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

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ը૾ݕࡧ ಛఆ෺ମೝࣝ ݹయख๏ɺϚονϯάɺਂ૚ֶशɺ,BHHMF େࡕେֶେֶӃ৘ใՊֶݚڀՊϏοάσʔλղੳ ήετ࿮ߨٛ খቌߞฏ !TNMZ גࣜձࣾϦΫϧʔτςΫϊϩδʔζ "5- 1/125

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

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

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

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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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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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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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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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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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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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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

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-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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Ԡ༻ྫɿը૾ͷ๓͍߹Θͤ *NBHF4UJUDIJOH ࢹ఺Λগͣͭͣ͠Βͨ͠࿈ଓࣸਅ͔ΒɺύϊϥϚࣸਅΛ࡞੒͢Δɻ $SFEJUIUUQBJTUBOGPSEFEVdTZZFVOHDWXFCUVUPSJBMIUNM 18/125

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

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

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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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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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scale f(I, ) $SFEJU5JOOF5VZUFMBBSTWJBIUUQTBHTDTVOJLMEFpMFBENJOJOG@BHTEJQTT%*1@44@MFD@$PSOFST@#MPCTQEG  23/125

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scale f(I, ) $SFEJU5JOOF5VZUFMBBSTWJBIUUQTBHTDTVOJLMEFpMFBENJOJOG@BHTEJQTT%*1@44@MFD@$PSOFST@#MPCTQEG  24/125

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scale f(I, ) $SFEJU5JOOF5VZUFMBBSTWJBIUUQTBHTDTVOJLMEFpMFBENJOJOG@BHTEJQTT%*1@44@MFD@$PSOFST@#MPCTQEG  25/125

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scale f(I, ) $SFEJU5JOOF5VZUFMBBSTWJBIUUQTBHTDTVOJLMEFpMFBENJOJOG@BHTEJQTT%*1@44@MFD@$PSOFST@#MPCTQEG  26/125

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scale f(I, ) $SFEJU5JOOF5VZUFMBBSTWJBIUUQTBHTDTVOJLMEFpMFBENJOJOG@BHTEJQTT%*1@44@MFD@$PSOFST@#MPCTQEG  27/125

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scale f(I, ) $SFEJU5JOOF5VZUFMBBSTWJBIUUQTBHTDTVOJLMEFpMFBENJOJOG@BHTEJQTT%*1@44@MFD@$PSOFST@#MPCTQEG  28/125

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

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4UFQεέʔϧۭؒͷ࡞੒ LoG LoG で畳み込み 37/125

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4UFQεέʔϧۭؒͷ࡞੒ LoG LoG で畳み込み 38/125

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4UFQεέʔϧۭؒͷ࡞੒ LoG LoG で畳み込み 39/125

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4UFQεέʔϧۭؒͷ࡞੒ LoG LoG で畳み込み 40/125

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4UFQεέʔϧۭؒͷ࡞੒ LoG LoG で畳み込み 41/125

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= 1.00 4UFQεέʔϧۭؒͷ࡞੒ 42/125

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= 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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= 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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= 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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= 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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= 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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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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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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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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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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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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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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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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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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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

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

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

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

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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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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

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

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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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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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ͦ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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ͦ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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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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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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-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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#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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సஔΠϯσοΫε ௥Ճ visual word visual word visual word λςɿWJTVBMXPSE*%ɺϤίɿJNBHF*% 72/125 4MJEFDSFEJU:BOOJT"WSJUIJTzIUUQTTJGEMWHJUIVCJPTMJEFTJOEFYQEG

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

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

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

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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

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)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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େ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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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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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

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

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

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⾣ ϞσϧύϥϝʔλΛܭࢉ͢ΔͨΊͷσʔλΛαϯϓϦϯά ⾣ Ϟσϧύϥϝʔλͷਪఆ ⾣ Ϟσϧͱ੔߹ੑͷ͋͏αϯϓϧΛJOMJFSTͱͯ͠Χ΢ϯτ͢Δ ⾣ ܁Γฦ͠ɻJOMJFST͕࠷େͱͳΔϞσϧύϥϝʔλΛճ౴͢Δ x0 = Ax ϞσϧɿΞϑΟϯม׵  ύϥϝʔλɿΞϑΟϯࣸ૾ߦྻ"  αϯϓϧ਺ɿ 94/125

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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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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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⾣ ϞσϧύϥϝʔλΛܭࢉ͢ΔͨΊͷσʔλΛαϯϓϦϯά ⾣ Ϟσϧύϥϝʔλͷਪఆ ⾣ Ϟσϧͱ੔߹ੑͷ͋͏αϯϓϧΛJOMJFSTͱͯ͠Χ΢ϯτ͢Δ ⾣ ܁Γฦ͠ɻJOMJFST͕࠷େͱͳΔϞσϧύϥϝʔλΛճ౴͢Δ x0 = Ax ϞσϧɿΞϑΟϯม׵  ύϥϝʔλɿΞϑΟϯࣸ૾ߦྻ"  αϯϓϧ਺ɿ 97/125

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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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⾣ ϞσϧύϥϝʔλΛܭࢉ͢ΔͨΊͷσʔλΛαϯϓϦϯά ⾣ Ϟσϧύϥϝʔλͷਪఆ ⾣ Ϟσϧͱ੔߹ੑͷ͋͏αϯϓϧΛJOMJFSTͱͯ͠Χ΢ϯτ͢Δ ⾣ ܁Γฦ͠ɻJOMJFST͕࠷େͱͳΔϞσϧύϥϝʔλΛճ౴͢Δ x0 = Ax ϞσϧɿΞϑΟϯม׵  ύϥϝʔλɿΞϑΟϯࣸ૾ߦྻ"  αϯϓϧ਺ɿ 99/125

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⾣ ϞσϧύϥϝʔλΛܭࢉ͢ΔͨΊͷσʔλΛαϯϓϦϯά ⾣ Ϟσϧύϥϝʔλͷਪఆ ⾣ Ϟσϧͱ੔߹ੑͷ͋͏αϯϓϧΛJOMJFSTͱͯ͠Χ΢ϯτ͢Δ ⾣ ܁Γฦ͠ɻJOMJFST͕࠷େͱͳΔϞσϧύϥϝʔλΛճ౴͢Δ x0 = Ax ϞσϧɿΞϑΟϯม׵  ύϥϝʔλɿΞϑΟϯࣸ૾ߦྻ"  αϯϓϧ਺ɿ 100/125

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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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⾣ ϞσϧύϥϝʔλΛܭࢉ͢ΔͨΊͷσʔλΛαϯϓϦϯά ⾣ Ϟσϧύϥϝʔλͷਪఆ ⾣ Ϟσϧͱ੔߹ੑͷ͋͏αϯϓϧΛJOMJFSTͱͯ͠Χ΢ϯτ͢Δ ⾣ ܁Γฦ͠ɻJOMJFST͕࠷େͱͳΔϞσϧύϥϝʔλΛճ౴͢Δ inliers count = 110 x0 = Ax ϞσϧɿΞϑΟϯม׵  ύϥϝʔλɿΞϑΟϯࣸ૾ߦྻ"  αϯϓϧ਺ɿ 102/125

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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

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ީิू߹͔ΒJOMJFSTDPVOUͰSFTDPSJOH ΠϯσοΫε͔Β  ಘͨީิը૾ *OMJFSTDPVOUॱͷ  ߱ॱʹฒͼସ͑ 2VFSZ )PXSBI#SJEHF *OEJB 4UPSZ#SJEHF "VTUSBMJB 7JDLTCVSH#SJEHF 64 104/125

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ͦ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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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

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ਂ૚ֶ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

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$POWPMVUJPOBM/FUXPSLT $// ϊʔυ͕ؒີ݁߹ͱͳΔ఻౷తͳ/FVSBM/FUXPSLTͱҟͳΓɺ $POWPMVUJPOMBZFSΛ༻͍Δ͜ͱͰεύʔεͳ݁߹ʹΑͬͯߏ੒͞ΕΔɻ ͜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 $SFEJU(PPEGFMMPXFUBM%FFQ-FBSOJOH CPPL 108/125 ˢʹ఻౷తͳ// ˢʹ$// $//ͷೖྗ͸Ұ෦ͷύϥϝʔλʹରͯ͠ͷΈӨڹɻ  ؔ਺ͷදݱྗ͸૚Λ૿΍͢͜ͱͰΧόʔɻ

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$//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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$//ͷશ݁߹૚ͷग़ྗΛ࢖͏<3B[BWJBO> Ϋϥε෼ྨͷͨΊͷ$//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

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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

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."$<5PMJBT> 1Z5PSDI࣮૷ɿ 7(( YY F.max_pool2d(x, (x.size(-2), x.size(-1))) 1PPMJOHͷࣜɿ *OQVU͸࠷ޙͷ$POWPMVUJPOMBZFSͷ  0VUQVUͰYY Y $POWPMVUJPOMBZFSʹΑͬͯಘͨہॴతͳಛ௃Λ·ͱΊΔɻ  ˠLݸͷ,FSOFMͷ൓ԠΛผʑʹ%ʹQPPMJOH͢Δ 4QBUJBMNBYQPPMJOH ʢNBYQPPMJOHͳͷͰɺͦΕͧΕͷʹΑΔ,FSOFMʹΑΔ൓Ԡͷ༗ແͷΑ͏ͳදݱʣ LFSOFMTJ[F ݸʑͷ,FSOFMͷશମ ˞આ໌ͷศ্ٓɺ7((Λ༻͍͍ͯΔ 112/125 *NBHF$SFEJU:BOOJT"WSJUIJTzIUUQTTJGEMWHJUIVCJPTMJEFTJOEFYQEG

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1Z5PSDI࣮૷ɿ 1PPMJOHͷࣜɿ ࠷ޙͷ$POWPMVUJPOMBZFSͷPVUQVUʹରͯ͠ɺ  4QBUJBMHFOFSBMJ[FENFBOQPPMJOHɻ-QOPSNͷΑ͏ͳQΛύϥϝʔλͱͨ͠ҰൠԽɻ (F.<3BEFOPWJ㶛> F.avg_pool2d(  x.clamp(min=eps).pow(p),  (x.size(-2), x.size(-1))  ).pow(1./p) gem 7(( YY Q@L͸ֶशՄೳͳϞσϧύϥϝʔλ ˞આ໌ͷศ্ٓɺ7((Λ༻͍͍ͯΔ 113/125 *NBHF$SFEJU:BOOJT"WSJUIJTzIUUQTTJGEMWHJUIVCJPTMJEFTJOEFYQEG

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

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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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$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

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্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

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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

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