.
SPoC
Babenko et al.
R-MAC
VLAD 
Jegou et al.
SIFT-based CNN-based
MAC
Tolias et al.
REMAP 
Bober-Irizar et al. ?
(manuscript submitted)
2019?
͜Ε·ͰͷาΈ
115/125

View Slide

116/125

View Slide

$713XPSLTIPQίϯϖςΟγϣϯ
⾣ ϥϯυϚʔΫ ཱྀߦऀͳͲʹͱͬͯ৔ॴΛಛఆ͢Δͷʹ໾ཱͭ໨ҹ
Λର৅ͱ
ͨ͠େن໛ը૾ݕࡧίϯςετɻ
⾣ ڝٕظؒɿdͷ໿ϲ݄
⾣ ධՁࢦඪɿN"1!
⾣ ϥϯυϚʔΫ਺ɿສઍछྨ
⾣ σʔλ਺ɿΫΤϦը૾ΠϯσοΫεը૾(# ສຕ

⾣ ΠϯσοΫεը૾͔Β4*'5Λநग़͢Δͱ.ݸ ԯݸ

⾣ 3PPU4*'5ʹม׵͢Δͱ.(#
117/125
$713`XPSLTIPQͷίϯϖςΟγϣϯͱͯ͠,BHHMFͰ։࠵ɻ
ݱ࣌఺Ͱ࠷΋େن໛ͳɺಛఆ෺ମೝࣝͷධՁσʔληοτɻ

View Slide

্Ґ͸$//CBTFE(MPCBMEFTDSJQUPS 
4JBNFTF5SJQMFUOFUXPSLʹΑΔ'JOFUVOJOH͕ओྲྀ

mAP@100
0
20
40
60
3BEFOPWJD
(F.
'5
1$"X&VDMJEJBOTFBSDI

3BEFOPWJD
(F.
'5
1$"X&VDMJEJBOTFBSDI%J⒎VTJPO
#PCFS*SJ[BS
&OTFNCMF1$"X%#"VH&VDMJEJBO2& JUFSBUJPOT

#PCFS*SJ[BS
3&."1 '5
1$"X&VDMJEJBOTFBSDI2& JUFSBUJPOT

#PCFS*SJ[BS
3&."1 '5
&VDMJEJBOTFBSDI

0[BLJ
%&-'52&41ˠ3FTDPSJOHCZ(F.
'5
%J⒎VTJPO
0[BLJ
%&-'52&41

0[BLJ
(F.
QSFUSBJOFE
1$"X&VDMJEJBOTFBSDI
.JTILJO
)FT"⒎/FU)BSE/FU41 
2VFSZFYQBOTJPOCZ%J⒎VTJPO

͸1VCMJD-#TDPSFʹ͓͚Δ਺ࣈͰ͋ΔͨΊɺଞͱएׯҟͳΔՄೳੑ͕͋Δ
118/125
-PDBMEFTDSJQUPSʹΑΔݕࡧΛϕʔεͱͨ݁͠Ռ
3&."1ɻ 
%J⒎VTJPOΛ༻͍ͣ&VDMJEJBOTFBSDI2&͚ͩͰ 
ඇৗʹߴ͍ਫ਼౓Λୡ੒͍ͯ͠Δɻ
TU UI UI UI

View Slide

3&."1<$74417JTVBM"UPNT5FBN NBOVTDSJQUTVCNJUUFE
>
⾣ -BOENBSL3FUSJFWBM$IBMMFOHFͰॳग़ͷ(MPCBMEFTDSJQUPSˍ405"ɻ
⾣ δϟʔφϧ౤ߘதʹ͖ͭɺৄࡉ͸$713`84ͷϓϨθϯςʔγϣϯͱ,BHHMF'PSVNͰͷ৘
ใ͕࠷΋ৄ͍͠ɻ
⾣ ʮ͢΂ͯͷ$POWPMVUJPO૚͔ΒʯͦΕͧΕ30*1PPMʹΑͬͯSFHJPOGFBUVSFTΛऔΓग़͢ɻ
&OUSPQZϕʔεͷXFJHIUJOHΛ༩͑ͯTVNQPPMJOHͯ͠࿈݁͢Δɻ
⾣ ೖྗ͕ߴղ૾ˍ෦෼తͳࣸਅ͕ͨ͘͞Μ͋ΔͷͰɺ30*1PPM͸ͱͯ΋༗ޮͦ͏ʂ
⾣ 0YGPSE 1BSJTͳͲ,BHHMFҎ֎ͷධՁσʔληοτͰ΋ൺֱ͞Ε͓ͯΓଞΛѹ౗͍ͯ͠Δɻ
⾣ RVFSZ NBUDI OPONBUDI
ͷUSJQMFUͰ3&."1Λܭࢉͯ͠USJQMFUMPTTʹΑΔpOFUVOJOH
Λߦ͏ɻ
3FGIUUQTXXXLBHHMFDPNDMBOENBSLSFUSJFWBMDIBMMFOHFEJTDVTTJPO
119/125

View Slide

View Slide

·ͱΊʗࡶײ
w ݹయతΞϓϩʔνʹΑΔख๏ͱ$//ϕʔεͷΞϓϩʔν
w 4*'5͸εέʔϧෆมɾճసෆมɾর໌ෆมͷੑ࣭Λ࣋ͭ
w 3"/4"$͸PVUMJFSʹରͯ͠ϩόετʹϞσϧύϥϝʔλΛࢉग़Մೳ
w $//ϕʔεͷ(MPCBMEFTDSJQUPS͸୯ҰͷϕΫτϧͰߴ͍ݕࡧਫ਼౓
w 4JBNFTF5SJQMFUOFUXPSLͰ'JOFUVOJOHʹΑΔਫ਼౓ఈ্͕͛Մೳ
w ίϯςετΛ௨ͯ͡ͷࡶײ
w େن໛ʹͳΔͱ-PDBMEFTDSJQUPS͸σʔλ਺͕๲େʹͳΔɻඞཁͱ͢Δܭࢉίετ΍Ϧιʔ
ε΋େ͖͘ͳΔͷͰ೉఺Λײ͡Δɻ
w زԿతͳݕূʹΑͬͯಘΒΕΔ݁Ռ͸ඇৗʹਫ਼౓͕ߴ͍ͨΊɺ-PDBMEFTDSJQUPSΛ࢖Θͣ
(MPCBMEFTDSJQUPS͚ͩͰྑ͍είΞΛୡ੒Ͱ͖Δ͜ͱʹ͸େมڻ͍ͨɻ
w (MPCBMEFTDSJQUPSͷ݁ՌͰ͸ࢁͳͲͷࣗવ؀ڥͷࣸਅʹର͢Δ3FDBMM͕-PDBMEFTDSJQUPS
ͱൺֱͯ͠ߴ͘ɺ͜Ε͕શମͷείΞʹӨڹΛ༩͑ͨͷͰ͸ͳ͍͔ͱࢥΘΕΔ ཁݕূ

125/125
ը૾ݕࡧʢಛఆ෺ମೝࣝʣͷݹయख๏ͱ$//ϕʔεͷख๏Λ঺հͨ͠ɻ

View Slide

画像検索 (特定物体認識) — 古典手法、マッチング、深層学習、Kaggle

画像検索 (特定物体認識) — 古典手法、マッチング、深層学習、Kaggle

@smly

More Decks by @smly

Other Decks in Technology

Featured

Transcript