Lucas-Kanade ヒストグラムマッチングによる対応点を用いない自動色補正 / Auto Color Correction without Correspondence by Lucas-Kanade Histogram Matching paper

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1. Lucas-Kanade ώετάϥϜϚονϯάʹΑΔରԠ఺Λ༻͍ͳ͍ࣗಈ৭ิਖ਼ দӬ ྗ גࣜձࣾ๎ӫ ࠤ૔ݚڀ։ൃηϯλʔ E-mail: matsunaga@for-a.co.jp Abstract ಉҰγʔϯΛҟͳΔࢹ఺͔ΒࡱӨͨ͠ը૾ؒͷΧϥʔ ϚονϯάΛ໨తͱͯ͠ɼըૉ஋ͷ 1 ࣍ݩً౓ɾ2 ࣍ݩ ৭ࠩɼ͋Δ͍͸ 3 ࣍ݩ RGB ώετάϥϜΛϚονϯά ͤ͞Δ͜ͱʹΑΓ৭ิਖ਼ͷࣗಈԽΛߦ͏ɽըૉ஋ώε τάϥϜΛը૾ͱݟͳͤ͹ɼը૾ؒͷزԿֶతͳҐஔ ߹Θͤʹ༻͍ΒΕΔ Lucas-Kanade ΞϧΰϦζϜΛద ༻͢Δ͜ͱ͕Ͱ͖Δɽ൓෮ຖʹϔοηߦྻΛܭࢉ͠ͳ ͍ٯ݁߹ Lucas-Kanade ΞϧΰϦζϜͷߋ৽Λ 1 ࣍ۙ ࣅͨۙ͠ࣅٯ݁߹ Lucas-Kanade ΞϧΰϦζϜʹϦʔ ୅਺ʹΑΔࢦ਺ࣸ૾Λಋೖ͢Δɽ͢΂ͯͷॲཧ͸ɼώ ετάϥϜಛ௃ۭؒʹ͓͚ΔϚονϯάͰ͋Γɼը૾ ؒͷزԿֶతͳҐஔ߹ΘͤΛߦΘͳ͍͚ͩͰͳ͘ɼԿ Βͷಛ௃఺ͷநग़΍ରԠ෇͚΋ඞཁͱ͠ͳ͍ɽ 1 ͸͡Ίʹ ࣍ੈ୅ςϨϏ์ૹͱͯ͠ͷ 4K/8K ʢεʔύʔϋΠϏδ ϣϯʣ௒ߴਫ਼ࡉө૾͸ɼղ૾౓͚ͩͰ͸ͳ͘ɼ޿৭Ҭɼߴ ϑϨʔϜϨʔτɼߴϏοτਂ౓͕ ITU-R קࠂ BT.2020 1 ͱͯ͠نఆ͞Ε͍ͯΔɽө૾ͷ໌Δ͞Λ֦ு͢ΔϋΠ μΠφϛοΫϨϯδʢHDRʣ΋ɼ֦ு͞Εͨ৴߸Ϩϕ ϧΛѹॖ͢ΔͨΊͷඇઢܗͷ఻ୡؔ਺͕ࠃࡍඪ४ͱ͠ ͯنఆ͞Εͨ2ɽ ৭Ҭม׵΍ HDR ม׵ΛؚΉ৭ิਖ਼ॲཧɼ͋Δ͍͸Χ ϥʔάϨʔσΟϯάʢColor gradingʣͱݺ͹Ε͍ͯΔ ॲཧ͸ө૾੍࡞ͷجຊͰ͋Δɽࢀর൘ʢΧϥʔνϟʔτ [17]ʣΛ༻͍ͨΧϝϥͷ৭ௐ੔͸ɼ৭ߍਖ਼ʢΧϥʔΩϟ ϦϒϨʔγϣϯʣͱͯ͠ɼҟͳΔػछͷΧϝϥؒͷ৭ ߹Θͤ͸ɼΧϥʔϚονϯάͱͯ͠஌ΒΕ͍ͯΔɽ ৭ิਖ਼ॲཧͱͯ͠͸ɼদӬΒ [15] ͸ɼ࠶ࡱϞχλ΍ ෳ਺୆ͷΧϝϥؒͷ৭Λ߹ΘͤΔͨΊʹɼઌ಄ϑϨʔ ϜʹࡱӨͨ͠ج४ͱͳΔΧϥʔνϟʔτΛࣗಈೝࣝ͠ 1 Recommendation ITU-R BT.2020-1, Parameter values for ultra-high definition television systems for production and in- ternational programme exchange (2014) 2 Recommendation ITU-R BT.2100, Image parameter values for high dynamic range television for use in production and international programme exchange (2016) ਤ 1 ࢀর൘ʢΧϥʔνϟʔτʣΛࡱӨͯ͠ɼΧϝϥ ؒͷ৭߹ΘͤΛߦ͏ [15, 13, 14]ɽ ͯɼ؍ଌޡࠩΛߟྀͯ͠৭ิਖ਼ύϥϝʔλΛ࠷దʹਪ ఆ͢Δͱͱ΋ʹɼΨϚοτޡࠩ [18] ؚ͕·Ε͍ͯΔө ૾ʹରͯ͠΋ɼϨϕϧ੍໿෇͖࠷దਪఆͱϞσϧબ୒ Λ૊Έ߹ΘͤΔ͜ͱʹΑͬͯɼଥ౰ͳ৭ิਖ਼݁ՌΛಘ ΔͨΊͷํ๏Λࣔͨ͠ɽ দӬ [13] ͸ɼࢀর൘ʢΧϥʔνϟʔτʣΛࡱӨͨ͠ը ૾͔Β RGB ըૉ஋σʔλΛநग़ͯ͠ɼ؍ଌޡࠩͷੑ࣭ Λߟྀͨ͠౷ܭతʹ࠷దͳ௒ਫ਼౓͘Γ͜Έ๏ [7] ʹΑΓ 3 ࣍ݩ RGB ৭ۭؒʹ͓͚Δ 3 ࣍ݩزԿֶม׵Λਪఆ͠ ͨɽͦͯ͠ɼෳ਺ͷҟͳΔࣗ༝౓ͷزԿֶม׵Ϟσϧͷ ਪఆ݁Ռ͔ΒɼزԿֶతϞσϧબ୒ [4] ʹΑΓɼϞσϧ ͷෳࡶ͞ͱ౰ͯ͸·ΓͷΑ͞Λόϥϯε͢Δ࠷దͳม ׵ϞσϧΛܾఆ͠ɼબ୒͞Εͨ 3 ࣍ݩزԿֶม׵ʹΑ Δ৭ิਖ਼ॲཧΛ 3 ࣍ݩϧοΫΞοϓςʔϒϧʢ3DLUTʣ ิؒ [8] ʹΑΓܭࢉͯ͠ɼҟͳΔػछͷ༷ʑͳσδλϧ ΧϝϥؒͷΧϥʔϚονϯάͷ݁ՌΛࣔͨ͠ɽ দӬ [14] ͸ɼ௒ਫ਼౓͘Γ͜Έ๏ʹΑΓ࠷దʹਪఆ͠ ͨ৭ิਖ਼ύϥϝʔλ݁Ռʹରͯ͠ɼࣄޙతͳิਖ਼Λߦ ͏͜ͱʹΑΓɼݫີͳϗϫΠτόϥϯεΛ࣮ݱ͢Δͱ ͱ΋ʹɼϨϕϧ੍໿Λ՝ͨ͠৔߹ͷߴࣗ༝౓ͳ৭ิਖ਼ Ϟσϧͷਪఆʹ͓͚Δա౰ͯ͸ΊΛزԿֶతϞσϧબ ୒ʹΑΓճආͨ͠3ɽ ͔͠͠ɼ࣮ࡍͷ৭ิਖ਼Λߦ͏৔໘Ͱ͸ɼΧϥʔνϟʔ τΛઃஔͯ͠ɼ৭ߍਖ਼͢Δ͜ͱ͕೉͍͠৔߹΋͋Δͩ Ζ͏ɽͦ͜ͰɼຊݚڀͰ͸ɼΧϥʔνϟʔτΛ༻͍ͣ ʹɼࡱӨͨ͠γʔϯը૾ؒͰΧϥʔϚονϯάΛߦ͏ ͜ͱΛߟ͑Δʢਤ 2ʣ ɽ SIFT ࡞༻ૉ [9] ʹΑΓಛ௃఺ͷநग़Λߦ͍ɼͦͷ఺ͷ RGB ஋Λ༻͍ͯ৭ิਖ਼Λߦͬͨݚڀ͕͋Δ [22, 2, 23]ɽ 3 [15] Ͱ͸ɼϨϕϧ੍໿Λ՝ͨ͠৭ิਖ਼Ϟσϧͷਪఆʹ͓͚Δա ౰ͯ͸ΊΛزԿֶతϞσϧબ୒ʹΑΓճආ͢Δํ๏ʹ͍ͭͯ͸ɼ؆ қͳ 1 ࣍ݩً౓ิਖ਼ͷ਺஋γϛϡϨʔγϣϯྫΛࣔͨ͠ͷΈͰ͋Δɽ
2. ͔͠͠ɼը૾தͷಛ௃఺͸ɼ“ըૉ஋” σʔλͱͯ͠͸ ద੾Ͱ͸ͳ͍ɽͳͥͳΒɼ෺ମʹ͓͚ΔίʔφʔɼΤο δ౳ͷಛ௃఺ͷ “ըૉ஋” ͸എܠͷӨڹΛड͚Δɽը૾ ѹॖʹΑΔϊΠζͷӨڹ΋ड͚΍͍͢ɽ৭ิਖ਼ͷͨΊ ʹ͸ɼͰ͖Δ͚ͩฏୱͳྖҬʹ͓͚Δ “ըૉ஋” Λσʔ λͱͯ͠༻͍Δ͜ͱ͕๬·͍͠ɽ দӬΒ [16] ͸ɼ3D ө૾ΛࡱӨ͢Δ 2 ୆ͷΧϝϥؒͷ ΧϥʔϚονϯάΛߦ͏ͨΊʹɼΧϥʔνϟʔτΛ༻ ͍ͣʹɼࠨӈ 2 ຕͷը૾ؒͷ RGB ຖͷώετάϥϜΛ Ϛονϯάͨ͠ɽReinhard Β [19] ͸ɼը૾ؒͷݟͨ໨ ͷ৭Λଗ͑ΔͨΊʹɼը૾Λ LMS ৭ۭؒʹม׵ͯ͠ɼ ͦΕΒͷฏۉ஋ɾඪ४ภࠩ஋Λଗ͑ΔॲཧΛߦͬͨɽ͍ ͣΕͷ৔߹΋ɼ৭ิਖ਼ͷϞσϧ͸ɼRGB/LMS ຖͷ 1 ࣍ݩΞϑΟϯม׵Ͱ͋Γɼຊ࿦จͰ͸ɼ͜ΕΛ͞Βʹߴ ࣍ݩɾߴࣗ༝౓ͳิਖ਼Ϟσϧʹ֦ு͢Δ͜ͱΛߟ͑Δɽ ຊ࿦จͰ͸ɼಉҰγʔϯΛҟͳΔࢹ఺͔ΒࡱӨͨ͠ ը૾ؒͷΧϥʔϚονϯάΛ໨తͱͯ͠ɼըૉ஋ͷ 1 ࣍ ݩً౓ɾ2 ࣍ݩ৭ࠩɼ͋Δ͍͸ 3 ࣍ݩ RGB ώετάϥ ϜΛϚονϯάͤ͞Δ͜ͱʹΑΓ৭ิਖ਼ͷࣗಈԽΛߦ ͏ɽըૉ஋ώετάϥϜΛը૾ͱݟͳͤ͹ɼը૾ؒͷ زԿֶతͳҐஔ߹Θͤʹ༻͍ΒΕΔ Lucas-Kanade Ξ ϧΰϦζϜΛద༻͢Δ͜ͱ͕Ͱ͖Δɽ൓෮ຖʹϔοη ߦྻΛܭࢉ͠ͳ͍ٯ݁߹ Lucas-Kanade ΞϧΰϦζϜ ͷߋ৽Λ 1 ࣍ۙࣅͨۙ͠ࣅٯ݁߹ Lucas-Kanade Ξϧ ΰϦζϜʹϦʔ୅਺ʹΑΔࢦ਺ࣸ૾Λಋೖ͢Δɽ͢΂ ͯͷॲཧ͸ɼώετάϥϜಛ௃ۭؒʹ͓͚ΔϚονϯ άͰ͋Γɼը૾ؒͷزԿֶతͳҐஔ߹ΘͤΛߦΘͳ͍ ͚ͩͰͳ͘ɼԿΒͷಛ௃఺ͷநग़΍ରԠ෇͚΋ඞཁͱ ͠ͳ͍ɽ ຊ࿦จͷߏ੒͸ɼ2 ষͰɼزԿֶม׵ʹΑΔ৭ิਖ਼Ϟ σϧͱͯ͠ͷ 1 ࣍ݩً౓ɼ2 ࣍ݩ৭ࠩɼͦͯ͠ɼ3 ࣍ݩ RGB ΞϑΟϯม׵ิਖ਼ϞσϧΛఆٛ͢Δɽ3 ষͰɼը૾ ؒͷزԿֶతͳҐஔ߹Θͤʹ༻͍ΒΕΔ Lucas-Kanade ΞϧΰϦζϜɼ͓Αͼͦͷٯ݁߹ɼۙࣅٯ݁߹ɼͦ͠ ͯɼϦʔ୅਺ʹΑΔࢦ਺ࣸ૾Λಋೖͨ͠ࢦ਺ࣸ૾ٯ݁ ߹ Lucas-Kanade ΞϧΰϦζϜʹ͍ͭͯઆ໌͢Δɽ4 ষ Ͱɼը૾γϛϡϨʔγϣϯ࣮ݧΛߦ͍ɼ5 ষͰవΊΔɽ 2 ৭ิਖ਼Ϟσϧ 1 ࣍ݩً౓/2 ࣍ݩ৭ࠩ/3 ࣍ݩ RGB ώετάϥϜϚο νϯάʹΑΔ৭ิਖ਼ʹ͸ɼ࣍ͷزԿֶม׵ϞσϧΛ༻ ͍Δɽ • 1 ࣍ݩً౓ΞϑΟϯม׵ิਖ਼Ϟσϧ y′ = (1 + p1 )y + p2 . (1) • 2 ࣍ݩ৭ࠩΞϑΟϯม׵ิਖ਼Ϟσϧ c′ b = (1 + p1 )cb + p2 cr + p3 , (2) c′ r = p4 cb + (1 + p5 )cr + p6 . (3) ਤ 2 ΧϥʔνϟʔτΛ༻͍ͣʹɼಉҰγʔϯΛҟͳ Δࢹ఺͔ΒࡱӨͨ͠ը૾ؒͰΧϥʔϚονϯάΛߦ͏ɽ • 3 ࣍ݩ RGB ΞϑΟϯม׵ิਖ਼Ϟσϧ r′ = (1 + p1 )r + p2 g + p3 b + p4 , (4) g′ = p5 r + (1 + p6 )g + p7 b + p8 , (5) b′ = p9 r + p10 g + (1 + p11 )b + p12 . (6) ΞϑΟϯม׵Λࢪͯ͠΋௚ઢੑ΍ฏ໘ੑ͸อͨΕΔɽ ͢ͳΘͪɼಉҰ௚ઢ্ͷ఺͸ಉҰ௚ઢ্ͷ఺ʹࣸ૾͞ ΕɼಉҰฏ໘্ͷ఺͸ಉҰฏ໘্ͷ఺ʹࣸ૾͞ΕΔɽ֤ ෦෼ͷ௕͞ͷൺ΋อͨΕΔɽͦͷ݁Ռɼฏߦͳ௚ઢ͸ ฏߦͳ௚ઢʹɼฏߦͳฏ໘͸ฏߦͳฏ໘ʹࣸ૾͞ΕΔɽ ͔͠͠ɼεέʔϧ΍֯౓͸มԽ͢ΔͷͰɼͨͱ͑͹ཱ ํମ͸ฏߦ࿡໘ମʹͳΔ [3, 7]ɽਤ 3 ʹ 3 ࣍ݩزԿֶม ׵ʹΑΔཱํମͷมܗΛࣔ͢ɽ ը૾ͷ৭Λදݱ͢Δํ๏ͱͯ͠ɼRGB ৭ۭ͕ؒ޿͘ ࢖ΘΕ͍ͯΔ͕ɼө૾৴߸Ͱ͸ɼਓؒͷࢹ֮ಛੑΛߟ ًྀͨ͠౓৭ࠩ YCbCr ͕༻͍ΒΕ͍ͯΔɽ໌Δ͞Λද ً͢౓৴߸ Y ͱ৭߹͍Λද͢৭ࠩ৴߸ CbCr ͔ΒͳΓɼ ਓؒͷࢹ֮͸ɼ໌Δ͞ʹରͯ͠৭ͷײ౓͕௿͍͜ͱ͔ Βɼਫฏɾਨ௚ํ޲ͷղ૾౓ΛؒҾ͘͜ͱʹΑΓɼ఻ૹɾ ஝ੵ౳ʹֻ͔ΔίετΛ௿ݮ͍ͯ͠Δɽ৭ࠩ৴߸ CbCr ͸ɼͦΕͧΕɼ੨৭ B ͔Βً౓஋ Y ΛҾ͍ͨ B − Y ɼ ੺৭ R ͔Βً౓஋ Y ΛҾ͍ͨ R − Y ͕ [−0.5, 0.5] ۠ ؒʹͳΔΑ͏ʹ܎਺Λֻ͚ͨ΋ͷͰ͋Δɽ 3 ώετάϥϜը૾ʹର͢ΔLucas-Kanade ΞϧΰϦζϜ 3.1 Lucas-Kanade ώετάϥϜϚονϯά ըૉ஋ʹΑΔώετάϥϜΛը૾ͱݟͳͤ͹ɼը૾ ؒͷزԿֶతͳҐஔ߹Θͤʹ༻͍ΒΕΔ Lucas-Kanade ΞϧΰϦζϜ [10, 1] Λద༻͢Δ͜ͱ͕Ͱ͖ΔɽLucas- Kanade ΞϧΰϦζϜ͸ըૉΛ௚઀ॲཧ͢ΔྖҬϕʔε ͷख๏Ͱ͋ΓɼԿΒͷը૾ಛ௃΍ରԠ෇͚Λඞཁͱ͠ ͳ͍ɽೖྗώετάϥϜը૾ hin(x) Λج४ώετάϥ Ϝը૾ href (x) ʹ߹ΘͤΔɽ͜͜Ͱɼ1 ࣍ݩً౓ώετ άϥϜͷ৔߹͸ɼx = (y, 1)⊤ Ͱ͋Γɼ2 ࣍ݩ৭ࠩώε τάϥϜ͸ɼx = (cb , cr , 1)⊤, 3 ࣍ݩ RGB ώετάϥ Ϝ͸ɼx = (r, g, b, 1)⊤ Ͱ͋ΓɼͦΕͧΕ “ըૉ஋” Ͱ ͋Δɽ ͕ͨͬͯ͠ɼLucas-Kanade ΞϧΰϦζϜ͸ɼج४ώ ετάϥϜը૾ href ͱج४ώετάϥϜը૾ͷ “ըૉ ஋” ࠲ඪʹม׵ͨ͠ೖྗώετάϥϜը૾ hin ͷؒͷ ࣍ͷΑ͏ͳࠩ෼ೋ৐૯࿨ʢSum of Squared Difference,
3. ਤ 3 3 ࣍ݩزԿֶม׵ɽ(a) ฒਐɼ(b) ߶ମɼ(c) ૬ࣅɼ(d) ΞϑΟϯɼ(e) ࣹӨɽ SSDʣΛ࠷খԽ͢Δ΋ͷͰ͋Δɽ ∑ x (hin(W (x; p))−href (x))2 . (7) ͜͜ͰɼW (x; p) ͸ “ώετάϥϜը૾” ͷزԿֶม ׵Ͱ͋Γɼp = (p1 , . . . , pn )⊤ ͸ม׵ύϥϝʔλͰ͋Δɽ ྫ͑͹ɼ3 ࣍ݩ RGB ΞϑΟϯม׵ͷ৔߹ɼ W (x; p)=      1 + p1 p2 p3 p4 p5 1 + p6 p7 p8 p9 p10 1 + p11 p12 0 0 0 1           r g b 1      , (8) Ͱ͋Δ4ɽ͍·ɼࣜ (7) ʹ͓͍ͯɼp → p + ∆p ͱઁಈ ͨ͠ͱ͢Δͱɼ ∑ x (hin(W (x; p+∆p))−href (x))2 , (9) Ͱ͋Γɼ͜ΕΛςΠϥʔల։͢Δͱɼ࣍ͷΑ͏ʹͳΔɽ ∑ x ( hin(W (x; p)) + ∇hin ∂W ∂p ∆p − href (x) )2 . (10) 3 ࣍ݩ RGB ৭ۭؒͷ৔߹ɼ∇hin = (∂hin/∂r, ∂hin/∂g, ∂hin/∂b, 1) ≡ (hin r , hin g , hin b , 1) ͸ೖྗώετάϥϜը૾ hin ͷ W (x; p) Ͱͷޯ഑Ͱ͋Γɼ∂W /∂p ͸ϠίϏߦྻ ͱݺ͹ΕɼW (x; p) = (Wr (x; p), Wg (x; p), Wb (x; p), W1 (x; p))⊤ ͱ͢Δͱɼ ∂W ∂p =              ∂Wr ∂p1 . . . ∂Wr ∂pn ∂Wg ∂p1 . . . ∂Wg ∂pn ∂Wb ∂p1 . . . ∂Wb ∂pn ∂W1 ∂p1 . . . ∂W1 ∂pn              , (11) Ͱ͋Δɽ3 ࣍ݩ RGB ΞϑΟϯม׵ͷ৔߹ʹ͸ɼ࣍ͷΑ ͏ʹͳΔɽ ∂W ∂p =      r g b 1 0 0 0 0 0 0 0 0 0 0 0 0 r g b 1 0 0 0 0 0 0 0 0 0 0 0 0 r g b 1 0 0 0 0 0 0 0 0 0 0 0 0      . (12) 4 ಉ࣍࠲ඪܗࣜͰ͋Δ͜ͱʹ஫ҙ͢Δɽ Lucas-Kanade ΞϧΰϦζϜ [10, 1] Iterate: 1: hin(W (x; p)) Λܭࢉ͢ΔͨΊʹೖྗը૾ hin Λ ύϥϝʔλ W (x; p) Ͱม׵͢Δɽ 2: ޡࠩը૾ href (x) − hin(W (x; p)) Λܭࢉ͢Δɽ 3: ޯ഑ ∇hin Λ W (x; p) Ͱม׵͢Δɽ 4: (x; p) ͰϠίϏߦྻ ∂W ∂p ΛධՁ͢Δɽ 5: ࠷ٸ߱Լը૾ ∇hin ∂W ∂p Λܭࢉ͢Δɽ 6: ࣍ͷϔοηߦྻΛܭࢉ͢Δɽ H = ∑x (∇hin ∂W ∂p )⊤ (∇hin ∂W ∂p ) 7: ࣍ͷ࠷ٸ߱Լը૾ͱޡࠩը૾ͷੵ࿨Λܭࢉ͢Δɽ ∑x (∇hin ∂W ∂p )⊤ (href (x) − hin(W (x; p))) 8: ࣍ͷߋ৽ྔ ∆p Λܭࢉ͢Δɽ ∆p = H−1 ∑x (∇hin ∂W ∂p )⊤ (href (x) − hin(W (x; p))) 9: ύϥϝʔλΛ࣍ͷΑ͏ʹߋ৽͢Δɽ p ← p + ∆p Until ∥∆p∥ ≤ εʢඍখ͖͍͠஋ʣ ਤ 4 Lucas-Kanade ΞϧΰϦζϜखॱ [10, 1]ɽ ࣜ (10) Λ ∆p ʹ͍ͭͯඍ෼͢Δͱɼ ∑ x ( ∇hin ∂W ∂p )⊤ ( hin(W (x; p))+∇hin ∂W ∂p ∆p−href (x) ) , (13) Ͱ͋Γɼ∆p ͸࣍ͷΑ͏ʹղ͘͜ͱ͕Ͱ͖Δɽ ∆p = H−1 ∑ x ( ∇hin ∂W ∂p )⊤ (href (x)−hin(W (x; p))). (14) ͜͜ͰɼH ͸࣍ͷΑ͏ͳϔοηߦྻͰ͋Δɽ H =∑ x ( ∇hin ∂W ∂p )⊤ ( ∇hin ∂W ∂p ) . (15) ͕ͨͬͯ͠ɼp ͸ద౰ͳॳظ஋͔Β ∆p Λ൓෮తʹղ͘ ͜ͱʹΑͬͯɼٻΊΔ͜ͱ͕Ͱ͖Δɽ͜Ε͸ɼϔοηߦ ྻΛܭࢉ͢Δͷʹ 2 ֊ඍ෼ΛߦΘͣʹۙࣅ͢ΔʮΨ΢ εɾχϡʔτϯ๏ʯͰ͋Δ [6]ɽLucas-Kanade ΞϧΰϦ ζϜͷखॱ [10, 1] Λਤ 4 ʹࣔ͢ɽ 3.2 ٯ݁߹ɾۙࣅٯ݁߹ Lucas-Kanade ώετά ϥϜϚονϯά Lucas-Kanade ΞϧΰϦζϜͷ໰୊͸ɼ൓෮ຖʹߋ৽ ͨ͠ิਖ਼ύϥϝʔλʹΑΓม׵ͨ͠ೖྗώετάϥϜ
4. ը૾ͷϔοηߦྻ H Λܭࢉ͠ͳ͚Ε͹ͳΒͳ͍͜ͱͰ ͋Δɽͦ͜Ͱɼج४ώετάϥϜը૾ͱೖྗώετά ϥϜը૾ͷ໾ׂΛަ׵͢Δɽ ∑ x (href (W (x; ∆p))−hin(W (x; p)))2 . (16) ͜ΕΛςΠϥʔల։͢Δͱɼ࣍ͷΑ͏ʹͳΔɽ ∑ x ( href (W (x; 0))+∇href ∂W ∂p ∆p−hin(W (x; p)) )2 . (17) W (x; 0) ͸ ∆p = 0 ͱͨ͠߃౳ม׵Ͱ͋Δͱͯ͠ɼҰ ൠੑΛࣦΘͳ͍ɽ͕ͨͬͯ͠ɼมԽྔ ∆p ͸ɼ ∆p = H−1 ∑ x ( ∇href ∂W ∂p )⊤ (hin(W (x; p))−href (x)), (18) Ͱ͋Γɼج४ώετάϥϜը૾ href (x) ͷϔοηߦྻ͸ɼ H =∑ x ( ∇href ∂W ∂p )⊤ ( ∇href ∂W ∂p ) , (19) ͱͳΔɽϠίϏߦྻ ∂W /∂p ͸ (x; 0) ͰධՁ͢Δɽ͜ Ε͸ύϥϝʔλʹΑΒͣɼ༧Ίܭࢉ͓ͯ͘͜͠ͱ͕Ͱ ͖Δɽ൓෮ຖʹೖྗώετάϥϜը૾ hin Λม׵͠ ͯɼج४ώετάϥϜը૾ͷ࠷ٸ߱ԼώετάϥϜը ૾ ∇href ∂W /∂p ͱޡࠩώετάϥϜը૾ href (x) − hin(W (x; p)) ͷੵ࿨Λܭࢉ͢Δɽͦͯ͠ɼ༧Ίܭࢉ͠ ͓͍ͯͨج४ώετάϥϜը૾ͷϔοηߦྻͷٯߦྻ H−1 Λֻ͚ͨ΋ͷΛมԽྔͱ͢Δ͕ɼͦͷߋ৽ํ๏͕ ҟͳΔɽ มԽྔΛՃࢉʹΑΓߋ৽͢ΔͷͰ͸ͳ͘ɼมԽྔʹ ΑΔม׵ߦྻͷٯߦྻΛ߹੒͢Δ͜ͱʹΑΓߋ৽͢Δɽ W (x; p) ← W (x; p) ◦ W (x; ∆p)−1 ≡ W (W (x; ∆p)−1; p). (20) ͜Ε͸ɼٯ݁߹ Lucas-Kanade ΞϧΰϦζϜʢInverse Compositional Algorithmʣͱݺ͹ΕɼLucas-Kanade ΞϧΰϦζϜͷޮ཰తͳํ๏ͱͯ͠ఏҊ͞Ε͍ͯΔ [1]ɽ ͔͠͠ɼม׵ͷ߹੒݁ՌΛ 1 ࣍ۙࣅͯ͠΋ɼ௨ৗ͸ ໰୊ͳ͍͜ͱ͕֬ೝͰ͖Δɽ͢ͳΘͪɼύϥϝʔλͷ ߋ৽͸ٯํ޲ͷՃࢉɼͭ·Γ “ݮࢉ” ʹΑͬͯͳ͞ΕΔ [11, 12]ɽ p ← p − ∆p. (21) ٯ݁߹ Lucas-Kanade ΞϧΰϦζϜ͸ɼٯม׵͕ଘࡏ ͯ͠ɼม׵ͷ݁߹ଇ͕੒ΓཱͭΑ͏ͳม׵ʹ͔͠ద༻Ͱ ͖ͳ͍ͱ͞Ε͍ͯΔ [1]ɽ͔͠͠ɼଟ߲ࣜม׵ͷΑ͏ͳ ߴ߲࣍Λ༗͢Δิਖ਼Ϟσϧʹ͓͍ͯ΋ɼ1 ࣍ۙࣅʹΑΔ ߋ৽͕Մೳͳ͜ͱ͕࣮ݧతʹ֬ೝͰ͖Δɽ͜ͷΑ͏ͳٯ ݁߹ͷ 1 ࣍ۙࣅͰ͋Δ “ݮࢉ” ʹΑͬͯɼLucas-Kanade ਤ 5 ແݶখม׵ͷϦʔ୅਺͸ม׵܈ Mp ͷ p ʹ͓ ͚Δ઀ۭؒ Tp(Mp) ͱݟͳͤΔɽϦʔ୅਺ʹ͓͍ͯܭ ࢉͨ͠૿෼ ∆p Λࢦ਺ؔ਺ exp G(∆p) ʹΑͬͯɼྡ ઀͢Δม׵܈ Mp ͷ఺ʹࣹӨ͢Δ [5]ɽ ΞϧΰϦζϜͷޮ཰Խ͕ਤΕΔ͜ͱ͔Βɼ͜ΕΛ “ۙࣅ ٯ݁߹ Lucas-Kanade ΞϧΰϦζϜ” ͱݺͿ [11, 12]ɽ 3.3 ࢦ਺ࣸ૾ٯ݁߹ Lucas-Kanade ώετάϥϜ Ϛονϯά ߋ৽ྔ ∆p ΛϦʔ୅਺ʹΑΓݫີͳม׵ߦྻͱͯ͠ ߋ৽͢Δ [5]ɽ͢ͳΘͪɼ W (x; p) ← exp G(−∆p)W (x; p). (22) ͜͜Ͱɼexp G(−∆p) ͸Ϧʔ୅਺ͷࢦ਺ࣸ૾Ͱ͋Γɼෛ ූ߸͸ٯม׵Λද͢ɽྫ͑͹ɼ3 ࣍ݩ RGB ΞϑΟϯม ׵ͷ৔߹ʹ͸ɼ࣍ͷΑ͏ʹͳΔɽ exp G(−∆p) = exp ( − 12 ∑ n=1 ∆pn Gn ) = I4×4 − 12 ∑ n=1 ∆pn Gn + 1 2 ( 12 ∑ n=1 ∆pn Gn )2 − · · · = ∞ ∑ k=0 ( − 12 ∑ n=1 ∆pn Gn )k k! . (23) I4×4 ͸ 4 ࣍୯ҐߦྻͰ͋ΔɽGn ͸ແݶখม׵ͷੜ੒ ࢠͰ͋Γɼ࣍ͷΑ͏ʹͳΔɽ G1 =      1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0      , G2 =      0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0      , . . . , G11 =      0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0      , G12 =      0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0      . (24) ࣜ (23) Ͱɼk = 1 ·Ͱͱ͢Δͱɼ઀ฏ໘ʹ͓͚Δ 1 ࣍ ۙࣅͰ͋Γɼۙࣅٯ݁߹ͷ৔߹ͷ൓෮ߋ৽ (21) ʹҰக ͢ΔɽϦʔ୅਺ʹΑΔࢦ਺ࣸ૾ͷزԿֶతͳҙຯΛਤ 5 ʹࣔ͢ɽٯ݁߹ [1]/ۙࣅٯ݁߹ [11, 12]/ࢦ਺ࣸ૾ٯ݁ ߹ Lucas-Kanade ΞϧΰϦζϜखॱΛਤ 6 ʹࣔ͢ɽख ॱͷ൪߸͸ɼਤ 4 ͷ Lucas-Kanade ΞϧΰϦζϜͱର
5. ٯ݁߹ [1]/ۙࣅٯ݁߹ [11, 12]/ ࢦ਺ࣸ૾ٯ݁߹ Lucas-Kanade ΞϧΰϦζϜ Pre-compute: 3: ج४ը૾ href (x) ͷޯ഑ ∇href ΛධՁ͢Δɽ 4: (x; 0) ͰϠίϏߦྻ ∂W ∂p ΛධՁ͢Δɽ 5: ࠷ٸ߱Լը૾ ∇href ∂W ∂p Λܭࢉ͢Δɽ 6: ࣍ͷϔοηߦྻͷٯߦྻΛܭࢉ͢Δɽ H = ∑x (∇href ∂W ∂p )⊤ (∇href ∂W ∂p ) Iterate: 1: hin(W (x; p)) Λܭࢉ͢ΔͨΊʹೖྗը૾ hin Λ ύϥϝʔλ W (x; p) Ͱม׵͢Δɽ 2: ޡࠩը૾ hin(W (x; p)) − href (x) Λܭࢉ͢Δɽ 7: ࣍ͷ࠷ٸ߱Լը૾ͱޡࠩը૾ͷੵ࿨Λܭࢉ͢Δɽ ∑x (∇href ∂W ∂p )⊤ (hin(W (x; p)) − href (x)) 8: ࣍ͷߋ৽ྔ ∆p Λܭࢉ͢Δɽ ∆p = H−1 ∑x (∇href ∂W ∂p )⊤ (hin(W (x; p)) − href (x)) 9: ύϥϝʔλΛ࣍ͷΑ͏ʹߋ৽͢Δɽ W (x; p) ← W (x; p) ◦ W (x; ∆p)−1 ʢٯ݁߹ʣ p ← p − ∆p ʢۙࣅٯ݁߹ʣ W (x; p) ← exp G(−∆p)W (x; p) ʢࢦ਺ࣸ૾ٯ݁߹ʣ Until ∥∆p∥ ≤ εʢඍখ͖͍͠஋ʣ ਤ 6 ٯ݁߹ [1]/ۙࣅٯ݁߹ [11, 12]/ࢦ਺ࣸ૾ٯ݁߹ Lucas-Kanade ΞϧΰϦζϜखॱɽखॱͷ൪߸͸ɼਤ 4 ͷ Lucas-Kanade ΞϧΰϦζϜͱରԠ͍ͯ͠Δɽख ॱ 9 ͷͦΕͧΕͷ৔߹ͷύϥϝʔλߋ৽ͷࣜͷҧ͍ʹ ஫ҙ͢Δɽ Ԡ͍ͯ͠Δɽखॱ 9 ͷͦΕͧΕͷ৔߹ͷύϥϝʔλߋ ৽ͷࣜͷҧ͍ʹ஫ҙ͢Δɽ 4 γϛϡϨʔγϣϯ࣮ݧ ਤ 7 ͸ Lucas-Kanade ώετάϥϜϚονϯάॲཧ શମͷϒϩοΫਤͰ͋Δɽج४ը૾ʢRefʣͱೖྗը૾ ʢInʣΛೖྗͯ͠ɼج४ը૾ͷ৭໌Δ͞ʹೖྗը૾Λ߹ ΘͤΔɽ͸͡ΊʹɼͦΕͧΕͷώετάϥϜΛܭࢉͯ͠ ʢHistogramʣ ɼ ώετάϥϜը૾ͱͯ͠ɼ Ψ΢γΞϯฏ׈ Խ ʢGaussian Smoothingʣ Λߦ͏ɽ ͦͯ͠ɼ ώετάϥϜ ը૾ͷϨϕϧΛτʔϯϚοϐϯάॲཧʢTone Mappingʣ [20] ʹΑΓม׵͢ΔɽϨϕϧม׵͞ΕͨώετάϥϜ ը૾Λ༻͍ͯɼLucas-Kanade ϚονϯάॲཧʢLucas- Kanade MatchingʣΛߦ͍ɼ৭ิਖ਼ύϥϝʔλΛਪఆ͢ Δɽਪఆͨ͠৭ิਖ਼ύϥϝʔλʢCorrect ParameterʣΛ ༻͍ͯɼೖྗը૾Λ৭ิਖ਼ʢColor Correctʣͯ͠ग़ྗ ʢOutʣ͢Δɽ ධՁ༻ը૾ͱͯ͠͸ɼ • ಉҰը૾ΛزԿֶม׵͢Δ͜ͱʹΑΓੜ੒ٖͨ͠ ࣅଟࢹ఺ը૾5 • ࿈ଓ͢Δಈը૾ྻ͔Βͷ 2 ը૾6 5 Middlebury Stereo Datasets, http://vision.middlebury. edu/stereo/data/ 6 Video Quality Experts Group (VQEG), https://www.its. ਤ 7 Lucas-Kanade ώετάϥϜϚονϯάॲཧ શମϒϩοΫਤɽ • εςϨΦը૾ 5 Λ༻͍ͯɼͦΕͧΕɼ3 ࣍ݩ RGB ৭ۭؒʹ͓͚Δ૬ࣅ ม׵ʹΑΓ৭ม׵ͨ͠ը૾ͷج४ը૾ʹର͢Δ৭ิਖ਼ ύϥϝʔλΛਪఆͯ͠ɼ৭ิਖ਼͢Δɽͦͯ͠ɼਅͷը ૾ͱ৭ิਖ਼ը૾ͷؒͷ৭ࠩ ∆E∗ ab ʹΑΓධՁ͢Δɽ৭ ࠩࣜʹ͸ CIEDE2000 (∆E∗ 00 ) Λ༻͍ͨ7ɽ ಉҰը૾ΛزԿֶม׵͢Δ͜ͱʹΑΓੜ੒ٖͨ͠ࣅ ଟࢹ఺ը૾ͱ͸ɼը૾தԝۣܗྖҬΛج४ը૾ͱͯ͠ɼ ͦͷ 4 ௖఺ͷըૉ࠲ඪʹਖ਼نཚ਺ΛՃࣹ͑ͯӨม׵Λ ܭࢉ͢Δɽͦͯ͠ɼܭࢉࣹͨ͠Өม׵ʹΑΓੜ੒ͨ͠ ม׵ը૾ͷதԝۣܗྖҬΛ੾Γग़ͨ͠΋ͷΛ৭ม׵͠ ͯ༻͍Δ΋ͷͰ͋Δɽ ૬ࣅม׵͸࣍ͷΑ͏ʹఆٛ͢Δɽฏۉ 0ɼඪ४ภࠩ 5×10−2 ͷਖ਼نཚ਺ʹΑΓੜ੒ͨ͠ 3×3 ߦྻΛ୯Ґߦ ྻʹՃࢉ͢ΔɽͦͷΑ͏ͳߦྻΛۃ෼ղʹΑΓɼ௚ަߦ ྻͱ൒ਖ਼஋ରশߦྻͷੵʹ෼ղͯ͠ɼ௚ަߦྻΛճసߦ ྻ R ͱ͢Δɽεέʔϧ s Λฏۉ 1, ඪ४ภࠩ 1×10−2 ͷ ਖ਼نཚ਺ɼฒਐϕΫτϧ t Λฏۉ 0ɼඪ४ภࠩ 5 × 10−2 ͷਖ਼نཚ਺ʹΑΓੜ੒ͯ͠8ɼ࠷ऴతͳ૬ࣅม׵ͱ͢Δɽ ͨͩ͠ɼ৭ม׵ը૾ʹ͓͚Δ૯ըૉ਺ʹର͢ΔΨϚο τޡࠩըૉ਺ͷׂ߹͕ 5 % ҎԼʹͳΔΑ͏ʹબͿɽ ද 1ʙ3 ͸ɼ֤ධՁ༻ը૾ 10 ૊ͷ݁ՌͰ͋Δɽ૬ࣅ ม׵ύϥϝʔλΛม͑ͯɼ1 ૊ʹ͖ͭ 100 ճߦͬͨɽٖ ࣅଟࢹ఺ը૾ͷ৔߹͸ɼਖ਼نཚ਺ʹΑΔࣹӨม׵΋ม ͍͑ͯΔɽ ʢॱํ޲ʣLucas-Kanade ΞϧΰϦζϜɼٯ݁ ߹ɾۙࣅٯ݁߹ Lucas-Kanade ΞϧΰϦζϜɼͦͯ͠ɼ ࢦ਺ࣸ૾ٯ݁߹ Lucas-Kanade ΞϧΰϦζϜΛ༻͍ͯɼ ͦΕͧΕ 1 ࣍ݩً౓ɾ2 ࣍ݩ৭ࠩώετάϥϜϚονϯ άɼ3 ࣍ݩ RGB ώετάϥϜϚονϯάʹΑΔ݁ՌͰ ͋ΔɽώετάϥϜͷϏϯ਺ʢ۠ؒ਺ʣ͸ɼͦΕͧΕ 64, 64×64, 64×64×64 ͱͨ͠ɽऩଋ৚݅͸ɼ͍ͣΕ΋ ύϥϝʔλߋ৽ྔϕΫτϧͷϊϧϜ ∥∆p∥ ͕ 1 × 10−3 ҎԼͱͨ͠ɽਅͷೖྗݪը૾ͱ৭ิਖ਼ը૾ͷؒͷࠩ෼ ೋ৐ը૾ͷฏۉ৭ࠩͱͱ΋ʹɼฏۉऩଋճ਺΋ࣔ͢ɽൺ ֱͷͨΊʹɼRGB ຖͷըૉ஋ͷฏۉඪ४ภࠩϚονϯ ά [16] ʹΑΔ݁Ռ΋ࣔ͢ɽ bldrdoc.gov/vqeg/downloads.aspx 7 ೔ຊ޻ۀن֨ JIS Z8730:2009 ৭ͷදࣔํ๏ – ෺ମ৭ͷ৭ ࠩ Colour specification - Colour differences of object colours, ܭࢉʹ͸ɼscikit-image: Image processing in Python, http:// scikit-image.org/ ʹ͓͚Δ skimage.color.deltaE_ciede2000 ؔ਺Λ༻͍ͨɽ 8 RGB ըૉ஋͸ [0 , 1] ਖ਼نԽ͞Ε͍ͯΔͱ͢Δɽ
6. ද 1 ΧϥʔϚονϯάධՁ݁Ռʢ1ʣɽٖࣅଟࢹ఺ը૾ͷ৔߹ɽݪը૾ͱ৭ิਖ਼ը૾ͷؒͷ৭ࠩ ∆E∗ ab ͷฏۉɼ ฏۉऩଋճ਺ʢً౓৭ࠩ৭ۭؒͷ৔߹ʹ͸ 2 ࣍ݩ৭ࠩώετάϥϜͷ݁Ռʣ ɽׅހ಺͸ඪ४ภࠩͰ͋Δɽ ৭ۭؒ ํ๏ ฏۉ৭ࠩ ฏۉऩଋճ਺ ً౓৭ࠩ Lucas-Kanade ώετάϥϜϚονϯά [10, 1] 2.152 (±2.528) 5.03 (±1.25) ٯ݁߹ Lucas-Kanade ώετάϥϜϚονϯά [1] 2.255 (±2.510) 4.73 (±1.10) ۙࣅٯ݁߹ Lucas-Kanade ώετάϥϜϚονϯά [11, 12] 2.313 (±3.304) 4.81 (±1.05) ࢦ਺ࣸ૾ٯ݁߹ Lucas-Kanade ώετάϥϜϚονϯά 2.114 (±1.357) 5.85 (±1.49) RGB Lucas-Kanade ώετάϥϜϚονϯά [10, 1] 0.474 (±0.330) 6.70 (±1.93) ٯ݁߹ Lucas-Kanade ώετάϥϜϚονϯά [1] 0.473 (±0.324) 6.21 (±1.71) ۙࣅٯ݁߹ Lucas-Kanade ώετάϥϜϚονϯά [11, 12] 0.473 (±0.324) 6.52 (±1.88) ࢦ਺ࣸ૾ٯ݁߹ Lucas-Kanade ώετάϥϜϚονϯά 0.473 (±0.324) 7.41 (±2.23) RGB ฏۉඪ४ภࠩϚονϯά [16] 1.187 (±0.467) – -100 0 100 200 300 -100 0 100 200 300 -100 0 100 200 300 B Reference Input R G B -100 0 100 200 300 -100 0 100 200 300 -100 0 100 200 300 B Reference Correct R G B (a) (b) (c) (d) 10-4 10-3 10-2 10-1 1 3 5 7 9 Iteration Residual FA IC Approx.IC expM Red Conv RGB LK Green Conv RGB LK 110 120 130 140 150 160 Blue Pixel val Conv RGB LK (e) (f) (g) (h) ਤ 8 ΧϥʔϚονϯάը૾ྫʢ1ʣ ɽٖࣅଟࢹ఺ը૾ͷ৔߹ɽ(a) ج४ը૾ͱͦͷࣹӨม׵ʹΑΔೖྗݪը૾ (b)ɼ(c) ج४ը૾ʢReferenceʣͱೖྗݪը૾ͷ৭ม׵ը૾ʢInputʣͷ RGB ըૉ஋ͷ 3 ࣍ݩϓϩοτɼ(d) ج४ը૾ͱ 3 ࣍ݩ RGB ώετάϥϜϚονϯάʹΑΔ৭ิਖ਼ը૾ʢCorrectʣͷ RGB ըૉ஋ͷ 3 ࣍ݩϓϩοτɼ(e) ೖྗݪը૾ͷ৭ม׵ ը૾ɼ(f) 3 ࣍ݩ RGB ώετάϥϜϚονϯάʹΑΔ৭ิਖ਼ը૾ɼ(g) 3 ࣍ݩ RGB ώετάϥϜϚονϯάʹ͓͚Δ൓ ෮ճ਺ʹର͢Δ࢒ࠩάϥϑɼ(h) ೖྗݪը૾ͱ৭ม׵/৭ิਖ਼ը૾ͷؒͷࠩ෼Φϑηοτը૾ͷ RGB ຖͷώετάϥϜɽ ͍ͣΕͷධՁը૾ͷ৔߹΋ɼً౓৭ࠩώετάϥϜ Ϛονϯάͷ݁ՌΑΓ΋ɼRGB ώετάϥϜϚονϯ άͷ݁Ռͷํ͕ɼ৭ࠩ ∆E∗ ab ͷฏۉ͕௿͘ɼRGB ฏۉ ඪ४ภࠩϚονϯάͷ݁ՌΑΓ΋௿͍ʢ∆E∗ ab ͕ 0 Ͱݫ ີʹҰக͢Δʣ ɽٖࣅଟࢹ఺ը૾ͷ৔߹ʹ͸ɼRGB ώ ετάϥϜϚονϯάͷ݁Ռͷೖྗݪը૾ͱ৭ิਖ਼ը ૾ͷؒͷ৭ࠩ͸ɼ࣮༻తͳڐ༰ݶքʢݫ֨৭ࠩʣΛӽ͑ ͍ͯΔɽ∆E∗ ab ʹ͓͚Δஸ౓Մ஌ࠩҟʢJust Noticeable Difference, JNDʣ͸ɼ2.3 ͱݴΘΕ͍ͯΔ [21]ɽԕํͷ γʔϯΛζʔϜʹΑΓࡱӨ͢Δ৔߹ʹ͸ɼฏ໘ͱݟͳ ͤΔͨΊɼฏ໘ࣹӨม׵ʹΑΓۙࣅ͕Ͱ͖ͯɼٖࣅత ͳଟࢹ఺ը૾ʹΑΔධՁ͸े෼ݱ࣮తͰ͋Δɽ ಉҰΧϝϥʹΑΔಈը૾ྻ͔Βͷ 2 ը૾͸ɼ͍ͣΕ ΋࣌ؒతʹ 10 ϑϨʔϜ཭Εͨ 2 ը૾Λ༻͍͕ͨɼ͋Δ ఔ౓ͷύϯɼνϧτɼζʔϜɼہॴతͳҠಈ෺ମʹΑΔ ΦΫϧʔδϣϯʹରͯ͠ɼώετάϥϜಛ௃͸ෆมͱݟ ͳͤΔɽ͔͠͠ɼεςϨΦը૾͸Ԟߦ͖ʹΑΔΦΫϧʔ δϣϯ͕େ͖͘ͳΔͨΊɼը૾΍৭ม׵ʹΑͬͯ͸ɼे ෼ͳิਖ਼݁Ռ͕ಘΒΕ͍ͯͳ͍ɽͦΕͰ΋ɼRGB ฏۉ ඪ४ภࠩϚονϯάΑΓ৭ࠩ͸௿͍ɽ RGB ฏۉඪ४ภࠩϚονϯά͸൓෮ΛߦΘͳ͍؆қ ͳํ๏Ͱ͋Δ΋ͷͷɼ৭ม׵͕ RGB ৭ۭؒʹ͓͚Δ ฒਐεέʔϧม׵ͱݟͳͤΔ৔߹ʹ͸ɼे෼ͳ৭ิਖ਼ ݁Ռ͕ಘΒΕΔɽ͔͠͠ɼRGB ৭ۭؒʹ͓͚Δճసʹ ΑΔ৭ม׵Λิਖ਼͢Δ͜ͱ͸Ͱ͖ͳ͍ɽΧϝϥͷύϯɼ νϧτɼζʔϜɼہॴతͳҠಈ෺ମʹΑΔΦΫϧʔδϣ ϯʹରͯ͠΋ɼे෼ͳิਖ਼͕ߦΘΕͳ͍ɽ ͍ͣΕͷධՁը૾ͷ৔߹΋ɼ৭ม׵͸ɼRGB ৭ۭؒ ʹ͓͚Δ૬ࣅม׵ʹΑΔ͕ɼً౓৭ࠩ৭ۭؒͰ͸े෼ ิਖ਼͢Δ͜ͱ͸Ͱ͖ͳ͍ɽΧϝϥͷ಺෦Ͱ͸ɼϦχΞ ϚτϦΫεॲཧͱͯ͠ɼRGB ࠞ߹ॲཧ͕ߦΘΕ͍ͯΔɽ ΧϥʔϚονϯάͷͨΊʹ͸ɼRGB ৭ۭؒʹΑΔิਖ਼ ͕ద͍ͯ͠ΔͩΖ͏ɽ Lucas-Kanade ΞϧΰϦζϜʹؔͯ͠͸ɼ͍ͣΕͷํ ๏Ͱ΋ऩଋ͸͓ͯ͠Γɼٯ݁߹ Lucas-Kanade ΞϧΰϦ ζϜ͕΍΍ऩଋ͕଎͘ɼۙࣅٯ݁߹ɼ ʢॱํ޲ʣLucas-
7. ද 2 ΧϥʔϚονϯάධՁ݁Ռʢ2ʣ ɽಈը૾ྻ͔Βͷ 2 ը૾ͷ৔߹ɽݪը૾ͱ৭ิਖ਼ը૾ͷؒͷ৭ࠩ ∆E∗ ab ͷฏۉɼ ฏۉऩଋճ਺ʢً౓৭ࠩ৭ۭؒͷ৔߹ʹ͸ 2 ࣍ݩ৭ࠩώετάϥϜͷ݁Ռʣ ɽׅހ಺͸ඪ४ภࠩͰ͋Δɽ ৭ۭؒ ํ๏ ฏۉ৭ࠩ ฏۉऩଋճ਺ ً౓৭ࠩ Lucas-Kanade ώετάϥϜϚονϯά [10, 1] 1.645 (±0.899) 4.70 (±0.84) ٯ݁߹ Lucas-Kanade ώετάϥϜϚονϯά [1] 1.629 (±0.891) 4.38 (±0.80) ۙࣅٯ݁߹ Lucas-Kanade ώετάϥϜϚονϯά [11, 12] 1.629 (±0.891) 4.51 (±0.87) ࢦ਺ࣸ૾ٯ݁߹ Lucas-Kanade ώετάϥϜϚονϯά 1.629 (±0.891) 5.48 (±1.34) RGB Lucas-Kanade ώετάϥϜϚονϯά [10, 1] 0.697 (±0.306) 6.64 (±1.36) ٯ݁߹ Lucas-Kanade ώετάϥϜϚονϯά [1] 0.703 (±0.300) 6.51 (±1.17) ۙࣅٯ݁߹ Lucas-Kanade ώετάϥϜϚονϯά [11, 12] 0.703 (±0.300) 6.68 (±1.18) ࢦ਺ࣸ૾ٯ݁߹ Lucas-Kanade ώετάϥϜϚονϯά 0.703 (±0.300) 7.57 (±1.75) RGB ฏۉඪ४ภࠩϚονϯά [16] 1.310 (±0.583) – -100 0 100 200 300 -100 0 100 200 300 -100 0 100 200 300 B Reference Input R G B -100 0 100 200 300 -100 0 100 200 300 -100 0 100 200 300 B Reference Correct R G B (a) (b) (c) (d) 10-4 10-3 10-2 10-1 1 3 5 7 9 Iteration Residual FA IC Approx.IC expM Red Conv RGB LK Green Conv RGB LK 110 120 130 140 150 160 Blue Pixel val Conv RGB LK (e) (f) (g) (h) ਤ 9 ΧϥʔϚονϯάը૾ྫʢ2ʣɽಈը૾ྻ͔Βͷ 2 ը૾ͷ৔߹ɽ(a) ج४ը૾ͱೖྗݪը૾ (b)ɼ(c) ج४ը૾ ʢReferenceʣͱೖྗݪը૾ͷ৭ม׵ը૾ʢInputʣͷ RGB ըૉ஋ͷ 3 ࣍ݩϓϩοτɼ(d) ج४ը૾ͱ 3 ࣍ݩ RGB ώε τάϥϜϚονϯάʹΑΔ৭ิਖ਼ը૾ʢCorrectʣͷ RGB ըૉ஋ͷ 3 ࣍ݩϓϩοτɼ(e) ೖྗݪը૾ͷ৭ม׵ը૾ɼ(f) 3 ࣍ݩ RGB ώετάϥϜϚονϯάʹΑΔ৭ิਖ਼ը૾ɼ(g) 3 ࣍ݩ RGB ώετάϥϜϚονϯάʹ͓͚Δ൓෮ճ਺ʹର ͢Δ࢒ࠩάϥϑɼ(h) ೖྗݪը૾ͱ৭ม׵/৭ิਖ਼ը૾ͷؒͷࠩ෼Φϑηοτը૾ͷ RGB ຖͷώετάϥϜɽ Kanade ΞϧΰϦζϜɼࢦ਺ࣸ૾ٯ݁߹ Lucas-Kanade ΞϧΰϦζϜͷॱʹऩଋ͕஗͘ͳΔ܏޲͕ݟΒΕΔɽ৭ ࠩͷฏۉ͸ɼ ʢॱํ޲ʣLucas-Kanade ΞϧΰϦζϜ͕΍ ΍௿͍Α͏Ͱ͋Δɽͦͷଞ͸ಉఔ౓Ͱ͋ͬͨɽ ਤ 8, 9 ͸ɼΧϥʔϚονϯάը૾ྫͰ͋Δɽ֤ਤத (g) ͸ɼLucas-Kanade ΞϧΰϦζϜͷ൓෮ճ਺ʹର͢ Δ࢒ࠩͷάϥϑͰ͋Γɼॱํ޲ʢFAʣɼٯ݁߹ʢICʣɼ ۙࣅٯ݁߹ʢApprox.ICʣ ɼࢦ਺ࣸ૾ٯ݁߹ʢexpMʣͰ ͋Δɽ(h) ೖྗݪը૾ͱ৭ม׵/৭ิਖ਼ը૾ͷؒͷࠩ෼ Φϑηοτը૾ʢࠩ෼஋ 0 ͕ 128ʣͷ RGB ຖͷώετ άϥϜ΋ɼೖྗ৭ม׵ը૾ʢConvʣ ɼRGB ຖͷฏۉඪ ४ภࠩϚονϯάʢRGBʣʹରͯ͠ɼ3 ࣍ݩ RGB ώε τάϥϜϚονϯάͷ݁ՌʢLKʣ͕ࠩ෼஋ 0 ʹूத͠ ͍ͯΔɽ 5 ·ͱΊ ಉҰγʔϯΛҟͳΔࢹ఺͔ΒࡱӨͨ͠ը૾ؒͷΧϥʔ ϚονϯάΛ໨తͱͯ͠ɼըૉ஋ͷ 1 ࣍ݩً౓ɾ2 ࣍ݩ ৭ࠩɼ͋Δ͍͸ 3 ࣍ݩ RGB ώετάϥϜΛϚονϯά ͤ͞Δ͜ͱʹΑΓ৭ิਖ਼ͷࣗಈԽΛߦͬͨɽըૉ஋ώε τάϥϜΛը૾ͱݟͳͤ͹ɼը૾ؒͷزԿֶతͳҐஔ ߹Θͤʹ༻͍ΒΕΔ Lucas-Kanade ΞϧΰϦζϜΛద ༻͢Δ͜ͱ͕Ͱ͖ͯɼ൓෮ຖʹϔοηߦྻΛܭࢉ͠ͳ ͍ٯ݁߹ Lucas-Kanade ΞϧΰϦζϜͷߋ৽Λ 1 ࣍ۙ ࣅͨۙ͠ࣅٯ݁߹ Lucas-Kanade ΞϧΰϦζϜʹϦʔ ୅਺ʹΑΔࢦ਺ࣸ૾Λಋೖͨ͠ɽ͢΂ͯͷॲཧ͸ɼώ ετάϥϜಛ௃ۭؒʹ͓͚ΔϚονϯάͰ͋Γɼը૾ ؒͷزԿֶతͳҐஔ߹ΘͤΛߦΘͳ͍͚ͩͰͳ͘ɼԿ Βͷಛ௃఺ͷநग़΍ରԠ෇͚΋ඞཁͱ͠ͳ͍ɽ ࠓޙͷ՝୊ͱͯ͠͸ɼ • ϚϧνίΞ CPU/GPU/FPGA ʹΑΔ࣮૷ͱө૾ ͷϦΞϧλΠϜॲཧ ͕ڍ͛ΒΕΔɽώετάϥϜϚονϯάʹΑΔਪఆ݁ ՌΛ 3 ࣍ݩϧοΫΞοϓςʔϒϧʢ3DLUTʣ[8] ʹల։ ͯ͠ɼ৭ิਖ਼Λߦ͏͜ͱ΋ՄೳͩΖ͏ɽ Ϧʔ୅਺ʹΑΔࢦ਺ࣸ૾Λಋೖͨ͠ࢦ਺ࣸ૾ٯ݁߹
8. ද 3 ΧϥʔϚονϯάධՁ݁Ռʢ3ʣɽεςϨΦը૾ͷ৔߹ɽݪը૾ͱ৭ิਖ਼ը૾ͷؒͷ৭ࠩ ∆E∗ ab ͷฏۉɼ ฏۉऩଋճ਺ʢً౓৭ࠩ৭ۭؒͷ৔߹ʹ͸ 2 ࣍ݩ৭ࠩώετάϥϜͷ݁Ռʣ ɽׅހ಺͸ඪ४ภࠩͰ͋Δɽ ৭ۭؒ ํ๏ ฏۉ৭ࠩ ฏۉऩଋճ਺ ً౓৭ࠩ Lucas-Kanade ώετάϥϜϚονϯά [10, 1] 2.693 (±1.427) 5.41 (±1.46) ٯ݁߹ Lucas-Kanade ώετάϥϜϚονϯά [1] 2.790 (±2.559) 5.25 (±1.12) ۙࣅٯ݁߹ Lucas-Kanade ώετάϥϜϚονϯά [11, 12] 2.710 (±1.418) 5.37 (±1.13) ࢦ਺ࣸ૾ٯ݁߹ Lucas-Kanade ώετάϥϜϚονϯά 2.705 (±1.419) 6.55 (±2.60) RGB Lucas-Kanade ώετάϥϜϚονϯά [10, 1] 1.122 (±0.531) 9.24 (±3.50) ٯ݁߹ Lucas-Kanade ώετάϥϜϚονϯά [1] 1.172 (±0.588) 8.94 (±2.48) ۙࣅٯ݁߹ Lucas-Kanade ώετάϥϜϚονϯά [11, 12] 1.172 (±0.588) 9.17 (±2.50) ࢦ਺ࣸ૾ٯ݁߹ Lucas-Kanade ώετάϥϜϚονϯά 1.172 (±0.588) 9.60 (±2.84) RGB ฏۉඪ४ภࠩϚονϯά [16] 1.754 (±0.652) – Lucas-Kanade ΞϧΰϦζϜ͸ɼߋ৽ྔ͕ߴ߲࣍ΛؚΉ ݫີͳม׵ߦྻʹͳΔ͜ͱ͔ΒɼऩଋͷՃ଎͕ظ଴͞ Ε͕ͨɼώετάϥϜϚονϯάʹ͓͚Δ࣮ݧ݁Ռ͸ ͦΕΛࢧ࣋͠ͳ͔ͬͨɽزԿֶతͳҐஔ߹Θͤ΁ͷద ༻΋ؚΊͨৄࡉͳධՁ΋ࠓޙͷ՝୊ͱ͍ͨ͠ɽ ँࣙɿ Ϧʔ୅਺ͱࢦ਺ࣸ૾ʹ͍ͭͯޚڭࣔ௖͍ͨۚ୩ ݈ҰԬࢁେֶ໊༪ڭतʹײँ͠·͢ɽ ࢀߟจݙ [1] S. Baker and I. Matthews, Lucas-Kanade 20 years on: A unifying framework, International Journal of Computer Vision, 56-3 (2004), 221–255. [2] S. A. Fezza, M. C. Larabi and K. M. Faraoun, Feature-based color correction of multiview video for coding and rendering enhancement, IEEE Transac- tions on Circuits and Systems for Video Technology, 24-9 (September 2014), 1486–1498. [3] R. Hartley and A. Zisserman, Multiple View Geom- etry in Computer Vision (2nd Edition), Cambridge University Press, New York, NY, USA, 2003. [4] K. Kanatani, Statistical Optimization for Geometric Computation: Theory and Practice, Elsevier Science, Amsterdam, The Netherlands, April 1996, reprinted Dover Publications, New York, NY, USA, July 2005. [5] K. Kanatani, Lie algebra method for pose optimiza- tion computation, In: O. Sergiyenko, W. Flores- Fuentes, P. Mercorelli (eds.), Machine Vision and Navigation, Springer, 2019, to appear. [6] ۚ୩ ݈Ұ, ʮ͜ΕͳΒ෼͔Δ࠷దԽ਺ֶ – جૅݪཧ͔Β ܭࢉख๏·Ͱ –ʯ, ڞཱग़൛, 2005 ೥ 9 ݄. [7] ۚ୩ ݈Ұ, ੁ୩ อ೭, ۚᖒ ༃, ʮ3 ࣍ݩίϯϐϡʔλϏ δϣϯܭࢉϋϯυϒοΫʯ, ৿๺ग़൛, 2016 ೥ 10 ݄. [8] H. R. Kang, Computational Color Technology, SPIE Publications, May 2006. [9] D. Lowe, Distinctive image features from scale- invariant keypoints, International Journal of Com- puter Vision, 60-2 (January 2004), 91–110. [10] B. D. Lucas and T. Kanade, An iterative image regis- tration technique with an application to stereo vision, Proceedings of the 7th International Joint Conference on Artificial Intelligence - Volume 2 (IJCAI’81), Van- couver, BC, Canada, August 1981, pp. 674–679. [11] দӬ ྗ, ը૾͔Βͷഒ཰৭ऩࠩͷࣗಈਪఆิਖ਼, ୈ 20 ճ ը૾ηϯγϯάγϯϙδ΢Ϝ (SSII2014) ߨԋ࿦จू, ԣ ඿ (ύγϑΟίԣ඿), 2014 ೥ 6 ݄. [12] দӬ ྗ, ରԠ఺Λ༻͍ͳ͍ϩʔϦϯάγϟ ολʔ࿪Έิ ਖ਼ͱө૾ͷ҆ఆԽ ʙ ฒਐ͔Βճస΁, ୈ 21 ճը૾ηϯ γϯάγϯϙδ΢Ϝ (SSII2015) ߨԋ࿦จू, ԣ඿ (ύγ ϑΟίԣ඿), 2015 ೥ 6 ݄. [13] দӬ ྗ, 3 ࣍ݩزԿֶม׵ͱزԿֶతϞσϧબ୒ʹΑΔ ࠷దΧϥʔϚονϯά/ΧϥʔΩϟϦϒϨʔγϣϯ, ୈ 23 ճը૾ηϯγϯάγϯϙδ΢Ϝ (SSII2017) ߨԋ࿦จू, ԣ඿ (ύγϑΟίԣ඿), 2017 ೥ 6 ݄. [14] দӬ ྗ, ࠷దϨϕϧิਖ਼ͱزԿֶతϞσϧબ୒ʹΑΔߴ ਫ਼౓৭ิਖ਼: ը૾ॲཧύΠϓϥΠϯͷߏஙΛ໨ࢦͯ͠, ViEW2017 Ϗδϣϯٕज़ͷ࣮ར༻ϫʔΫγϣ οϓߨԋ࿦ จू, ԣ඿ (ύγϑΟίԣ඿), 2017 ೥ 12 ݄. [15] দӬ ྗɼ᪅ Ԇ܉ɼ࿨ా խಙ, ΧϥʔνϟʔτΛ༻͍ͨ ෳ਺ͷ࠶ࡱϞχλͱΧϝϥͷ࠷ద৭ิਖ਼, ୈ 16 ճը૾η ϯγϯάγϯϙδ΢Ϝ (SSII2010) ߨԋ࿦จू, ԣ඿ (ύ γϑΟίԣ඿), 2010 ೥ 6 ݄. [16] দӬ ྗɼ᪅ Ԇ܉ɼ࿨ా խಙ, 3D ө૾ͷͨΊͷࣗಈ৭ ิਖ਼, ୈ 17 ճը૾ηϯγϯάγϯϙδ΢Ϝ (SSII2011) ߨԋ࿦จू, ԣ඿ (ύγϑΟίԣ඿), 2011 ೥ 6 ݄. [17] C. S. McCamy, H. Marcus and J. G. Davidson, A color-rendition chart, Journal of Applied Pho- tographic Engineering, 2-3 (Summer 1976), 95–99. http://www.xrite.com/ [18] J. Moroviˇ c, Color Gamut Mapping, John Wiley & Sons Ltd., August 2008. [19] E. Reinhard, M. Ashikhmin, B. Gooch and P. Shirley, Color transfer between images, IEEE Transactions on Computer Graphics and Applications, 21-5 (2001), 34–41. [20] E. Reinhard, G. Ward, S. Pattanaik, and P. De- bevec, High Dynamic Range Imaging: Acquisition, Display, and Image-based Lighting, Amsterdam, El- sevier/Morgan Kaufmann, 2005. [21] G. Sharma, Digital Color Imaging Handbook, CRC Press, December 2002. [22] Q. Wang, X. Sun, and Z. Wang, A robust algorithm for color correction between two stereo images, Pro- ceedings of the 9th Asian conference on Computer Vision – Volume Part II (ACCV’09), Xi’an, China, September 2009, pp. 405–416. [23] H. Zeng, K.-K. Ma, C. Wang and C. Cai, SIFT-flow- based color correction for multi-view video, Image Communication, 36-C (August 2015), 53–62.