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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
July 27, 2018

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

(7/24) 大阪大学大学院情報科学研究科、ビッグデータ解析のゲストスピーカー担当分講義の資料をアップしました。画像検索とコンテストの話です。

@smly

July 27, 2018
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  1. ը૾ݕࡧ ಛఆ෺ମೝࣝ
    Š
    ݹయख๏ɺϚονϯάɺਂ૚ֶशɺ,BHHMF
    େࡕେֶେֶӃ৘ใՊֶݚڀՊϏοάσʔλղੳ ήετ࿮ߨٛ

    খቌߞฏ !TNMZ

    גࣜձࣾϦΫϧʔτςΫϊϩδʔζ "5-

    1/125

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  2. ࣗ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

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

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  4. "HFOEB
    ը૾ݕࡧ ಛఆ෺ମೝࣝ
    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。

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  5. 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
    "HFOEB
    ը૾ݕࡧ ಛఆ෺ମೝࣝ
    ʹ͍ͭͯ঺հ͠·͢ɻ
    5/125

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  6. 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

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  7. Ԡ༻ྫɿ(PPHMF*NBHF4FBSDI
    Ξοϓϩʔυͨࣸ͠ਅ͔Β
    ύϧςΦϯਆ఼ͱೝࣝɻ

    ؔ࿈৘ใΛදࣔ
    $SFEJUIUUQTJNBHFTHPPHMFDPN
    ͪ͜Β͸ྨࣅը૾
    7/125

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  8. Ԡ༻ྫɿ.FSDBSJ঎඼ը૾ݕࡧ
    Ξοϓϩʔυͨࣸ͠ਅ͔Β

    طग़ͷಉҰ঎඼Λݕࡧɻ

    ঎඼໊΍ΧςΰϦΛࣗಈೖྗ
    $SFEJUIUUQTUFDINFSDBSJDPNFOUSZ
    8/125

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  9. 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

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  10. ಛఆ෺ମೝࣝͷ೉͍͠ͱ͜Ζ
    ࢹ఺ʜಉ͡෺ମͰ͋ͬͯ΋ࢹ఺ͷҧ͍ʹΑͬͯݟ͑ํ͕มԽ͢Δ
    The Cube Houses in Rotterdam
    ▶ スケール

    ▶ 視点

    ▶ オクルージョン

    ▶ 照明

    ▶ 時間変化

    ▶ 阻害

    10/125

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  11. ಛఆ෺ମೝࣝͷ೉͍͠ͱ͜Ζ
    ΦΫϧʔδϣϯʜલํʹผͷ෺ମ͕ࣸΓࠐΜͰର৅ͱͳΔ෺ମ͕Ӆ
    ΕΔ
    ▶ スケール

    ▶ 視点

    ▶ オクルージョン

    ▶ 照明

    ▶ 時間変化

    ▶ 阻害
    11/125

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  12. ಛఆ෺ମೝࣝͷ೉͍͠ͱ͜Ζ
    র໌ʜ໷ʹࡱӨ͞ΕͨɺனʹࡱӨ͞ΕͨɺேʹࡱӨ͞Εͨ
    ▶ スケール

    ▶ 視点

    ▶ オクルージョン

    ▶ 照明

    ▶ 時間変化

    ▶ 阻害
    12/125

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  13. ಛఆ෺ମೝࣝͷ೉͍͠ͱ͜Ζ
    ࣌ؒมԽʜ࣌ؒతͳҧ͍ʹΑͬͯੜ͡Δࠩ
    ▶ スケール

    ▶ 視点

    ▶ オクルージョン

    ▶ 照明

    ▶ 時間変化

    ▶ 阻害
    13/125

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  14. ಛఆ෺ମೝࣝͷ೉͍͠ͱ͜Ζ
    ્֐෺ʜं΍໦ͳͲಛఆ෺ମͷೝࣝʹؔ܎ͳ͍ීวతʹग़ݱ͢Δύ
    λʔϯɻਖ਼͍͠ೝࣝΛ๦֐͠GBMTFQPTJUJWFΛ૿Ճͤ͞Δɻ
    GBMTFQPTJUJWF
    ෆਖ਼ղ͕ͩγεςϜ͕ਖ਼͍͠ͱޡճ౴͢Δࣄྫ
    ▶ スケール

    ▶ 視点

    ▶ オクルージョン

    ▶ 照明

    ▶ 時間変化

    ▶ 阻害
    14/125

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  15. ݹయతͳಛఆ෺ମೝࣝͷΞϓϩʔν

    ը૾ू߹͔Βہॴಛ௃ -PDBMEFTDSJQUPS
    Λநग़

    ہॴಛ௃͔ΒݕࡧΠϯσοΫεΛ࡞੒

    ΫΤϦը૾͔Βہॴಛ௃Λநग़ͯ͠ΠϯσοΫε͔ΒީิΛऔಘ

    ہॴతͳಛ௃ͷ഑ஔʹزԿతͳ੔߹ੑ͕ͱΕ͍ͯΔ͜ͱΛ֬ೝ
    DB DB
    ը૾ू߹ ΫΤϦը૾
    ݕࡧ

    ΠϯσοΫε
    ఏࣔީิ
    ݕࡧ

    ΠϯσοΫε






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

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  16. ݹయతͳಛఆ෺ମೝࣝͷΞϓϩʔν

    ը૾ू߹͔Βہॴಛ௃ -PDBMEFTDSJQUPS
    Λநग़

    ہॴಛ௃͔ΒݕࡧΠϯσοΫεΛ࡞੒

    ΫΤϦը૾͔Βہॴಛ௃Λநग़ͯ͠ΠϯσοΫε͔ΒީิΛऔಘ

    ہॴతͳಛ௃ͷ഑ஔʹزԿతͳ੔߹ੑ͕ͱΕ͍ͯΔ͜ͱΛ֬ೝ
    DB DB
    ը૾ू߹ ΫΤϦը૾
    ݕࡧ

    ΠϯσοΫε
    ఏࣔީิ
    ݕࡧ

    ΠϯσοΫε






    ہॴతͳಛ௃Λநग़ͯ͠ݕࡧΠϯσοΫεߏஙɻ<4JWJD -PXF +ÉHPV ʜ>
    16/125

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  17. -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

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  18. Ԡ༻ྫɿը૾ͷ๓͍߹Θͤ *NBHF4UJUDIJOH

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

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  19. Ԡ༻ྫɿίϯςφͷҠಈΛՄࢹԽ
    ҟͳΔ࣌ؒʹࡱӨͨ͠ߤۭࣸਅΛ-PDBMEFTDSJQUPSΛ࢖ͬͯϚονϯ
    άͯ͠ɺࣹӨม׵ߦྻΛٻΊΔɻॏͶ߹Θͤͯࠩ෼ΛՄࢹԽ͢Δɻ
    $SFEJUIUUQTXXXLBHHMFDPNDESBQFSTBUFMMJUFJNBHFDISPOPMPHZEJTDVTTJPO

    %BUB%SBQFS4BUFMMJUF*NBHF$ISPOPMPHZIUUQTXXXLBHHMFDPNDESBQFSTBUFMMJUFJNBHFDISPOPMPHZEBUB
    19/125

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  20. ͲͷΑ͏ͳੑ࣭Λ͍࣋ͬͯΔ͜ͱ͕๬·͍͠ʁ
    -PDBMEFTDSJQUPS͸ͲͷΑ͏ͳੑ࣭Λ͍࣋ͬͯΔ͜ͱ͕๬·͍͔͠ʁ

    ΧϝϥͷҐஔ΍޲͖ͷҧ͍ʹରͯ͠ؤ݈ͳੑ࣭͕๬·͍͠ɻ
    ⾣ εέʔϧෆม
    ⾣ ճసෆม
    ⾣ র໌มԽෆม
    ⾣ ΞϑΟϯม׵ෆม
    20/125

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  21. 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

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  22. 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, )

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  23. scale
    f(I, )
    $SFEJU5JOOF5VZUFMBBSTWJBIUUQTBHTDTVOJLMEFpMFBENJOJOG@BHTEJQTT%*1@44@MFD@$PSOFST@#MPCTQEG

    23/125

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  24. scale
    f(I, )
    $SFEJU5JOOF5VZUFMBBSTWJBIUUQTBHTDTVOJLMEFpMFBENJOJOG@BHTEJQTT%*1@44@MFD@$PSOFST@#MPCTQEG

    24/125

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  25. scale
    f(I, )
    $SFEJU5JOOF5VZUFMBBSTWJBIUUQTBHTDTVOJLMEFpMFBENJOJOG@BHTEJQTT%*1@44@MFD@$PSOFST@#MPCTQEG

    25/125

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  26. scale
    f(I, )
    $SFEJU5JOOF5VZUFMBBSTWJBIUUQTBHTDTVOJLMEFpMFBENJOJOG@BHTEJQTT%*1@44@MFD@$PSOFST@#MPCTQEG

    26/125

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  27. scale
    f(I, )
    $SFEJU5JOOF5VZUFMBBSTWJBIUUQTBHTDTVOJLMEFpMFBENJOJOG@BHTEJQTT%*1@44@MFD@$PSOFST@#MPCTQEG

    27/125

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  28. scale
    f(I, )
    $SFEJU5JOOF5VZUFMBBSTWJBIUUQTBHTDTVOJLMEFpMFBENJOJOG@BHTEJQTT%*1@44@MFD@$PSOFST@#MPCTQEG

    28/125

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  29. 正規化:固定⻑⾧長サイズに Rescale する
    $SFEJU5JOOF5VZUFMBBSTWJBIUUQTBHTDTVOJLMEFpMFBENJOJOG@BHTEJQTT%*1@44@MFD@$PSOFST@#MPCTQEG

    29/125

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  30. 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

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  31. -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

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

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  33. ิ଍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

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  34. -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

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  35. -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

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  36. 4UFQεέʔϧۭؒͷ࡞੒
    LoG
    LoG で畳み込み
    36/125

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  37. 4UFQεέʔϧۭؒͷ࡞੒
    LoG
    LoG で畳み込み
    37/125

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  38. 4UFQεέʔϧۭؒͷ࡞੒
    LoG
    LoG で畳み込み
    38/125

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  39. 4UFQεέʔϧۭؒͷ࡞੒
    LoG
    LoG で畳み込み
    39/125

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  40. 4UFQεέʔϧۭؒͷ࡞੒
    LoG
    LoG で畳み込み
    40/125

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  41. 4UFQεέʔϧۭؒͷ࡞੒
    LoG
    LoG で畳み込み
    41/125

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  42. = 1.00
    4UFQεέʔϧۭؒͷ࡞੒
    42/125

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  43. = 3.11
    4UFQεέʔϧۭؒͷ࡞੒
    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

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  44. = 7.33
    4UFQεέʔϧۭؒͷ࡞੒
    スケール係数を変えて LoG 適⽤用。
    スケール空間を作る。
    44/125

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  45. = 11.5
    4UFQεέʔϧۭؒͷ࡞੒
    スケール係数を変えて LoG 適⽤用。
    スケール空間を作る。
    45/125

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  46. = 15.7
    4UFQεέʔϧۭؒͷ࡞੒
    スケール係数を変えて LoG 適⽤用。
    スケール空間を作る。
    46/125

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  47. = 20.0
    4UFQεέʔϧۭؒͷ࡞੒
    スケール係数を変えて LoG 適⽤用。
    スケール空間を作る。
    47/125

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  48. Input image
    = 1.00
    = 20.0
    = 15.7
    = 3.11
    = 7.33
    = 11.5
    スケール係数を変えて LoG 適⽤用。
    スケール空間を作る。
    4UFQεέʔϧۭؒͷ࡞੒
    48/125

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  49. 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

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


    4UFQہॴ࠷େ஋Λݟ͚ͭΔ
    50/125

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


    4UFQہॴ࠷େ஋Λݟ͚ͭΔ
    51/125

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


    4UFQہॴ࠷େ஋Λݟ͚ͭΔ
    51/125

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


    4UFQہॴ࠷େ஋Λݟ͚ͭΔ
    52/125

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


    4UFQہॴ࠷େ஋Λݟ͚ͭΔ
    54/125

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


    4UFQہॴ࠷େ஋Λݟ͚ͭΔ
    55/125

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  56. 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
    4UFQہॴ࠷େ஋Λݟ͚ͭΔ

    View Slide

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

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

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  59. -PDBM%FTDSJQUPSͷݕग़ͱهड़
    ͲͷΑ͏ͳہॴతͳؔ৺ྖҬɾϙΠϯτΛݕग़͢Δʁ
    ⾣ ΧϝϥͷҐஔ΍޲͖ͷҧ͍ʹରͯ͠ؤ݈ͳੑ࣭͕๬·͍͠
    ⾣ εέʔϧෆม
    ⾣ ճసෆม
    ⾣ র໌มԽෆม
    ⾣ ΞϑΟϯม׵ෆม
    59/125

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  60. 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

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  61. 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

  62. -PDBM%FTDSJQUPSͷݕग़ͱهड़
    ͲͷΑ͏ͳہॴతͳؔ৺ྖҬɾϙΠϯτΛݕग़͢Δʁ
    ⾣ ΧϝϥͷҐஔ΍޲͖ͷҧ͍ʹରͯ͠ؤ݈ͳੑ࣭͕๬·͍͠
    ⾣ εέʔϧෆม
    ⾣ ճసෆม
    ⾣ র໌มԽෆม
    ⾣ ΞϑΟϯม׵ෆม
    62/125

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  63. 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

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  64. 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

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  65. ͦ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

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  66. ͦ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

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  67. 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

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  68. ࢀߟࢿྉ
    .*36νϡʔτϦΞϧɿ4*'5ͱͦΕҎ߱ͷΞϓϩʔν

    ౻٢߂࿱ઌੜ

    IUUQTXXXTMJEFTIBSFOFUIJSPOPCVGVKJZPTIJNJSVTJGU
    $4"ߨٛࢿྉ
    -FDUVSF%FUFDUPSTBOE%FTDSJQUPST

    'FJ'FJ-Jઌੜ
    IUUQWJTJPOTUBOGPSEFEVUFBDIJOHDTB@BVUVNOMFDUVSF

    MFDUVSF@EFUFDUPST@EFTDSJQUPST@DTBQEG
    68/125

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  69. ݹయతͳಛఆ෺ମೝࣝͷΞϓϩʔν

    ը૾ू߹͔Βہॴಛ௃ -PDBMEFTDSJQUPS
    Λநग़

    ہॴಛ௃͔ΒݕࡧΠϯσοΫεΛ࡞੒

    ΫΤϦը૾͔Βہॴಛ௃Λநग़ͯ͠ΠϯσοΫε͔ΒީิΛऔಘ

    ہॴతͳಛ௃ͷ഑ஔʹزԿతͳ੔߹ੑ͕ͱΕ͍ͯΔ͜ͱΛ֬ೝ
    DB DB
    ը૾ू߹ ΫΤϦը૾
    ݕࡧ

    ΠϯσοΫε
    ఏࣔީิ
    ݕࡧ

    ΠϯσοΫε






    ہॴతͳಛ௃Λநग़ͯ͠ݕࡧΠϯσοΫεߏஙɻ<4JWJD -PXF +ÉHPV ʜ>
    69/125

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  70. -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

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  71. #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

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  72. సஔΠϯσοΫε ௥Ճ

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

    View Slide

  73. సஔΠϯσοΫε ݕࡧ

    visual word
    visual word
    visual word
    λςɿWJTVBMXPSE*%ɺϤίɿJNBHF*%
    73/125
    4MJEFDSFEJU:BOOJT"WSJUIJTzIUUQTTJGEMWHJUIVCJPTMJEFTJOEFYQEG

    View Slide

  74. సஔΠϯσοΫε ݕࡧ

    visual word
    visual word
    visual word
    λςɿWJTVBMXPSE*%ɺϤίɿJNBHF*%
    74/125
    4MJEFDSFEJU:BOOJT"WSJUIJTzIUUQTTJGEMWHJUIVCJPTMJEFTJOEFYQEG

    View Slide

  75. సஔΠϯσοΫε ݕࡧ

    4MJEFDSFEJU:BOOJT"WSJUIJTzIUUQTTJGEMWHJUIVCJPTMJEFTJOEFYQEG
    visual word
    visual word
    visual word
    λςɿWJTVBMXPSE*%ɺϤίɿJNBHF*%
    75/125

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  76. సஔΠϯσοΫε ݕࡧ

    visual word
    visual word
    visual word
    λςɿWJTVBMXPSE*%ɺϤίɿJNBHF*%
    ランキングされた

    検索候補
    76/125
    4MJEFDSFEJU:BOOJT"WSJUIJTzIUUQTTJGEMWHJUIVCJPTMJEFTJOEFYQEG

    View Slide

  77. )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

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  78. େ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

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  79. 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

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  80. ݹయతͳಛఆ෺ମೝࣝͷΞϓϩʔν

    ը૾ू߹͔Βہॴಛ௃ -PDBMEFTDSJQUPS
    Λநग़

    ہॴಛ௃͔ΒݕࡧΠϯσοΫεΛ࡞੒

    ΫΤϦը૾͔Βہॴಛ௃Λநग़ͯ͠ΠϯσοΫε͔ΒީิΛऔಘ

    ہॴతͳಛ௃ͷ഑ஔʹزԿతͳ੔߹ੑ͕ͱΕ͍ͯΔ͜ͱΛ֬ೝ
    DB DB
    ը૾ू߹ ΫΤϦը૾
    ݕࡧ

    ΠϯσοΫε
    ఏࣔީิ
    ݕࡧ

    ΠϯσοΫε






    ہॴతͳಛ௃Λநग़ͯ͠ݕࡧΠϯσοΫεߏஙɻ<4JWJD -PXF +ÉHPV ʜ>
    80/125

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  81. 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

  82. 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

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  83. 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

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  84. ྫɿઢܗճؼϞσϧ
    Ϟσϧɿઢܗճؼ ZBYC
    ɺύϥϝʔλɿB Cɺαϯϓϧ਺ɿ̎
    $SFEJU3PCFSU$PMMJOTIUUQXXXDTFQTVFEVdSUD$4&MFDUVSFQEG
    y = ax + b
    )ZQPUIFUJDBMJOMJFST
    84/125

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  85. http://www.cse.psu.edu/~rtc12/CSE486/lecture15.pdf
    $SFEJU3PCFSU$PMMJOTIUUQXXXDTFQTVFEVdSUD$4&MFDUVSFQEG
    ྫɿઢܗճؼϞσϧ
    Ϟσϧɿઢܗճؼ ZBYC
    ɺύϥϝʔλɿB Cɺαϯϓϧ਺ɿ̎
    y = ax + b
    )ZQPUIFUJDBMJOMJFST
    *OMJFST
    ڐ༰ޡࠩ
    85/125

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  86. http://www.cse.psu.edu/~rtc12/CSE486/lecture15.pdf
    $SFEJU3PCFSU$PMMJOTIUUQXXXDTFQTVFEVdSUD$4&MFDUVSFQEG
    ྫɿઢܗճؼϞσϧ
    Ϟσϧɿઢܗճؼ ZBYC
    ɺύϥϝʔλɿB Cɺαϯϓϧ਺ɿ̎
    y = ax + b
    )ZQPUIFUJDBMJOMJFST
    *OMJFST
    ڐ༰ޡࠩ
    86/125

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  87. http://www.cse.psu.edu/~rtc12/CSE486/lecture15.pdf
    $SFEJU3PCFSU$PMMJOTIUUQXXXDTFQTVFEVdSUD$4&MFDUVSFQEG
    ྫɿઢܗճؼϞσϧ
    Ϟσϧɿઢܗճؼ ZBYC
    ɺύϥϝʔλɿB Cɺαϯϓϧ਺ɿ̎
    y = ax + b
    )ZQPUIFUJDBMJOMJFST
    *OMJFST
    ڐ༰ޡࠩ
    87/125

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  88. http://www.cse.psu.edu/~rtc12/CSE486/lecture15.pdf
    $SFEJU3PCFSU$PMMJOTIUUQXXXDTFQTVFEVdSUD$4&MFDUVSFQEG
    ྫɿઢܗճؼϞσϧ
    Ϟσϧɿઢܗճؼ ZBYC
    ɺύϥϝʔλɿB Cɺαϯϓϧ਺ɿ̎
    y = ax + b
    )ZQPUIFUJDBMJOMJFST
    *OMJFST
    ڐ༰ޡࠩ
    88/125

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  89. http://www.cse.psu.edu/~rtc12/CSE486/lecture15.pdf
    $SFEJU3PCFSU$PMMJOTIUUQXXXDTFQTVFEVdSUD$4&MFDUVSFQEG
    ྫɿઢܗճؼϞσϧ
    Ϟσϧɿઢܗճؼ ZBYC
    ɺύϥϝʔλɿB Cɺαϯϓϧ਺ɿ̎
    y = ax + b
    )ZQPUIFUJDBMJOMJFST
    *OMJFST
    ڐ༰ޡࠩ
    89/125

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  90. http://www.cse.psu.edu/~rtc12/CSE486/lecture15.pdf
    $SFEJU3PCFSU$PMMJOTIUUQXXXDTFQTVFEVdSUD$4&MFDUVSFQEG
    ྫɿઢܗճؼϞσϧ
    Ϟσϧɿઢܗճؼ ZBYC
    ɺύϥϝʔλɿB Cɺαϯϓϧ਺ɿ̎
    y = ax + b
    )ZQPUIFUJDBMJOMJFST
    *OMJFST
    ڐ༰ޡࠩ
    90/125

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  91. http://www.cse.psu.edu/~rtc12/CSE486/lecture15.pdf
    $SFEJU3PCFSU$PMMJOTIUUQXXXDTFQTVFEVdSUD$4&MFDUVSFQEG
    ྫɿઢܗճؼϞσϧ
    Ϟσϧɿઢܗճؼ ZBYC
    ɺύϥϝʔλɿB Cɺαϯϓϧ਺ɿ̎
    y = ax + b
    )ZQPUIFUJDBMJOMJFST
    *OMJFST
    ڐ༰ޡࠩ
    91/125

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  92. http://www.cse.psu.edu/~rtc12/CSE486/lecture15.pdf
    $SFEJU3PCFSU$PMMJOTIUUQXXXDTFQTVFEVdSUD$4&MFDUVSFQEG
    ྫɿઢܗճؼϞσϧ
    Ϟσϧɿઢܗճؼ ZBYC
    ɺύϥϝʔλɿB Cɺαϯϓϧ਺ɿ̎
    y = ax + b
    92/125

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  93. ⾣ ϞσϧύϥϝʔλΛܭࢉ͢ΔͨΊͷσʔλΛαϯϓϦϯά
    ⾣ Ϟσϧύϥϝʔλͷਪఆ
    ⾣ Ϟσϧͱ੔߹ੑͷ͋͏αϯϓϧΛJOMJFSTͱͯ͠Χ΢ϯτ͢Δ
    ⾣ ܁Γฦ͠ɻJOMJFST͕࠷େͱͳΔϞσϧύϥϝʔλΛճ౴͢Δ
    x0 = Ax
    ϞσϧɿΞϑΟϯม׵

    ύϥϝʔλɿΞϑΟϯࣸ૾ߦྻ"

    αϯϓϧ਺ɿ
    93/125

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  94. ⾣ ϞσϧύϥϝʔλΛܭࢉ͢ΔͨΊͷσʔλΛαϯϓϦϯά
    ⾣ Ϟσϧύϥϝʔλͷਪఆ
    ⾣ Ϟσϧͱ੔߹ੑͷ͋͏αϯϓϧΛJOMJFSTͱͯ͠Χ΢ϯτ͢Δ
    ⾣ ܁Γฦ͠ɻJOMJFST͕࠷େͱͳΔϞσϧύϥϝʔλΛճ౴͢Δ
    x0 = Ax
    ϞσϧɿΞϑΟϯม׵

    ύϥϝʔλɿΞϑΟϯࣸ૾ߦྻ"

    αϯϓϧ਺ɿ
    94/125

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  95. 3"/4"$ͷྫ ⾣ ϞσϧύϥϝʔλΛܭࢉ͢ΔͨΊͷσʔλΛαϯϓϦϯά
    ⾣ Ϟσϧύϥϝʔλͷਪఆ
    ⾣ Ϟσϧͱ੔߹ੑͷ͋͏αϯϓϧΛJOMJFSTͱͯ͠Χ΢ϯτ͢Δ
    ⾣ ܁Γฦ͠ɻJOMJFST͕࠷େͱͳΔϞσϧύϥϝʔλΛճ౴͢Δ
    ४උɿ͋Β͔͡Ί̎ը૾ͷରԠ఺Λ࠷ۙ๣୳ࡧʹΑΓٻΊ͓ͯ͘
    ͢΂ͯͷ*NBHFͷ%FTDSJQUPS͔Βɺ*NBHFʹ͓͚Δ%FTDSJQUPS
    ʹରͯ͠࠷ۙ๣Λ୳ࡧɻڑ཭͕͖͍͠஋ҎԼͷϙΠϯτͷΈ࢒͢ɻ
    95/125

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  96. ⾣ ϞσϧύϥϝʔλΛܭࢉ͢ΔͨΊͷσʔλΛαϯϓϦϯά
    ⾣ Ϟσϧύϥϝʔλͷਪఆ
    ⾣ Ϟσϧͱ੔߹ੑͷ͋͏αϯϓϧΛJOMJFSTͱͯ͠Χ΢ϯτ͢Δ
    ⾣ ܁Γฦ͠ɻJOMJFST͕࠷େͱͳΔϞσϧύϥϝʔλΛճ౴͢Δ
    Hypothetical inliers
    x0 = Ax
    ϞσϧɿΞϑΟϯม׵

    ύϥϝʔλɿΞϑΟϯࣸ૾ߦྻ"

    αϯϓϧ਺ɿ
    96/125

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  97. ⾣ ϞσϧύϥϝʔλΛܭࢉ͢ΔͨΊͷσʔλΛαϯϓϦϯά
    ⾣ Ϟσϧύϥϝʔλͷਪఆ
    ⾣ Ϟσϧͱ੔߹ੑͷ͋͏αϯϓϧΛJOMJFSTͱͯ͠Χ΢ϯτ͢Δ
    ⾣ ܁Γฦ͠ɻJOMJFST͕࠷େͱͳΔϞσϧύϥϝʔλΛճ౴͢Δ
    x0 = Ax
    ϞσϧɿΞϑΟϯม׵

    ύϥϝʔλɿΞϑΟϯࣸ૾ߦྻ"

    αϯϓϧ਺ɿ
    97/125

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  98. ⾣ ϞσϧύϥϝʔλΛܭࢉ͢ΔͨΊͷσʔλΛαϯϓϦϯά
    ⾣ Ϟσϧύϥϝʔλͷਪఆ
    ⾣ Ϟσϧͱ੔߹ੑͷ͋͏αϯϓϧΛJOMJFSTͱͯ͠Χ΢ϯτ͢Δ
    ⾣ ܁Γฦ͠ɻJOMJFST͕࠷େͱͳΔϞσϧύϥϝʔλΛճ౴͢Δ
    inliers count = 20
    x0 = Ax
    ϞσϧɿΞϑΟϯม׵

    ύϥϝʔλɿΞϑΟϯࣸ૾ߦྻ"

    αϯϓϧ਺ɿ
    98/125

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  99. ⾣ ϞσϧύϥϝʔλΛܭࢉ͢ΔͨΊͷσʔλΛαϯϓϦϯά
    ⾣ Ϟσϧύϥϝʔλͷਪఆ
    ⾣ Ϟσϧͱ੔߹ੑͷ͋͏αϯϓϧΛJOMJFSTͱͯ͠Χ΢ϯτ͢Δ
    ⾣ ܁Γฦ͠ɻJOMJFST͕࠷େͱͳΔϞσϧύϥϝʔλΛճ౴͢Δ
    x0 = Ax
    ϞσϧɿΞϑΟϯม׵

    ύϥϝʔλɿΞϑΟϯࣸ૾ߦྻ"

    αϯϓϧ਺ɿ
    99/125

    View Slide

  100. ⾣ ϞσϧύϥϝʔλΛܭࢉ͢ΔͨΊͷσʔλΛαϯϓϦϯά
    ⾣ Ϟσϧύϥϝʔλͷਪఆ
    ⾣ Ϟσϧͱ੔߹ੑͷ͋͏αϯϓϧΛJOMJFSTͱͯ͠Χ΢ϯτ͢Δ
    ⾣ ܁Γฦ͠ɻJOMJFST͕࠷େͱͳΔϞσϧύϥϝʔλΛճ౴͢Δ
    x0 = Ax
    ϞσϧɿΞϑΟϯม׵

    ύϥϝʔλɿΞϑΟϯࣸ૾ߦྻ"

    αϯϓϧ਺ɿ
    100/125

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  101. ⾣ ϞσϧύϥϝʔλΛܭࢉ͢ΔͨΊͷσʔλΛαϯϓϦϯά
    ⾣ Ϟσϧύϥϝʔλͷਪఆ
    ⾣ Ϟσϧͱ੔߹ੑͷ͋͏αϯϓϧΛJOMJFSTͱͯ͠Χ΢ϯτ͢Δ
    ⾣ ܁Γฦ͠ɻJOMJFST͕࠷େͱͳΔϞσϧύϥϝʔλΛճ౴͢Δ
    inliers count = 63
    x0 = Ax
    ϞσϧɿΞϑΟϯม׵

    ύϥϝʔλɿΞϑΟϯࣸ૾ߦྻ"

    αϯϓϧ਺ɿ
    101/125

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  102. ⾣ ϞσϧύϥϝʔλΛܭࢉ͢ΔͨΊͷσʔλΛαϯϓϦϯά
    ⾣ Ϟσϧύϥϝʔλͷਪఆ
    ⾣ Ϟσϧͱ੔߹ੑͷ͋͏αϯϓϧΛJOMJFSTͱͯ͠Χ΢ϯτ͢Δ
    ⾣ ܁Γฦ͠ɻJOMJFST͕࠷େͱͳΔϞσϧύϥϝʔλΛճ౴͢Δ
    inliers count = 110
    x0 = Ax
    ϞσϧɿΞϑΟϯม׵

    ύϥϝʔλɿΞϑΟϯࣸ૾ߦྻ"

    αϯϓϧ਺ɿ
    102/125

    View Slide

  103. ⾣ ϞσϧύϥϝʔλΛܭࢉ͢ΔͨΊͷσʔλΛαϯϓϦϯά
    ⾣ Ϟσϧύϥϝʔλͷਪఆ
    ⾣ Ϟσϧͱ੔߹ੑͷ͋͏αϯϓϧΛJOMJFSTͱͯ͠Χ΢ϯτ͢Δ
    ⾣ ܁Γฦ͠ɻJOMJFST͕࠷େͱͳΔϞσϧύϥϝʔλΛճ౴͢Δ
    inliers count = 162
    x0 = Ax
    ϞσϧɿΞϑΟϯม׵

    ύϥϝʔλɿΞϑΟϯࣸ૾ߦྻ"

    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

  104. ީิू߹͔ΒJOMJFSTDPVOUͰSFTDPSJOH
    ΠϯσοΫε͔Β

    ಘͨީิը૾
    *OMJFSTDPVOUॱͷ

    ߱ॱʹฒͼସ͑
    2VFSZ
    )PXSBI#SJEHF *OEJB

    4UPSZ#SJEHF "VTUSBMJB

    7JDLTCVSH#SJEHF 64

    104/125

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  105. ͦ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

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  106. ΞδΣϯμ
    ը૾ݕࡧ ಛఆ෺ମೝࣝ
    ʹ͍ͭͯ঺հ͠·͢ɻ
    106/125
    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

    View Slide

  107. ਂ૚ֶ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
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    ͷେ෯ͳվળ
    107/125

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  108. $POWPMVUJPOBM/FUXPSLT $//

    ϊʔυ͕ؒີ݁߹ͱͳΔ఻౷తͳ/FVSBM/FUXPSLTͱҟͳΓɺ
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    ͜ΕʹΑͬͯύϥϝʔλΛେ෯ʹ࡟ݮ͍ͯ͠Δɻ
    〜 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 〜
    ୯Ұͷ-BZFSʹ͓͚Δೖྗͱग़ྗͷؔ܎Λ

    ໛ࣜతʹදͨ͠΋ͷɻ
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    108/125
    ˢʹ఻౷తͳ//
    ˢʹ$// $//ͷೖྗ͸Ұ෦ͷύϥϝʔλʹରͯ͠ͷΈӨڹɻ

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  109. $//Ͱ&OEUP&OEʹֶश͞ΕΔΧʔωϧ
    $//Ͱֶशͨ͠$POWPMVUJPOͷ,FSOFMΛՄࢹԽͨ͠΋ͷɻ
    〜 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 〜
    *NBHFGSPN<,SJ[IFWTLZ>
    Τοδ΍#MPCʹ൓Ԡͦ͠͏ͳΧʔωϧ͔Βɺෳࡶͳ΋ͷ·Ͱଟ༷ɻ

    #MPCݕग़ثͰ༻͍ͨ-P(ͷΑ͏ͳΧʔωϧΛσʔλ͔ΒࣗಈͰशಘ͢Δɻ
    109/125

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  110. $//ͷશ݁߹૚ͷग़ྗΛ࢖͏<3B[BWJBO>
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    ྨࣅυϝΠϯͷը૾σʔληοτͰpOFUVOJOH͢Δͱɺ4*'5ΑΓྑ͍݁Ռʹɻ
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    110/125
    Conv Conv MP
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    ը૾ΛͭͷϕΫτϧͱͯ͠දݱͯ͠ϢʔΫϦουڑ཭Ͱݕࡧ͢Δɻ

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  111. 1Z5PSDI࣮૷ɿ
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    ˠLݸͷ,FSOFMͷ൓ԠΛผʑʹ%ʹQPPMJOH͢Δ 4QBUJBMlTVNzQPPMJOH

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

    View Slide

  112. ."$<5PMJBT>
    1Z5PSDI࣮૷ɿ
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    ˠLݸͷ,FSOFMͷ൓ԠΛผʑʹ%ʹQPPMJOH͢Δ 4QBUJBMNBYQPPMJOH

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

    ˞આ໌ͷศ্ٓɺ7((Λ༻͍͍ͯΔ

    112/125
    *NBHF$SFEJU:BOOJT"WSJUIJTzIUUQTTJGEMWHJUIVCJPTMJEFTJOEFYQEG

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  113. 1Z5PSDI࣮૷ɿ
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    ࠷ޙͷ$POWPMVUJPOMBZFSͷPVUQVUʹରͯ͠ɺ

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    (F.<3BEFOPWJ㶛>
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    x.clamp(min=eps).pow(p),

    (x.size(-2), x.size(-1))

    ).pow(1./p)






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    113/125
    *NBHF$SFEJU:BOOJT"WSJUIJTzIUUQTTJGEMWHJUIVCJPTMJEFTJOEFYQEG

    View Slide

  114. %&-' $//CBTFE-PDBMEFTDSJQUPS

    ࠷ۙͷϕϯνϚʔΫ<3BEFOPWJ㶛C>Ͱ͸$//CBTFE-PDBM
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    Β$POWPMVUJPOMBZFSͱ"UUFOUJPOMBZFSΛֶश͢Δɻ
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    -BOENBSLͰ͸ͳ͍ਓͷإͳͲ

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    *NBHFDSFEJU)ZFPOXPP/PIIUUQTBSYJWPSHQEGQEG
    114/125

    View Slide

  115. 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

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  116. 116/125

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  117. $713XPSLTIPQίϯϖςΟγϣϯ
    ⾣ ϥϯυϚʔΫ ཱྀߦऀͳͲʹͱͬͯ৔ॴΛಛఆ͢Δͷʹ໾ཱͭ໨ҹ
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    ⾣ ΠϯσοΫεը૾͔Β4*'5Λநग़͢Δͱ.ݸ ԯݸ

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    117/125
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  118. ্Ґ͸$//CBTFE(MPCBMEFTDSJQUPS

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    20
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    118/125
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  119. 3&."1<$74417JTVBM"UPNT5FBN NBOVTDSJQUTVCNJUUFE
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    ⾣ 0YGPSE 1BSJTͳͲ,BHHMFҎ֎ͷධՁσʔληοτͰ΋ൺֱ͞Ε͓ͯΓଞΛѹ౗͍ͯ͠Δɻ
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    119/125

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  120. View Slide

  121. ·ͱΊʗࡶײ
    w ݹయతΞϓϩʔνʹΑΔख๏ͱ$//ϕʔεͷΞϓϩʔν
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    w $//ϕʔεͷ(MPCBMEFTDSJQUPS͸୯ҰͷϕΫτϧͰߴ͍ݕࡧਫ਼౓
    w 4JBNFTF5SJQMFUOFUXPSLͰ'JOFUVOJOHʹΑΔਫ਼౓ఈ্͕͛Մೳ
    w ίϯςετΛ௨ͯ͡ͷࡶײ
    w େن໛ʹͳΔͱ-PDBMEFTDSJQUPS͸σʔλ਺͕๲େʹͳΔɻඞཁͱ͢Δܭࢉίετ΍Ϧιʔ
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    w زԿతͳݕূʹΑͬͯಘΒΕΔ݁Ռ͸ඇৗʹਫ਼౓͕ߴ͍ͨΊɺ-PDBMEFTDSJQUPSΛ࢖Θͣ
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    w (MPCBMEFTDSJQUPSͷ݁ՌͰ͸ࢁͳͲͷࣗવ؀ڥͷࣸਅʹର͢Δ3FDBMM͕-PDBMEFTDSJQUPS
    ͱൺֱͯ͠ߴ͘ɺ͜Ε͕શମͷείΞʹӨڹΛ༩͑ͨͷͰ͸ͳ͍͔ͱࢥΘΕΔ ཁݕূ

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

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