ಈը‫ࡧݕ‬Λ༻͍ͨਫγʔϯը૾ͷΞχϝʔγϣϯ
Animating Pictures of Water Scenes using Video RetrievalԬ෦ ੣ ∗
Makoto OKABE∗,౔‫ٓ ڮ‬య †Yoshinori DOBASHI†҆ੜ ݈Ұ ‡and Ken ANJYO‡∗ The University of Electro-Communications∗ ి‫ؾ‬௨৴େֶ† ๺ւಓେֶ† Hokkaido University‡ ‫ࣜג‬ձࣾΦʔɾΤϧɾΤϜɾσδλϧ ‡ OLM Digital, Inc.
E-mail: ∗m.o@acm.org, †doba@ime.ist.hokudai.ac.jp, ‡anjyo@olm.co.jp

1͸͡Ίʹ෮‫͢ݩ‬ΔͨΊͷςΫενϟ߹੒Λద༻Ͱ͖Δ [2, 4]ɽ͜ΕʹΑΓ༉ֆ౳ͷελΠϧ͕సૹ͞Ε࣭‫͕ײ‬ҡ࣋͞ΕΔɽֆը΍ࣸਅ౳ͷ୯Ұը૾ΛΞχϝʔγϣϯͤ͞Δٕज़͸ɼCG ෼໺Ͱ‫͞ڀݚʹൃ׆‬Ε͍ͯΔɽҰํɼࣗવͳਫͷΞχϝʔγϣϯ͸ະͩղܾ͞Ε͍ͯͳ͍ɽա‫ʹڈ‬΋ෳ਺ͷࢼΈ͕ൃද͞Ε͖͕ͯͨɼ୯ௐͳಈ͖ͷΈ͕ର৅ͩͬͨΓɼ‫ܭ‬ࢉίετ͕ߴ͍౳ͷ໰୊͕͋ͬͨ [1, 2, 3, 4]ɽ·ͨɼ‫ط‬ଘख๏ͷ݁Ռ͸ԿΕ΋࣮ࡍͷਫΛࡱӨͨ͠ө૾ͱൺֱ͢Δͱෆࣗવͩͬͨɽ୯Ұը૾͔ΒࣗવͰߴը࣭ͳਫͷΞχϝʔγϣϯΛੜ੒͢Δ͜ͱ͸ະͩୡ੒͞Ε͍ͯͳ͍ɽ‫ط‬ଘख๏͸࣮ࡍͷྲྀମͷಈ͖ʹ͍ͭͯҰ෦ͷ৘ใ͔͠ѻ͓ͬͯΒͣɼ͜Ε͕ෆࣗવͳ݁ՌΛ΋ͨΒ͍ͯ͠Δɽྲྀਤ 1: ೖྗը૾ɼਫྖҬΛࣔ͢ΞϧϑΝϚεΫ (ୌͱ઒ͷ 2ͭͷྖҬ)ɼਫͷྲྀΕํ޲ͷεέονɽମͷ༳Β͗ʹؔ͢Δ౷‫ྔܭ‬ͷΈͰ͸ඍົͳ‫܁‬Γฦ͠ͷมಈ͔͠ද‫[ ͍ͳ͖Ͱݱ‬1]ɽ୯ҰಈըͷΈ͔ΒͰ͸ྲྀମͷଟ༷ͳಈ͖Λද‫[ ͍ͳ͖Ͱݱ‬2, 3]ɽখ͞ͳύονʹ‫ॴہ͖ͮج‬తͳ৘ใΛѻ͏ͷ͸ྑ͍Ξϓϩʔν͕ͩɼେ‫ہ‬తͳߏ଄ͷ৘ใ͕͚͍ܽͯͨ [5, 4]ɽ͜ΕΒͷ໰୊Λղܾ͢ΔͨΊɼզʑ͸σʔλϕʔεதͷෳ਺ͷಈըΛͳΔ΂ͦ͘ͷ··࢖͏͜ͱΛࢼΈΔɽఏҊख๏͸ฒྻԽ͕؆୯ͰɼϢʔβ͸ૉૣ͍ϑΟʔυόοΫ͕ಘΒΕΔɽ୯Ұը૾͔Β༷ʑͷਫγʔϯͷΞχϝʔγϣϯ͕ੜ੒Ͱ͖Δ͜ͱΛࣔ͢ɽ2ఏҊख๏ਤ 1 ʹࣔ͢Α͏ʹɼఏҊख๏ͷೖྗ͸ 3 ͭ͋ΓɼϢʔβ͕Ξχϝʔγϣϯ͍ͤͨ͞ը૾ɼਫྖҬΛࣔ͢ΞϧϑΝϚεΫɼ ਫͷྲྀΕํ޲ͷεέονͰ͋Δɽ͜ΕΒ͕༩͑ΒΕਤ 2: ୌͱ઒ͷྖҬʹର͢Δ 4 ͭͷީิΞχϝʔγϣϯɽΔͱɼఏҊख๏͸‫ͨݟ‬໨ͱಈ͖͕ೖྗʹϚον͢ΔΑ͏ͳಈըΛσʔλϕʔε͔Β‫͢ࡧݕ‬ΔɽͦΕͧΕͷྖҬʹର͠ɼ࠷΋Ϛονͨ͠ಈըΛ‫͠ࡧݕ‬ɼީิΞχϝʔγϣϯΛ߹੒ͯ͠ϢʔβʹҰཡͰ‫ͤݟ‬Δɽྫͱͯ͠ɼ2 ͭͷྖҬʢୌͱ

2.1໰୊ઃఆ

ਤ 3 ʹఏҊख๏ͷΞΠσΞΛࣔ͢ɽਤ 3-a Λೖྗը૾ɼ

઒ʣʹର͢Δ 4 ͭͷީิΞχϝʔγϣϯΛਤ 2 ʹࣔ͢ɽϢʔ

ਤ 3-b ΛϢʔβ͕ਫྖҬʹࢦఆͨ͠ΞϧϑΝϚεΫͱ͢Δɽβ͸ީิΞχϝʔγϣϯΛ‫͠࡯؍‬ɼ࠷΋ద੾ͱ‫͡ײ‬Δ΋ͷ͜͜Ͱɼਤ 3-c ͷಈըΛσʔλϕʔε͔Β‫͠ࡧݕ‬ɼਤ 3-dΛબ୒͢Δɽ͜ͷΠϯλϑΣʔε͸ [6] Λࢀߟʹ։ൃͨ͠ɽͷΑ͏ʹೖྗը૾ͷୌͷ্ʹॏͶ߹ΘͤΔɽ2 ͭͷୌ͸‫ݟ‬શͯͷྖҬʹରͯ͠બ୒Λ‫Ͱ఺࣌ͨྃ͠׬‬Ξχϝʔγϣϯͨ໨͕ࣅ͓ͯΓɼ·ͨಈ͖΋ࣅ͍ͯΔͱਪ࡯͞ΕΔɽΑ͕ͬ‫׬‬੒͢Δɽ࠷‫ʹޙ‬Φϓγϣϯͱͯ͠ೖྗը૾ͷ‫ͨݟ‬໨Λͯɼ྆ऀΛ߹੒͠ɼೖྗը૾ͷΞχϝʔγϣϯ͕ಘΒΕΔɽͷྲྀΕํ޲ͷࢦඪʹ૬౰͢ΔɽྲྀΕํ޲Λද͢ 2 ࣍‫ݩ‬ϕΫτϧͷϖΞ͕༩͑ΒΕΔͱɼؔ਺ S f low ͸ྨࣅ౓Λ‫͢ࢉܭ‬Δɽࣜ 5 ͸ 4) ͷਫͷ‫ڍ‬ಈʹؔ͢Δࢦඪʹ૬౰͢Δɽmp (I)͸ I ͷਫͷ‫ڍ‬ಈΛ p ͷҐஔͰਪఆ͢Δؔ਺ͱ͢Δɽࣜ 6 ͸ྨࣅ౓ධՁ͕ೖྗը૾ͱಈըͷਫͷྖҬ಺෦ͰߦΘΕΔ͜ͱΛอূ͢Δ߲Ͱ͋Δɽ
զʑͷΞϧΰϦζϜ͸ɼ·ͣɼr ൪໨ͷྖҬຖʹɼarg maxi,t S ɼΛ‫͢ࢉܭ‬Δɽͭ·Γɼؔ਺ S ͕࠷େʹͳΔΑ͏ͳಈըͷΠϯσοΫε i ͱฏߦҠಈྔ t ΛಘΔɽͦͯ͠ɼi ൪໨ͷಈըਤ 3: ఏҊख๏ͷΞΠσΞɽΛ t ͰฒߦҠಈͤͨ͞΋ͷΛೖྗը૾ͱ߹੒͢Δ͜ͱͰɼ͜ͷΞΠσΞʹ‫ߴ͖ͮج‬ը࣭ͳ݁ՌΛಘΔͨΊɼ࣍ͷ 4ͭͷࢦඪΛߟ͑Δɽ1) ೖྗը૾ͱಈըͷؒͰਫྖҬͷॏͳΓ͸ͳΔ΂͘େ͖͋͘Δ΂͖ɽ2) ೖྗը૾ͱಈըͷ‫ͨݟ‬໨͸ͳΔ΂͘ྨࣅ͢΂͖ɽ3) ೖྗը૾ͱಈըͷྲྀΕํ޲͸ͳΔ΂͘ྨࣅ͢΂͖ɽ4) ೖྗը૾͔Βਪ࡯͞ΕΔਫͷ‫ڍ‬ಈͱಈըͷਫͷ‫ڍ‬ಈ͸ͳΔ΂͘ྨࣅ͢΂͖ɽຊ‫Ͱڀݚ‬͸ਤ 3 ͷୌͷΑ͏ͳɼେ‫ہ‬తͳ‫ͨݟ‬໨͸มԽ͠ͳ͍͕‫ॴہ‬తʹಈ͖ͷ͋ΔΞχϝʔγϣϯΛѻ͏ [7]ɽσʔλϕʔεதͷಈը΋ಉ༷ͷಛ௃Λ࣋ͭͨΊɼࠓ‫ޙ‬͸֤ಈըͷ‫ͨݟ‬໨ͷද‫ͯ͠ͱݱ‬ɼ୯Ұͷ୅දը૾ͷΈΛߟ͑Δɽ্ͷ 4 ͭͷࢦඪʹ‫͖ͮج‬ɼྨࣅ౓ධՁؔ਺Λಋೖ͢Δɽ
͜͜ͰɼIɼAr ɼF Λೖྗը૾ɼr ൪໨ͷྖҬͷΞϧϑΝϚεΫɼྲྀΕํ޲ͷεέον͔ΒಘΒΕΔྲྀΕ৔ͱ͢Δɽ2
஋ϚεΫ Mr Λ࣍ͷΑ͏ʹఆٛ͢Δ:⎧⎨1 A (p) ≥ tmask ,rMr (p) =⎩0 otherwise.

r ൪໨ͷྖҬͷΞχϝʔγϣϯΛੜ੒͢Δɽ
ͱ͜Ζ͕ɼS ͷ࠷େԽ͸೉͍͠ɽࣜ 2ɼࣜ 3ɼࣜ 4ɼࣜ 6͸ɼͦ͜ʹొ৔͢Δશͯͷؔ਺͕ద੾ʹఆٛͰ͖ɼ·ͨඞཁͳ৘ใ΋ϢʔβʹΑͬͯ༩͑ΒΕ͍ͯΔͨΊɼ‫͕ࢉܭ‬ՄೳͰ͋Δɽ͔͠͠ɼࣜ 5 ͸୯Ұը૾͔Βਫͷ‫ڍ‬ಈΛਪఆ͢Δؔ਺ m Λ‫ؚ‬ΜͰ͍Δ͕ɼͦͷΑ͏ͳؔ਺͸ະ஌Ͱ͋Γɼద੾ʹ࣮૷͢Δͷ͕೉͍͠ɽͦ͜Ͱɼզʑͷ S Λ࠷େԽ͢Δઓུ͸ɼ·ͣɼࣜ 2ɼࣜ 3ɼࣜ 4ɼࣜ 6 ͔Β੒Δ S  Λߟ͑ɼ͜ΕΛશͯͷՄೳͳ i ͱ t ͷ૊Έ߹Θͤʹରͯ͠‫ࢉܭ‬͢Δɽ࣍ʹɼߴ͍ྨࣅ౓ S  Λ༩͑ͨ i ͱ t ʹର͠ɼͦͷ i൪໨ͷಈըΛ t ͰฏߦҠಈͤͨ͞΋ͷΛ߹੒ͯ͠ީิΞχϝʔγϣϯ࡞ͬͯϢʔβʹ‫ͤݟ‬Δɽ࠷‫ʹޙ‬Ϣʔβ͕࠷΋ྑ͍ͱ‫ͨ͡ײ‬ಈըΛબͿɼͭ·ΓɼϢʔβࣗ਎ʹࣜ 5 Λ࠷େԽͯ͠΋Β͏͜ͱͰ S ͷ࠷େԽΛߦ͏ɼͱ͍͏ͷ͕զʑͷઓུͰ͋Δɽ

(1)2.2

ಈըσʔλϕʔε͜͜Ͱ p = (px , py ) ͸ϐΫηϧҐஔΛද͢ɽVi ɼMVi ɼ202 ‫ݸ‬ͷਫͷಈըΛूΊͨʢ෇࿥ͷαϜωΠϧҰཡΛࢀFVi ͸ i ൪໨ͷಈըͷ࠷ॳͷϑϨʔϜը૾ɼͦͷϑϨʔϜরʣɽղ૾౓͸ 1280 × 720 ϐΫηϧͰ͋Δɽ֤ಈըͷࠨ಺ͷਫྖҬɼͦͷϑϨʔϜͰͷྲྀΕ৔ͱ͢Δɽྨࣅ౓ධՁӈϑϦοϓͨ͠όʔδϣϯΛ༻ҙ͍ͯ͠ΔͷͰɼಈըͷ਺ؔ਺ S Λ࣍ͷ༷ʹఆٛ͢Δ:͸ 2 ഒͷ 404 ‫͋Ͱݸ‬Δɽi ൪໨ͷಈըʹର͠ɼͦͷྲྀΕ৔S

=A(Mr ∩ T (MVi , t)) ×(2)FVi ɼ2 ஋ϚεΫ MVi ɼΞϧϑΝϚεΫ Ai,t Λ༧Ί‫͠ࢉܭ‬͓ͯ͘ɽ͜ͷͨΊʹɼΦϓςΟΧϧϑϩʔ [8] ʹΑͬͯྲྀ

S f eature (fp (I), fp−t (Vi )) ×(3)Ε৔ FVi ΛಘΔͱಉ࣌ʹɼਫྖҬΛૈ͘ਪఆͨ͠‫ޙ‬ɼᮢ஋

S f low (F(p), FVi (p − t)) ×(4)pSmotion(mp (I), mp−t (Vi )) ×

Mr (p)MVi(p − t).

ॲཧʹΑͬͯ 2 ஋ϚεΫ MVi ΛಘΔɽਤ 4 ʹಈըͱ 2 ஋ϚεΫͷྫΛࣔ͢ɽΞϧϑΝϚεΫ Ai,t ͸৭ώετάϥϜ

(5)
(6)

ࣜ 2 ͸ 1) ͷॏͳΓͷେ͖͞ʹؔ͢Δࢦඪʹ૬౰͢ΔɽA(M)͸ 2 ஋ϚεΫ M ͷ໘ੵΛ‫͢ࢉܭ‬Δؔ਺Ͱ͋ΔɽT (M, t) ͸2 ஋ϚεΫ M Λ 2 ࣍‫ݩ‬ϕΫτϧ t = (tx , ty ) ͰฒߦҠಈͤ͞
Δؔ਺Ͱ͋Δɽt ͷൣғ͸ −wI < tx < wI ͱ −hI < ty < hI
Ͱ͋Δɽ͜͜ͰɼwI ͱ hI ͸ೖྗը૾ I ͷ෯ͱߴ͞Ͱ͋Δɽ
ࣜ 3 ͸ 2) ͷ‫ͨݟ‬໨ͷྨࣅੑʹؔ͢Δࢦඪʹ૬౰͢Δɽؔ਺f ͸ಛ௃‫ه‬ड़ࢠͰ͋Γɼfp (I) ͸ p ͷҐஔͰͷ I ͷ‫ͨݟ‬໨ʹؔ͢Δಛ௃ϕΫτϧΛ༩͑Δɽಛ௃ϕΫτϧͷϖΞ͕༩͑ΒΕΔͱɼؔ਺ S f eature ͕ྨࣅ౓Λ‫͢ࢉܭ‬Δɽࣜ 4 ͸ 3)

ਤ 4: (a) ಈըͷϑϨʔϜɽ (b) 2 ஋ϚεΫ MVi ɽʹΑΔը૾ͷηάϝϯςʔγϣϯ [9] Λ༻͍ͯಘͨɽ

प೾੒෼ʢਤ 7-fʣΛՃࢉ͢Δ͜ͱͰ݁ՌΛಘΔʢਤ 7-cʣɽਤ 5: (a) ಈըͷϑϨʔϜɽ (b) ΞϧϑΝϚεΫɽ2.3ಈը‫ࡧݕ‬ߴ͍ྨࣅ౓ධՁ஋ S  Λ༩͑ΔΑ͏ͳಈըͷΠϯσοΫ
ε i ͱฏߦҠಈྔ t ͷू߹Λ‫͚ͭݟ‬ΔͨΊʹશ୳ࡧΛߦ͏ɽਤ 7: ߹੒ͷϓϩηεɽ‫ࢉܭ‬Λ؆ུԽ͢ΔͨΊɼೖྗը૾ͱಈըϑϨʔϜʹର͠ɼૄͳάϦου্ʹಛ௃఺Λߟ͑Δʢਤ 6ʣɽಛ௃఺ͷִؒ͸ຊ࣮‫Ͱݧ‬͸ 16 ϐΫηϧͱ͢ΔɽैͬͯɼฏߦҠಈྔ t ΋16 ϐΫηϧִؒͰߟ͑Δɽ·ͨɼಛ௃఺͸ϚεΫ্ʹͷΈଘࡏ͢Δɽैͬͯɼࣜ 6 ͷ߲͸‫࠷ʹط‬େԽ͞Ε͍ͯΔͱ‫ݟ‬ͳ͢͜ͱ͕Ͱ͖Δɽࣜ 2 ͷධՁ͸ೖྗը૾্ͱಈը্ʹಉ࣌ʹଘࡏ͢Δಛ௃఺Λ਺͑Δ͜ͱͱಉ஋ͱͳΔɽ

3݁Ռͱٞ࿦
ਤ 8 ʹఏҊख๏Ͱ࡞ͬͨ 11 ‫ݸ‬ͷ݁ՌΛࣔ͢ɽਤ 8-a ͔Βਤ 8-i ͸ 640 × 480 ϐΫηϧͷࣸਅɼਤ 8-j ͱਤ 8-k ͸ 17ੈ‫ʹل‬ඳ͔Εͨ Jacob van Ruisdael ͷ༉ֆͰ͋Γɼղ૾౓͸ͦΕͧΕ 680 × 878 ϐΫηϧͱ 990 × 704 ϐΫηϧͰ͋ΔɽΞϧϑΝϚεΫͷ࡞੒͸ Adobe Photoshop CC 2014ɼྲྀΕํ޲ͷεέον͸ઐ༻ͷιϑτ΢ΣΞΛ։ൃͯ͠༻͍ͨɽಈը‫ࡧݕ‬ʢS  ͷ‫ࢉܭ‬ʣ͸ 100 ίΞͷ CPU Λ༻͍ͯฒਤ 6: ૄͳάϦου্ʹಛ௃఺Λߟ͑Δɽྻʹߦ͍ɼ਺ेඵͷ࣌ؒΛཁ͢Δɽಈը‫͕ࡧݕ‬ऴΘΔͱɼ

16 ‫ݸ‬ͷީิΞχϝʔγϣϯ͕ 4 × 4 ͷάϦουঢ়ʹදࣔ͞
ࣜ 3 ʹ͍ͭͯ͸ɼ֤ಛ௃఺Λத৺ͱ͢Δ 64×64 ϐΫηϧΕɼϢʔβʹબ୒Λଅ͢ (෇࿥ͷಈըࢀর)ɽ

ͷύονʹର͠ը૾ޯ഑ͷώετάϥϜΛߟ͑Δɽ͜Ε͸ɼճసෆมੑͱεέʔϧෆมੑΛແࢹͨ͠ SIFT ಛ௃ྔͱಉओ‫؍‬ධՁ౳Ͱ͋Δ [10]ɽಛ௃ྔͷϖΞ͕༩͑ΒΕΔͱɼͦͷϢʔΫඃ‫ऀݧ‬͸ 13 ਓͷֶੜͰ͋Δɽਤ 8 ͷΞχϝʔγϣϯΛ‫ݟ‬Ϧου‫ ͍ࣜͯͮجʹ཭ڑ‬3 Λ༩͑Δɽͯɼ֤݁Ռͷ࣭ʹର͠ɼ1 ఺ʢ࠷௿ը࣭ʣ͔Β 5 ఺ʢ࠷ߴ݁Ռͷ࣭ΛධՁ͢ΔͨΊʹओ‫؍‬ධՁΛߦͬͨɽࣜ 4 ʹ͍ͭͯ͸, ରԠ͢Δಛ௃఺ͷؒͰྲྀΕ৔ͷྨࣅੑը࣭ʣͷൣғͰ࠾఺ͯ͠΋Βͬͨɽ݁ՌΛਤ 9 ʹࣔ͢ɽ࠷Λ‫͢ࢉܭ‬Δɽೖྗը૾্ʹ͸ྲྀΕํ޲ͷεέον͕ૄʹඳʮඒ͠ߴ఺͸ਤ 8-g ͕֫ಘͨ͠ɽෳ਺ͷඃ‫͔ऀݧ‬Βʮࣗવʯ͔Ε͍ͯΔ͚ͩͳͷͰɼಉ‫جܘ‬ఈؔ਺ (RBF) Λ༻͍ͯิ͍ʯͱίϝϯτ͕ಘΒΕͨɽ࠷௿఺͸ਤ 8-c ͕֫ಘͨ͠ɽί‫ྲྀ͠׬‬Ε৔ΛಘΔɽ2 ࣍‫ݩ‬ϕΫτϧͷϖΞ͕༩͑ΒΕΔͱɼϝϯτʹΑΔͱɼ݁ՌதʹϒϩοΫϊΠζ͕‫ݟ‬ΒΕΔɼͱͦͷؒͷ֯౓ʹ‫ ͍ࣜͯͮج‬4 Λ༩͑Δɽ͍͏ͷ͕େ͖ͳ‫ݪ‬ҼͰ͋Δɽ͜ͷϊΠζ͸‫ݩ‬ͷಈը͕͍࣋ͬͯΔ΋ͷͰ͋ͬͨɽσʔλϕʔεʹొ࿥͢Δಈըͷ࣭ʹ

2.4Ξχϝʔγϣϯͷ߹੒ୌ΍Տ઒౳ͷయ‫ܕ‬తͳਫͷಈ͖Λ‫ݟ‬Δͱɼେ‫ہ‬తʹ͸‫ݟ‬஫ҙ͢΂͖Ͱ͋ͬͨɽൺֱ‫ط‬ଘख๏ [4] ͱൺֱΛߦͬͨɽ‫ط‬ଘख๏Ͱ͸ਤ 8-e ͱͨ໨͕มΘΒͳ͍͕ɼ‫ॴہ‬తʹ͸ਫඈລ౳ͷಈ͖͕‫ݟ‬ΒΕ

ਤ 8-k ͷ݁Ռ͕͋Δɽ͜ΕΒΛͦΕͧΕ e’ ͱ k’ ͱ‫Ϳݺ‬ɽ্Δɽͦ͜ͰɼఏҊख๏Ͱ͸େ‫ہ‬తͳ‫ͨݟ‬໨ɼͭ·Γɼ௿पͱಉ༷ͷओ‫؍‬ධՁΛߦ͏ͱɼਤ 9 ͷ੨͍όʔͷΑ͏ʹͳͬ೾੒෼Λೖྗը૾͔Βಘͯɼ‫ॴہ‬తͳಈ͖ɼͭ·Γɼߴपͨɽe ͱ e’ Λൺ΂ΔͱɼఏҊख๏͕ߴಘ఺Λಘ͓ͯΓɼख೾੒෼Λಈը͔Βಘͯ߹੒͢Δ͜ͱͰ໨తͷΞχϝʔγϣ๏ͷ༏Ґੑ͕࢕͑ΔɽҰํɼk ͱ k’ ͷൺֱͰ͸ɼఏҊखϯΛಘΔɽਤ 7 ʹϓϩηεΛࣔ͢ɽೖྗը૾ʢਤ 7-aʣΛ๏͕΍΍ߴ͍఺਺Λಘͨɽෳ਺ͷඃ‫ऀݧ‬ͷίϝϯτʹΑΔΨ΢εϒϥʔͰ΅͔͠ɼ௿प೾੒෼ʢਤ 7-bʣΛಘΔɽ࣍ͱɼ‫ط‬ଘख๏ͷ݁Ռ k’ ͸ղ૾౓͕௿͘΅΍͚͍ͯΔ͕ɼ͔ʹɼಈըϑϨʔϜʢਤ 7-dʣΛΨ΢εϒϥʔͰ΅͔ͨ͠ըͱ‫ͯͬݴ‬ෆշͰ͸ͳ͍ͷͰ௿ධՁͱ͠ͳ͔ͬͨɼͱͷ͜ͱ

૾ʢਤ 7-eʣΛ‫ݩ‬ͷಈըϑϨʔϜ͔Β‫͢ࢉݮ‬Δ͜ͱͰߴपͩͬͨɽҰํɼ‫ط‬ଘख๏͸‫ ʹࢉܭ‬1 ࣌ؒఔ౓΋අ΍͢ɽఏ೾੒෼ʢਤ 7-fʣΛಘΔɽ࠷‫ʹޙ‬௿प೾੒෼ʢਤ 7-bʣͱߴҊख๏ͷํ͕ಉ౳ͷ݁ՌΛૉૣ͘ಘΒΕΔͱ‫͑ݴ‬Δɽਤ 8: ֤ϖΞ͸ೖྗը૾ʢࠨʣɼΞϧϑΝϚεΫʢӈʣɼྲྀΕํ޲ͷεέονʢ໼ҹʣΛࣔ͢ɽ࣮ࡍͷΞϧϑΝϚεΫ͸
άϨʔεέʔϧ͕ͩɼ্Ͱ͸৭෇͚ͯ͠ՄࢹԽ͍ͯ͠Δɽ࡞੒ͨ͠ΞϧϑΝϚεΫͷ਺΋ࣔ͢ɽਤ 10: య‫ܕ‬తͳࣦഊྫɽ

ਤ 9: ओ‫؍‬ධՁͷ݁Ռɽ֤όʔ͸ฏ‫఺ۉ‬Λද͢ɽΤϥʔόʔ͸ඪ४ภࠩɽ
ࣦഊྫ

ਤ 10 ͸య‫ܕ‬తͳࣦഊྫͰ͋Δɽਤ 10-a ͸ਫͷ๐͕ൃੜ͍ͯ͠Δେ͖ͳന͍ྖҬ͕͋Γɼ͜ͷ෦෼͸ܹ͘͠ಈ͘͸ͣͰ͋Δ͕ɼ݁Ռʹ͸ͦͷΑ͏ͳਫͷ‫ڍ‬ಈ͕‫ݟ‬ΒΕͳ͍ɽ͜Ε͸‫͞ࡧݕ‬ΕͨಈըʹͦͷΑ͏ͳ‫ڍ‬ಈΛ࣋ͬͨ΋ͷ͕ͳ͔ͬͨͷ͕‫ݪ‬ҼͰ͋Δɽ·ͨɼਤ 10-b ͸খ͞ͳୌ͕େ͖ͳୌͷഎ‫͍ͯ͑ݟʹޙ‬Δ͕ɼ͜ΕΒ΋ಈ͔͢͜ͱ͕ग़དྷ͍ͯͳ͍ɽཧ༝͸ಉ͘͡‫͞ࡧݕ‬Εͨಈը͕ͦͷΑ͏ͳখ͞ͳୌΛ‫ؚ‬ΜͰ͍ͳ͔ͬͨͨΊͰ͋Δɽ3.1‫ݶ‬քͱࠓ‫ޙ‬ͷల๬ࠓճ͸ਫͷΈΛѻ͕ͬͨɼࠓ‫ޙ‬͸Ԍ΍Ԏ౳ɼଞͷྲྀମʹ΋ख๏Λ֦ு͍ͨ͠ɽ·ͨɼۙ೥ͷ໨͍֮͠ը૾ཧղٕज़ͷਐาΛ‫ݟ‬Ε͹ɼਫྖҬ΍ྲྀΕํ޲ͷࣗಈਪఆ΋ՄೳͩͱࢥΘΕΔɽ஌తͳγεςϜΛߏங͠ɼࣗಈԽΛ໨ࢦ͍ͨ͠ɽࢀߟจ‫ݙ‬[1] Y.-Y. Chuang, D. B. Goldman, K. C. Zheng, B. Curless,
D. H. Salesin, and R. Szeliski, “Animating pictures withstochastic motion textures,” in Proc. SIGGRAPH 2005,2005, pp. 853–860.
[2] M. Okabe, K. Anjyo, T. Igarashi, and H.-P. Seidel,“Animating pictures of ﬂuid using video examples,”Computer Graphics Forum (Proc. EUROGRAPHICS),vol. 28, no. 2, pp. 677–686, 2009.
[3] Y. Gui, L. Ma, C. Yin, and C. Z, “Preserving global features of ﬂuid animation from a single image using videoexamples,” Journal of Zhejian University - Science C,
vol. 13, no. 7, pp. 510–519, 2012.
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