3次元ビデオによる人体3次元計測とその応用

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(1)Vol.2013-CG-153 No.18 Vol.2013-CVIM-189 No.18 2013/11/29. ৘ใॲཧֶձ‫ڀݚ‬ใࠂ IPSJ SIG Technical Report. ̏࣍‫ݩ‬ϏσΦʹΑΔਓମ̏࣍‫ܭݩ‬ଌͱͦͷԠ༻ Ԇ‫ ݪ‬ষฏ1,a). ֓ཁɿ̏࣍‫ݩ‬ϏσΦͱ‫ݺ‬͹ΕΔଟࢹ఺ө૾Λೖྗͱͨ͠ਓମͷ̏࣍‫ܗݩ‬ঢ়ɾӡಈ‫ܭ‬ଌ͸ɼͦͷඇ઀৮ɾඇ߆ ଋͳಛ௃͔Βແ‫ܗ‬จԽࡒͷσΟδλϧΞʔΧΠϒΛ࢝Ίͱͯ͠ɼϚʔΧϨεϞʔγϣϯΩϟϓνϟγεςϜ ͱͯ͠ͷར༻΍ɼશपғࣗ༝ࢹ఺ཱମө૾ੜ੒΁ͷԠ༻ͳͲɼ༷ʑͳ৔໘ͰΑΓ࣮༻తͳٕज़͕ఏҊ͞Ε ͖͓ͯͯΓɼ·͞ʹ‫ࣨڀݚ‬Ϩϕϧ͔Β࣮Ԡ༻΁ͱ‫ڀݚ‬։ൃͷஈ֊͕ਐ΋͏ͱ͍ͯ͠ΔɽຊߘͰ͸̏࣍‫ݩ‬Ϗ σΦͷྺ࢙ͱͦͷ‫ج‬ຊతͳΞϧΰϦζϜΛ঺հ͠ɼ༷ʑͳԠ༻ྫͱͱ΋ʹࠓ‫ޙ‬ͷ‫ڀݚ‬՝୊ʹ͍ͭͯड़΂Δɽ. 1. ̏࣍‫ݩ‬ϏσΦͱ͸ ̏࣍‫ݩ‬ϏσΦʢ3D videoʣͱ͸ɼγʔϯͷશपғ̏࣍‫ܗݩ‬ ঢ়ɾද໘ςΫενϟΛ‫ه‬࿥͠ɼࣗ༝ͳࢹ఺͔Βཱମఏࣔ͢ ɽ͜ͷΑ͏ͳҙ Δ͜ͱ͕Ͱ͖Δө૾ϝσΟΞͰ͋Δʢਤ 1ʣ ຯͰͷ̏࣍‫ݩ‬ϏσΦ͸ɼ1997 ೥ʹ Moezzi Β [1] ͱ Kanade Β [2] ʹΑͬͯఏҊ͞Εɼͦͷ‫ޙ‬ଟ͘ͷάϧʔϓʹΑͬͯ ‫ڀݚ‬ɾ։ൃ͕ଓ͚ΒΕ͍ͯΔ [3][4][5][6][7][8][9][10][11][12]ɽ ̏࣍‫ݩ‬ϏσΦͷಛ௃͸ɼର৅ͷશपғ̏࣍‫ݩ‬ද໘‫ܗ‬ঢ়ͱ ӡಈ৘ใΛཅʹ࣋ͭ఺Ͱ͋Γɼ͜ͷ఺ʹ͓͍༷ͯʑͳʮ̏. ਤ 1. ଟࢹ఺ө૾ʢ্ஈʣ͔Βੜ੒͞Εͨ̏࣍‫ݩ‬ϏσΦʹΑΔࣗ༝ࢹ ఺ө૾ੜ੒ʢԼஈʣ. ࣍‫ݩ‬ʯٕज़ͱରൺ͢Δ͜ͱ͕Ͱ͖Δɽ. 3D ςϨϏɾөը 3D ςϨϏ͓Αͼ 3D өը͕࣋ͭө૾৘ ใ͸εςϨΦө૾ͱ‫ݺ‬͹Εɼࠨӈͷ໨ʹࢹࠩͷ෇͍ͨ ө૾Λఏࣔ͢Δ͜ͱʹΑͬͯࢹௌऀࣗ਎ͷ೴͕΋ͭࢹ ֮‫ػ‬ೳʹ̏࣍‫ݩ‬γʔϯΛཧղͤ͞Δ఺ʹಛ௃͕͋Δɽ ࠨӈͷ໨ʹҟͳͬͨө૾Λಧ͚ΔͨΊʹ͸ภޫϝΨω ΍ࢹࠩόϦΞͳͲԿΒ͔ͷ࢓ֻ͚͕ඞཁͱͳΔ͕ɼө ૾ͦͷ΋ͷ͸௨ৗͷΧϝϥͰࡱӨͨ͠΋ͷͱ౳Ձͳͨ Ίɼө૾඼࣭͕ߴ͍ɽ͔͠͠ҰํͰɼ௨ৗͷө૾͕ࠨ ӈ྆‫༻ʹ༻؟‬ҙ͞Ε͍ͯΔ͚ͩͰ͋Δ͜ͱ͔Βɼࣗ༝ ͳࢹ఺มߋ΍ɼγʔϯͷ̏࣍‫ݩ‬৘ใʹ‫ͮ͘ج‬ฤूͳͲ ΛՃ͑Δ͜ͱ͸ࠔ೉Ͱ͋Δɽ. 3D ਂ౓ɾϨϯδηϯα Ұൠʹ 3D ਂ౓ηϯα΋͘͠͸ Ϩϯδηϯαͱͯ͠ѻΘΕΔ΋ͷʹ͸ɼࢹࠩਪఆʹ‫ج‬ ͮ͘ํࣜͱɼޫ͕ԟ෮͢Δ࣌ؒʢTime-of-Flightʣͷ ‫ܭ‬ଌʹ‫ࣜํͮ͘ج‬ͷ̎λΠϓʹ෼ྨͰ͖Δɽࢹࠩਪఆ ʹ‫ࣜํͮ͘ج‬͸ɼ͍ΘΏΔडಈ΋͘͠͸ೳಈεςϨΦ ๏Λ̍ͭͷσόΠεͱ࣮ͯ͠૷ͨ͠΋ͷͰ͋Γɼۙ೥ Ͱ͸ Microsoft Kinect[13] ͕޿͘࢖༻͞Ε͍ͯΔɽ· 1 a). ‫౎ژ‬େֶେֶӃ৘ใֶ‫ڀݚ‬Պ ‫۠ژࠨࢢ౎ژ‬٢ాຊொɼ606-8501 [email protected]. c 2013 Information Processing Society of Japan . ͨޫ͕ԟ෮͢Δ࣌ؒʢ΋͘͠͸Ґ૬ࠩʣΛ‫ܭ‬ଌ͢Δη ϯα͸ɼ̍఺ͣͭ૸ࠪ͢Δ LIDAR ͱɼ໘શମΛҰ౓ ʹ‫ܭ‬ଌ͢Δ ToF Χϝϥʹ෼ྨ͞Εɼಛʹ ToF Χϝϥ ͸ۙ೥௿Ձ֨Խ͕ਐΜͰ͍Δ [14][15][16]ɽ͜ΕΒ͸Χ ϝϥ͔Β‫͍ͯ͑ݟ‬Δൣғɼͭ·Γର৅ͷखલଆͷΈΛ Ωϟϓνϟ͢Δ΋ͷͰ͋Γɼશपғͷ̏࣍‫ݩ‬৘ใΛ̍ ୆ͰऔಘͰ͖ΔΘ͚Ͱ͸ͳ͍ɽͭ·Γਖ਼֬ʹ͸ 2.5D ৘ใΛऔಘ͢ΔͨΊͷ΋ͷͰ͋Δ͕ɼಛʹ LIDAR ͸ ‫ܭ‬ଌਫ਼౓͕ߴ͘ɼେ‫ܕ‬༗‫ܗ‬จԽࡒͷΞʔΧΠϒԽͳͲ ʹ΋༻͍ΒΕ͍ͯΔ [17]ɽ. 3D ϞʔγϣϯΩϟϓνϟ 3D ϞʔγϣϯΩϟϓνϟ͸ ର৅ද໘ʹϚʔΧʔΛऔΓ෇͚ɼͦͷಈ͖Λ‫ݕ‬ग़͢Δ ͜ͱʹΑͬͯϚʔΧʔ‫܈‬ͷӡಈΛऔಘ͢Δٕज़Ͱ͋ Δɽྫ͑͹ϚʔΧʔΛମઅͷ֤෦ҐʹऔΓ෇͚Δ͜ͱ ʹΑͬͯɼࠎ֨ߏ଄ͷӡಈΛ‫ٻ‬Ίɼ͜ΕΛ 3D CG Ωϟ ϥΫλʔͷৼΓ෇͚΁ͱ࢖༻͢Δྫ͕༗໊Ͱ͋Δɽ. 3D CG Ξχϝʔγϣϯ 1990 ೥୅͔Β޿͘࢖༻͞Ε͍ͯ Δ 3D CG ΞχϝʔγϣϯͰ͸ɼͦͷ‫ܗ‬ঢ়ɾӡಈ৘ใ ͕ΞχϝʔλʔʹΑ੍ͬͯ࡞͞ΕΔͷʹରͯ͠ɼ̏࣍ ‫ݩ‬ϏσΦͰ͸ඃࣸମͷ‫ܗ‬ঢ়ɾӡಈ͕ͦͷ··औಘ͞Ε. 1.

(2) Vol.2013-CG-153 No.18 Vol.2013-CVIM-189 No.18 2013/11/29. ৘ใॲཧֶձ‫ڀݚ‬ใࠂ IPSJ SIG Technical Report. ... Multi-view images. Visual hull. 3D video. ... Multi-view silhouettes. Photo hull ਤ 2 ̏࣍‫ݩ‬ϏσΦੜ੒ͷྲྀΕ. ଟࢹ఺Χϝϥ‫܈‬Λඋ͑ͨελδΦͰࡱӨ͞ΕΔ [21][20] [3]ɽ ͜͜Ͱ̏࣍‫ݩ‬ϏσΦࡱӨ͕ՄೳͱͳΔൣғ͸ɼ֤Χϝϥ ͷը֯ͱඃࣸքਂ౓ͷ‫ڞ‬௨ྖҬͱܾͯ͠ఆ͞Εɼ֤Χϝϥ. Object. ͷࡱӨՄೳൣғΑΓ΋ຊ࣭తʹ‫ͳ͘ڱ‬ΔɽͦͷͨΊղ૾౓. 16 Cameras 6m. Floor. Λ٘ਜ਼ʹͤͣʹ޿ൣғࡱӨΛ࣮‫͢ݱ‬Δʹ͸ɼ୯७ʹΧϝϥ. 6m. ୆਺Λ૿΍ͯ͠ҟͳΔۭؒྖҬΛ୲౰ͤ͞Δ͔ɼ΋͘͠͸ (a). ਤ 3. (b). ύϯνϧτՄೳͳೳಈΧϝϥ‫ʹ܈‬Αͬͯ௥੻ࡱӨΛߦ͏ඞ. Մൖࣜ̏࣍‫ݩ‬ϏσΦࡱӨελδΦ [20] ͷ (a) ֎‫( ͱ؍‬b) Χϝ ϥ഑ஔਤ. ཁ͕͋Δɽ ͔͠͠௨ৗͷ෺ମ௥੻ࡱӨͱҟͳΓɼ̏࣍‫ݩ‬ϏσΦੜ੒ ͷͨΊʹ͸. Δ఺͕ҟͳΔɽ ࣗ༝ࢹ఺ TV. ࣗ ༝ ࢹ ఺ TV. ( 1 ) ֤࣌ࠁͰର৅෺ମΛશͯͷํ޲͔Βे෼ͳղ૾౓Ͱࡱ (Free-viewpoint. TV,. FTV)[18][19] ʹؔ͢Δ‫ݩ࣍̏ͱڀݚ‬ϏσΦ͸ɼଟࢹ఺ Χϝϥө૾Λೖྗͱͯࣗ͠༝ࢹ఺ө૾Λੜ੒͢Δͱ͍. ӨͰ͖Δ͜ͱ. ( 2 ) ֤ࡱӨ࣌ࠁͰͷΧϝϥͷ಺෦ɾ֎෦ύϥϝʔλ͕े෼ ͳਫ਼౓ͰಘΒΕΔ͜ͱ. ͏‫ڞͰ఺؍‬௨఺͕ଟ͍͕ɼ̏࣍‫ݩ‬ϏσΦ͕̏࣍‫ܗݩ‬ঢ়. Λอূ͢ΔΑ͏ʹɼৗʹ֤ΧϝϥΛ੍‫͠ޚ‬ଓ͚ͳͯ͘͸ͳ. ৘ใΛཅʹ‫ٻ‬ΊΔ͜ͱͰɼͦΕΛ‫ͨ͠ʹج‬ӡಈਪఆͳ. Βͳ͍ɽ͜ΕΛ࣮‫͢ݱ‬ΔͨΊͷख๏ͱͯ͠ɼචऀΒ͸ηϧ. ͲΛՄೳͱ͢Δͷʹରͯ͠ɼFTV Ͱ͸ࣗ༝ࢹ఺ө૾. ํࣜͱ‫Ϳݺ‬ίϯηϓτʹ‫͍ͯͮج‬ɼλʔήοτͱ͢ΔࡱӨ. ੜ੒ͷͨΊʹ̏࣍‫ܗݩ‬ঢ়৘ใ͕ؒ઀తʹ༻͍ΒΕɼཅ. ۭؒ಺Λࣗ༝ʹӡಈ͢Δඃࣸମͷ̏࣍‫ݩ‬ϏσΦࡱӨΛ࣮‫ݱ‬. ʹ͸‫͢ࢉܭ‬Δ͜ͱΛॏࢹ͠ͳ͍఺ʹಛ௃͕͋Δɽ. ͢ΔΞϧΰϦζϜΛఏҊ͍ͯ͠Δ [22][3]ɽ. 2. ̏࣍‫ݩ‬ϏσΦͷੜ੒ϓϩηε. 2.2 ର৅ྖҬநग़. ̏࣍‫ݩ‬ϏσΦੜ੒ͷ‫ج‬ຊతͳྲྀΕΛਤ 2 ʹࣔ͢ɽ·ͣ̏. ର৅ྖҬநग़͸ԿΒ͔ͷࣄલ஌ࣝʹ‫ࡱ͍ͯͮج‬Өը૾Λ. ࣍‫ݩ‬ϏσΦੜ੒ͷೖྗͱͳΔଟࢹ఺ө૾͔Βର৅ը૾ྖҬ. ର৅ʢલ‫ܠ‬ʣྖҬͱഎ‫ྖܠ‬Ҭʹ෼ׂ͢ΔॲཧͰ͋Γɼγϧ. ʢγϧΤοτʣΛநग़͠ɼ͜ΕΛ‫ ͯ͠ʹج‬visual hull ΛಘΔɽ. Τοτநग़ɼ͋Δ͍͸ (alpha) matting ͳͲͱ΋‫ݺ‬͹ΕΔɽ. ͍࣍ͰςΫενϟ৘ใ͕࠷΋੔߹͢Δʢphoto-consistecy. ͜ͷ͏ͪ matting ͱ‫ݺ‬Μͩ৔߹͸ಛʹલ‫ͱܠ‬എ‫ܠ‬ͷ‫ڥ‬ք. ͕࠷΋ߴ͍ʣ‫ܗ‬ঢ়ͱͯ͠ photo hull Λਪఆͨ͠‫ʹޙ‬ɼ͜Ε. ෦෼ʹ͓͍ͯըૉͷЋ஋ɼ͢ͳΘͪલ‫ͱܠ‬എ‫ܠ‬ͷࠞ߹཰Λ. ͷද໘ςΫενϟΛੜ੒͢Ε͹ɼࣗ༝ͳࢹ఺͔Βө૾ԽͰ. ΋ਪఆ͢Δ͜ͱΛ໨తͱ͢Δ͜ͱ͕ଟ͍ [23]ɽҰํͰγϧ. ͖Δ̏࣍‫ݩ‬ϏσΦ͕ੜ੒͞ΕΔɽҎ߱Ͱ͸֤εςοϓʹͭ. Τοτநग़ͱ‫ݺ‬Μͩ৔߹͸Ћ஋͕ 0 ͱ 1 ͷೋ஋ͱͯ͠໰୊. ͍ͯɼͦͷུ֓Λड़΂Δɽ. Λ؆୯Խ͍ͯ͠Δ৔߹͕ଟ͍ɽ. 2.1 ଟࢹ఺ө૾ࡱӨ. ‫ࠩܠ‬෼΍ΫϩϚΩʔ͕୅දతͰ͋Δɽഎ‫ࠩܠ‬෼ͱ͸ɼ·ͣ. ର৅ྖҬநग़ʹ༻͍ΒΕΔ۩ମతͳࣄલ஌ࣝͱͯ͠͸എ ̏࣍‫ݩ‬ϏσΦੜ੒ʹ༻͍Δଟࢹ఺ө૾͸ɼਤ 3 ͷΑ͏ʹ. c 2013 Information Processing Society of Japan . 2.

(3) Vol.2013-CG-153 No.18 Vol.2013-CVIM-189 No.18 2013/11/29. ৘ใॲཧֶձ‫ڀݚ‬ใࠂ IPSJ SIG Technical Report. Object. ର৅͕ଘࡏ͠ͳ͍ঢ়ଶͰࣄલʹը૾ΛࡱӨ͓͖ͯ͠ɼ࣮ࡍ. Background. Reflectance. ʹର৅͕ଘࡏ͢Δঢ়ଶͰͷը૾ͱͷࠩΛ‫ݕ‬ग़͢Δ͜ͱʹ‫ج‬. Shape. ͔ͷܾ·ͬͨ৭ҬͰ౷Ұ͠ʢਤ 3(a)ʣɼࡱӨը૾ͷ֤ըૉ. Interreflection. Highlight. ஋͕ͦͷ৭Ҭʹ͚ۙΕ͹എ‫ܠ‬ɼԕ͚Ε͹લ‫͢ͳݟͱܠ‬ख๏. Reflection. ͮ͘ख๏Ͱ͋Δɽ͢ͳΘͪҰఆ஋Ҏ্ͷࠩ෼͕ଘࡏ͢Ε͹. Reflectance. Lighting. Texture. Texture. Shape. લ‫ܠ‬ɼͦ͏Ͱͳ͚Ε͹എ‫͢ͱܠ‬ΔɽҰํΫϩϚΩʔͰ͸ɼ എ‫ܠ‬৭ΛϒϧʔɼάϦʔϯɼάϨʔɼϗϫΠτͳͲͳΜΒ. Ͱ͋Δ*1 ɽ. Shading. Shadow. Light field. Refraction. Scattering. Occlusion (Silhouette). Disparity. ͔͍ͣ͠͠Εͷख๏ʹ͓͍ͯ΋ɼ֤ըૉಠཱʹલ‫ܠ‬ɾഎ ‫ܠ‬ͷ൑அΛߦͬͯ͠·ͬͯ͸ϊΠζʹऑ͘‫ͳ݈ؤ‬ର৅ྖ Ҭநग़Λ࣮‫͢ݱ‬Δ͜ͱ͸೉͍͠ɽͦͷͨΊྡ઀͢Δըૉ. I1. ಉ࢜Ͱͷલ‫ܠ‬ɾഎ‫΁ܠ‬ͷ෼ྨʹ࿈ଓੑΛ࣋ͨͤΔख๏͕Ұ. I2. C1. ൠʹ࢖༻͞Εɼಛʹલ‫ܠ‬ɾഎ‫ܠ‬ͷೋ஋ʹ෼ྨ͢Δ໰୊͸ɼ. IN. C2. ^. I. CN. ^. C. ਤ 4 ̏࣍‫ݩ‬ϏσΦͷ‫ࢉܭ‬Ϟσϧ [3]. min-cut/max-flow ໰୊ʹม‫ີݫͯ͠׵‬ղΛ‫ٻ‬ΊΔΑ͏ʹ. Object. ΞϧΰϦζϜԽ͞ΕΔ͜ͱ͕ଟ͍ [24][25]ɽ. Shape. ͢Δଟࢹ఺ը૾͸‫ؔʹ͍ޓ‬࿈ͷͳ͍ը૾ͷू߹Ͱ͸ͳ͘ɼ ಉ͡ର৅ΛҟͳΔํ޲͔ΒࡱӨͨ͠΋ͷͰ͋ΔɽͦͷͨΊ. Lambertian reflection. ԿΒ͔ͷ‫ؒ఺ࢹͰܗ‬ͷؔ܎Λ࢖༻͠ɼΑΓ‫ͳ݈ؤ‬ର৅ྖҬ Λ࣮‫͢ݱ‬Δख๏΋ఏҊ͞Ε͍ͯΔɽ ྫ͑͹ಉ͡ର৅ΛҟͳΔํ޲͔ΒࡱӨͨ͠ͱ͍͏ࣄ࣮͔. Lighting Shap. e-fro. -Stereo. Texture. Shape-from. ߦΘΕΔҰൠతͳख๏Ͱ͋Δ͕ɼ̏࣍‫ݩ‬ϏσΦࡱӨͰ࢖༻. Background. Reflectance. ·্ͨ‫ه‬ͷഎ‫ࠩܠ‬෼ɾΫϩϚΩʔ͸ը૾̍ຕຖʹಠཱʹ. Shading. m-S. Reflectance. Texture. Shape. ilhou. ette. Shadow. Occlusion (Silhouette). Light field. Disparity. Βɼ‫ج‬ຊతʹ͸લ‫ͱܠ‬എ‫ܠ‬ͷ৭ώετάϥϜ͸ࢹ఺͕ม Θͬͯ΋େ͖ͳมԽ͕ੜ͡ͳ͍͜ͱ͕‫ظ‬଴Ͱ͖Δͱ͢Δɽ ͜ͷԾఆʹ‫͖ͮج‬ɼ͋Δࢹ఺Ͱ͋Δըૉ஋Λલ‫͋ܠ‬Δ͍͸ എ‫͏͍ͱͨ͠ͱܠ‬൑அ݁Ռ͕ผͷࢹ఺Ͱ΋ҙຯΛ࣋ͭͱ‫ݟ‬. I1. I2. C1. ͳ͠ɼલ‫ܠ‬ɾഎ‫ܠ‬ͷ൑அ݁ՌΛࢹ఺ؒͰ఻ൖͤ͞Δख๏͕. ਤ 5. C2. IN. CN. ̏࣍‫ܗݩ‬ঢ়෮‫ݩ‬ͷ‫ࢉܭ‬Ϟσϧ [3]. ఏҊ͞Ε͍ͯΔ [26]ɽ ͞Βʹɼ֤ࢹ఺Ͱಠཱʹର৅ྖҬநग़Λͯ͠͠·ͬͯ͸ɼ. Λද͠ɼͦͷ͏ͪഁઢ͸؆୯ԽͷͨΊʹແࢹ͞ΕΔӨ‫ڹ‬Λ. ͦͷ݁Ռ͕͋Δ‫ڞ‬௨ͷ̏࣍‫ܗݩ‬ঢ়ͷ౤Ө૾ͱͯ͠ໃ६͕. ද͢ɽࠇ৭࣮ઢ͸̏࣍‫ܗݩ‬ঢ়෮‫ٯͯ͠ͱݩ‬໰୊Λղ͘աఔ. ແ͍͜ͱΛอূ͢Δ͜ͱ͕Ͱ͖ͳ͍ɽ͜Ε͸ intersection. Λ͍ࣔͯ͠Δɽ͢ͳΘͪӄӨ΍ӄɼ۶ં΍൓ࣹɾࢄཚͷӨ. consistency[27] ͱ‫ݺ‬͹Εɼ௚‫ײ‬తʹ͸֤ࢹ఺ͰಘΒΕͨγ. ‫ڹ‬͸ߟྀ͞Εͣɼ෺ମද໘ʹ͓͚Δ‫׬‬શ֦ࢄ൓ࣹͱɼ·ͨ. ϧΤοτ͔Βࢹମੵަࠩ๏ʹΑͬͯ visual hull Λ‫͠ࢉܭ‬ɼ. ର৅ࣗ਎ʹΑΔഎ‫ܠ‬ͷःณؔ܎ͷΈ͕ѻΘΕΔɽ. ͜ΕΛ࠶౤Өͨ͠৔߹ʹ‫ݩ‬ͷγϧΤοτͱҰக͠ͳͯ͘. ͜ͷΑ͏ͳԾఆʹ‫ͱͮ͘ج‬ɼը૾ؒͷըૉ஋ʢ‫͑ݟ‬ʣͷൺ. ͸ͳΒͳ͍ɼͱ͍͏੍໿Ͱ͋Δɽ͜ͷΑ͏ʹΩϟϦϒϨʔ. ֱʹΑΔࢹࠩਪఆ͕༗ޮʹಇͨ͘ΊʹεςϨΦ๏ [35][36]. γϣϯ৘ใΛར༻ͨ͠ଟࢹ఺ର৅ྖҬͷಉ࣌ਪఆ๏͕ଟ͘. ͕ՄೳͱͳΓɼ·ͨର৅ʹΑΔഎ‫ܠ‬ͷःณؔ܎͔Βγϧ. ఏҊ͞Ε͍ͯΔ [27][28][29][30][31][32][33][34]ɽ. Τοτ͕ಘΒΕɼࢹମੵަࠩ๏ [37][38][39] ͕࣮ߦՄೳͱ ͳΔɽ. 2.3 ̏࣍‫ܗݩ‬ঢ়෮‫ݩ‬. ͜͏ͯ͠ଟࢹ఺ө૾͔Βਓ෺ͷ࣌‫ܗݩ࣍̏ྻܥ‬ঢ়Λ෮‫ݩ‬. ̏࣍‫ݩ‬ϏσΦʹ͓͚Δ‫ࢉܭ‬Ϟσϧ͸ɼຊདྷਤ 4 ͷΑ͏ʹ. ͢Δ‫ڀݚ‬͸ɼର৅ͷςΫενϟ৘ใΛ༻͍ΔΞϓϩʔν. ଟ༷ͳޫֶ‫ݱ‬৅Λ‫ؚ‬ΉੈքͰ͋Δɽ͜Εʹରͯ̏࣍͠‫ܗݩ‬. ͱɼγϧΤοτ৘ใΛ༻͍ΔΞϓϩʔνͷ̎छྨ͔Βε. ঢ়෮‫ͯ͠ࡍʹݩ‬͸͜ΕΛ؆୯Խͨ͠ਤ 5 ͷΑ͏ͳϞσϧ͕. λʔτͨ͠ɽ۩ମతʹ͸લऀ͸௨ৗͷεςϨΦ๏Λϕʔε. ޿͘Ծఆ͞ΕΔɽ͜ͷਤʹ͓͍ͯࣼΊͷ໢ֻ͚͕͞Εۣͨ. ʹɼ2.5 ࣍‫ܗݩ‬ঢ়ʢdepth-mapʣΛషΓ߹ΘͤΔ͜ͱͰશप. ‫ܗ‬͸؆୯ԽͷͨΊʹແࢹ͞Εͨޫֶ‫ݱ‬৅Λද͠ɼԣઢͷ໢. ғ̏࣍‫ܗݩ‬ঢ়෮‫ݩ‬Λߦͬͨ Kanade Βͷ‫[ ڀݚ‬2] ͱ 2.5 ࣍. ֻ͚͕͞Εͨԁ͸‫ط‬஌ͱ͞ΕͨΧϝϥΩϟϦϒϨʔγϣϯ. ‫ܗݩ‬ঢ়Λհͣ͞ʹ௚઀̏࣍‫ܗݩ‬ঢ়Λ‫ٻ‬ΊΔ Seitz Βͷ‫ڀݚ‬. Λද͢ɽ·ͨփ৭໼ҹ͸෺ཧੈքͰͷੜ੒աఔʢॱ໰୊ʣ. ʢvolumetric stereoʣ[40] ͕ɼ‫ऀޙ‬͸ࢹମੵަࠩ๏ͰಘΒΕ. *1. http://www.alphamatting.com/ ʹ [23] ͷϕϯνϚʔΫ͓Αͼ ͍͔ͭ͘ͷαϯϓϧίʔυ͕ެ։͞Ε͍ͯΔɼ. c 2013 Information Processing Society of Japan . Δ visual hull Λϕʔεʹͨ͠ Moezzi Βͷ‫[ ڀݚ‬1] ͕ɼ‫ڞ‬ ʹ 90 ೥୅‫ޙ‬൒ʹఏҊ͞Ε͍ͯΔɽ. 3.

(4) Vol.2013-CG-153 No.18 Vol.2013-CVIM-189 No.18 2013/11/29. ৘ใॲཧֶձ‫ڀݚ‬ใࠂ IPSJ SIG Technical Report. ·ͨ 2000 ೥୅ʹೖΔͱςΫενϟ৘ใͱγϧΤοτ৘ ใΛಉ࣌ʹ༻͍ΔΞϓϩʔν͕ଟ͘‫͞ڀݚ‬ΕΔΑ͏ʹͳͬ ͨ [41] [42] [4] [43] [44] [45] [46] [47] [48] [21] [10] [49] ɽ͜ Ε͸ςΫενϟϚονϯάʹΑΔ‫ܗ‬ঢ়෮‫͕ݩ‬ʮࢹ఺ؒͷର. (a). Ԡ෇͚͕ܾ·Ε͹ର৅ද໘‫ܗ‬ঢ়Λਖ਼͘͠‫͖Ͱࢉܭ‬Δ͕ɼࢹ ఺ؒͷରԠ෇͚Λৗʹਖ਼͘͠ߦ͏͜ͱ͸༰қͰ͸ͳ͍ʯͱ ͍͏ಛ௃Λ༗͍ͯ͠Δͷʹରͯ͠ɼγϧΤοτΛ༻͍ͨ‫ܗ‬ ঢ়෮‫ݩ‬͸ʮର৅ͷ֓‫ܗ‬ʢvisual hullʣ͔͠‫·ٻ‬Βͳ͍͕ɼࢹ ఺ؒͷରԠ෇͚͕ෆཁͰൺֱత҆ఆʹ‫ܗ‬ঢ়͕‫·ٻ‬Δʯͱ͍ ͏૬ิతͳؔ܎Λ͍࣋ͬͯΔͱ͍͏෼ੳʹ‫͍͍ͯͮج‬Δɽ ͢ͳΘͪɼ·ͣଟࢹ఺γϧΤοτ͔Β visual hull ͱͯ͠. (b). ʮର৅͕ඞͣଘࡏ͢ΔൣғʯΛ҆ఆʹ‫ٻ‬Ίɼ͍࣍Ͱ͜ͷൣғ ಺ͰςΫενϟͷҰக౓ʢphoto-consistencyʣΛ࠷େԽ͢. ਤ 6. (c). (d). ̏࣍‫ݩ‬ϏσΦ͔Βͷ‫͓إ‬Αͼࢹઢํ޲ਪఆ [60]ɽ(a) ೖྗଟࢹ. Δ‫ܗ‬ঢ়ʢphoto hullʣΛ‫ٻ‬ΊΔɼͱ͍͏ߟ͑ํͰ͋Δʢਤ. ఺ө૾ɼ(b) ෮‫͞ݩ‬Εͨ̏࣍‫ܗݩ‬ঢ়্Ͱ‫ݕ‬ग़͞Εͨ‫ྖإ‬Ҭɼ(c). 2ʣɽ. ‫ྖإ‬Ҭͷ௒ղ૾ϨϯμϦϯάɼ(d) ࢹઢํ޲ਪఆɽ. ·্ͨ‫ه‬ͷΑ͏ʹ̍࣌ࠁͷ̏࣍‫ܗݩ‬ঢ়Λಠཱʹ‫ٻ‬ΊΔͩ ͚Ͱͳ͘ɼෳ਺࣌ࠁͷ‫ܗ‬ঢ়Λಉ࣌ʹ෮‫͢ݩ‬Δํ๏ [50][51]. ͞Βʹ‫ܗ‬ঢ়෮‫ݩ‬΍Χϝϥͷ಺෦ɾ֎෦ΩϟϦϒϨʔγϣ. ΍ɼ͋Δ࣌ࠁʹ͓͚Δର৅‫ܗ‬ঢ়Λ·ͣ෮‫͠ݩ‬ɼ͜ΕΛΩʔ. ϯʹ‫ޡ‬Γ͕ଘࡏ͢Δͱ‫ͱ͢ͳݟ‬ɼඍখྖҬͷࡱӨΧϝϥ΁. ϑϨʔϜͱͯ͠ྡ઀͢Δ࣌ࠁͷ‫ܗ‬ঢ়΁ͱஞ࣍ม‫͢ܗ‬Δ͜ͱ. ͷ౤Өઌ͕‫ز‬ԿతʹͣΕ͍ͯΔ͜ͱΛߟྀ͠ͳͯ͘͸ͳΒ. Ͱ‫ܗ‬ঢ়ͱӡಈΛಉ࣌ʹ෮‫͢ݩ‬Δํ๏ [52][53] ͷΑ͏ʹ̏࣍. ͳ͍ɽ͜ͷҐஔͣΕΛԾ૝ࢹ఺ҐஔʹԠͯ͡దԠతʹमਖ਼. ‫ܗݩ‬ঢ়ͱಉ࣌ʹӡಈΛਪఆ͢Δख๏΋‫͞ڀݚ‬Ε͍ͯΔɽ. ͢Δํ๏ͱͯ͠ɼFloating Texture Mappting ๏ [54] Ͱ͸ ‫ݸ‬ผͷ࣮Χϝϥը૾͚ͩΛ࢖༻ͯ͠ϨϯμϦϯάͨ͠ը૾. 2.4 ςΫενϟੜ੒. Λ༻ҙͯ͠ɼͦΕΒͷؒͷΦϓςΟΧϧϑϩʔΛ‫ͯ͠ࢉܭ‬. ͜͜·Ͱͷ࣌఺Ͱɼର৅ਓ෺ͷ̏࣍‫ݩ‬ද໘‫ܗ‬ঢ়Λ֫ಘ͢. ิؒը૾Λੜ੒͠ɼҰํͰ Harmonized Texture Mapping. Δ͜ͱ͕Ͱ͖ͨͨΊɼ࠷‫ͦʹޙ‬ͷද໘ςΫενϟΛ‫ܗ‬ঢ়෮. ๏ [55] Ͱ͸࣮Χϝϥը૾ΛదԠతʹม‫ͤ͞ܗ‬Δ͜ͱͰҐஔ. ‫͍ͨ༻ʹݩ‬ଟࢹ఺ө૾͔Βੜ੒͢Δɽ͜͜ͰॏཁͱͳΔͷ. ͣΕͷແ͍ߴਫ਼ࡉςΫενϟΛੜ੒͢Δɽ·ͨԾ૝ࢹ఺Ґ. ͸ɼ֤ද໘ྖҬΛࡱӨ͍࣮ͯͨ͠ࢹ఺͸ෳ਺ଘࡏ͢Δͱ͍. ஔʹԠͯ͡ɼదԠతʹ̏࣍‫ܗݩ‬ঢ়Λ࠷దԽ͢Δ͜ͱͰϨϯ. ͏఺ͱɼ̏࣍‫ݩ‬ϏσΦͷදࣔʹࡍͯ͠͸ʮͲͷࢹ఺͔Βද. μϦϯά඼࣭ͷ޲্ΛਤΔ͜ͱ΋Ͱ͖Δ [56]ɽ. ࣔ͢Δͷ͔ʯΛද͢Ծ૝ࢹ఺ͱ͍͏֓೦͕ՃΘΔͱ͍͏఺ ˆ ʣɽ Ͱ͋Δʢਤ 4 ͷ C. ର৅ද໘ͷςΫενϟ͸Ͳͷࢹ఺ʹΑΔࡱӨ૾͔Βੜ੒͠. ·ͣɼର৅ਓ෺ͷ̏࣍‫ݩ‬ද໘‫ܗ‬ঢ়্ͷඍখྖҬʹ͸ɼͦ. ͯ΋Ұக͢Δ͸ͣͰ͋Γɼਖ਼͘͠ CG ͱಉ༷ͷɼ̍ϙϦΰ. ‫( ه্ʹٯ‬1) ͔Β (4) ͍ͣΕ΋੒ΓཱͭͱԾఆ͢Δͱɼ. ΕΛ‫؍‬ଌՄೳͳΧϝϥ͕Ұൠʹෳ਺ଘࡏ͢Δͱ‫͑ݴ‬Δɽ͜. ϯʹ͖ͭ̍ຕͷςΫενϟը૾Λੜ੒͢Δ͜ͱ͕Ͱ͖Δɽ. ͜ͰͦͷΑ͏ͳඍখྖҬΛ‫؍‬ଌՄೳΧϝϥͦΕͧΕ΁ͱ౤. ·ͨ͜ͷͱ͖ɼෳ਺ࢹ఺ʹΑΔࡱӨ૾͸͋Δ‫ڞ‬௨ͷද໘ς. Өͨ͠ͱ͖ʹɼ౤ӨઌͰͷըૉ஋͕Ұக͢Δͷ͸. ΫενϟΛҟͳΔ֨ࢠ఺ͰαϯϓϦϯάͨ݁͠ՌͰ͋Δͱ. ( 1 ) ඍখྖҬͷ̏࣍‫ܗݩ‬ঢ়͕‫׬‬શʹਖ਼͘͠ɼ. ‫͖Ͱ͕ͱ͜͢ͳݟ‬Δɽ͜ͷͨΊԾ૝ࢹ఺ϨϯμϦϯάͷࡍ. ( 2 ) ඍখྖҬ͕‫׬‬શ֦ࢄ໘ʢLambertian surfaceʣͰ͋Γɼ. ʹ௒ղ૾ॲཧΛߦ͏ख๏ [57] ΍ɼର৅ද໘্Ͱ௒ղ૾ॲཧ. ( 3 ) Χϝϥͷ಺෦ɾ֎෦ύϥϝʔλਪఆʹ‫͕ࠩޡ‬ແ͘ɼ. Λߦ͏ख๏ [58] ͕ఏҊ͞Ε͍ͯΔɽ. ( 4 ) ֤Χϝϥͷ෼ޫ‫׬͕౓ײ‬શʹҰக͍ͯ͠Δ. ·ͨߴ඼ҐϨϯμϦϯάͱ͸‫ٯ‬ͷ໰୊ઃఆͱͯ͠ɼԾʹ. ͱ͍͏ཧ૝తͳ৔߹ʹ‫ݶ‬ΒΕɼ͜ͷ͍ͣΕ͔͕੒ཱ͠ͳ͍. ্‫( ه‬4) ͷΈ͕੒Γཱͨͳ͍ͱԾఆ͢ΔͳΒ͹ɼ֤ࢹ఺Ͱ. ৔߹͸ࢹ఺ؒͰըૉ஋͕Ұக͠ಘͳ͍ɽ. ͷըૉ஋ͷࠩҟ͸Χϝϥͷ෼ޫ‫౓ײ‬ͷࠩʹ‫ى‬Ҽ͍ͯ͠Δͱ. ͜ͷΑ͏ͳߟ͑ʹ‫ͱͮ͘ج‬ɼԾʹ (2) ͷΈ͕੒ཱ͠ͳ͍ ͱԾఆͨ͠৔߹ɼըૉ஋ͷࠩ͸ର৅ද໘ͷ non-Lambertian ͳ൓ࣹಛੑɼ͢ͳΘͪͦͷද໘ͷํ޲ґଘͳ‫͑ݟ‬ͷมԽΛ. ‫͖Ͱ͕ͱ͜͢ͳݟ‬Δɽ͜ͷ͜ͱΛར༻ͯ͠ɼΧϝϥͷ෼ޫ ‫౓ײ‬ΛΩϟϦϒϨʔγϣϯ͢Δख๏΋ఏҊ͞Ε͍ͯΔ [59]ɽ. ‫ه‬࿥͍ͯ͠Δͱ‫͑ݴ‬ΔɽͦͷͨΊ̏࣍‫ݩ‬ϏσΦͷදࣔʹࡍ. 3. Ԡ༻ྫ. ͯ͠͸ɼԾ૝ࢹ఺ʹΑΓ͍࣮ۙࢹ఺͔Β༏ઌతʹςΫε. 3.1 ̏࣍‫ࢹݩ‬ઢํ޲ਪఆ͓ΑͼҰਓশࢹ఺ө૾ੜ੒. νϟΛੜ੒͢Ε͹ɼΑΓ࣮ࣸʹ͍ۙϨϯμϦϯά͕Մೳͱ. લड़ͷΑ͏ʹɼ̏࣍‫ݩ‬ϏσΦͷಛ௃͸ର৅ͷ̏࣍‫ܗݩ‬ঢ়. ͳΔͱ‫ظ‬଴͞ΕΔɽ͜ͷߟ͑ํ͸ࢹ఺ґଘϨϯμϦϯάͱ. Λཅʹਪఆ͢Δ఺Ͱ͋Γɼ͜ΕΛ‫ͯ͠༻׆‬ඃࣸମͷ‫إ‬ͷ̏. ‫ݺ‬͹ΕΔ [4][10]ɽ. ࣍‫ݩ‬ҐஔΛਪఆ͠ʢਤ 6(b) ഽ৭ྖҬʣɼ͞Βʹͦͷ‫ྖإ‬Ҭ. c 2013 Information Processing Society of Japan . 4.

(5) Vol.2013-CG-153 No.18 Vol.2013-CVIM-189 No.18 2013/11/29. ৘ใॲཧֶձ‫ڀݚ‬ใࠂ IPSJ SIG Technical Report. ਤ 8 ෳࡶͳਓ෺࢟੎ͷਪఆ [61]ɽ্ஈɿೖྗը૾ͷҰ෦ɼԼஈɿ෮ ‫͞ݩ‬Εͨ‫ܗ‬ঢ়ʢփ৭ʣͱɼਪఆ͞Εͨࠎ֨࢟੎ʢ੺৭ʣ ɽ ਤ 9. ෳ਺ਓ෺ͷΠϯλϥΫγϣϯΠϕϯτฤू [72]. ͷਖ਼໘ʹԾ૝ΧϝϥΛஔ͘͜ͱͰԾ૝ਖ਼໘‫إ‬ը૾ʢਤ 6(c)ʣ Λ࡞੒͢Δ͜ͱ͕Ͱ͖Δɽ͜͏ͯ͠ಘΒΕͨਖ਼໘‫إ‬ը૾͔ ΒಏΛ‫ݕ‬ग़ͯ͠ࢹઢํ޲Λਪఆ͢Δ͜ͱͰɼඇ߆ଋɾඇ઀ ৮Ͱର৅ʹࣗ༝ͳӡಈΛ‫ࢹݩ࣍̏ͨ͠ڐ‬ઢํ޲ਪఆ͕࣮‫ݱ‬ Ͱ͖Δ [60]ɽ ·ͨߋʹɼಘΒΕͨ‫إ‬Ґஔͱࢹઢํ޲ʹҰக͢ΔΑ͏ʹ ϨϯμϦϯά༻ͷԾ૝ࢹ఺Λઃఆ͢Δͱɼਤ 7 ͷΑ͏ʹඃ. (a). ࣸମࣗ਎͕‫͍ͨͯݟ‬Α͏ͳҰਓশࢹ఺ͷө૾Λੜ੒͢Δ͜. (b). ͱ΋ՄೳͰ͋Δɽ. 3.2 ̏࣍‫ݩ‬ӡಈਪఆ. (c). (e). (d). (f). ํ๏ʹେผ͞Εɼલऀ͸֤࣌ࠁͷ‫ܗ‬ঢ়ಉ࢜Λൺֱ͠ɼ̏࣍. (g). (h). (i). (j). ‫ݩ‬ද໘্Ͱ‫ʹ͍ޓ‬ରԠ͢Δ఺Λ‫ٻ‬ΊΔ͜ͱͰӡಈΛ‫ٻ‬ΊΔ. ਤ 10. ਓ෺ͷ̏࣍‫ݩ‬ϏσΦɼ͢ͳΘͪର৅ͷ࣌‫ܗݩ࣍̏ྻܥ‬ঢ় ͱςΫενϟ͕ಘΒΕͨͱԾఆ্ͨ͠Ͱɼର৅ͷ̏࣍‫ݩ‬ӡ ಈΛਪఆ͢Δ‫਺͕ڀݚ‬ଟ͘ͳ͞Ε͍ͯΔɽ͜ΕΒ͸Ұൠʹ. (1) Ϛονϯάʹ‫ํͮ͘ج‬๏ͱ (2) τϥοΩϯάʹ‫ͮ͘ج‬ ෳ਺ਓ෺ͷΠϯλϥΫγϣϯΠϕϯτฤू݁Ռ [72]. ख๏Ͱ͋Γɼඞͣ͠΋࿈ଓ͢Δ࣌ࠁؒͰϚονϯά͢Δඞ ཁ͕ͳ͍఺ʹಛ௃͕͋Δ [62] [63] [64] [65]ɽ Ұํ‫ऀޙ‬͸ΩʔϑϨʔϜϝογϡϞσϧͷม‫ܗ‬ʢϝο γϡτϥοΩϯάʣΛஞ࣍తʹ‫܁‬Γฦ͢͜ͱͰӡಈΛ‫ٻ‬Ί Δख๏Ͱ͋Δ [66] [67]ɽ͞ΒʹɼΩʔϑϨʔϜϝογϡϞ σϧʹࠎ֨ߏ଄ΛຒΊࠐΈɼϝογϡม‫ܗ‬Λࠎ֨ӡಈͰ‫ه‬ ड़͢Δ͜ͱͰਓ෺ͷଟؔઅ߶ମͱͯ͠ͷӡಈΛਪఆ͢Δ‫ݚ‬ ‫ڀ‬΋ߦΘΕ͍ͯΔ [68][69][70][61][71]ɽྫ͑͹ [61] Ͱ͸̏ ࣍‫ݩ‬ϏσΦʹಛ௃తͳɼΦΫϧʔδϣϯʹΑΔ phantom. ਤ 11. ෳ਺ਓ෺ͷΠϯλϥΫγϣϯΠϕϯτฤू݁ՌͷҰਓশࢹ఺ ϨϯμϦϯά [72]. volume ΍ɼ‫ܗ‬ঢ়෮‫ݩ‬ͷᐆດ͞ʹ‫ى‬Ҽ͢Δ‫ܗ‬ঢ়ͷ‫ޡ‬ΓΛߟ ɼ·ͨ [71] Ͱ͸‫͍ޓ‬ ྀͨ͠ӡಈਪఆ͕ߦΘΕ͓ͯΓʢਤ 8ʣ ΛΧϝϥ͔Βःณ͢ΔΑ͏ͳҐஔؔ܎ʹ͋Δෳ਺ਓ෺ͷӡ ಈΛಉ࣌ʹਪఆ͢Δ͜ͱʹऔΓ૊·Ε͍ͯΔɽ. c 2013 Information Processing Society of Japan . 3.3 ෳ਺ਓ෺ͷΠϯλϥΫγϣϯΠϕϯτฤू ෳ਺ਓ෺ʹΑΔΠϯλϥΫγϣϯʢྫ͑͹ѲखͳͲʣΛ ̏࣍‫ݩ‬ϏσΦͰࡱӨ͢Δࡍʹ͸ɼର৅ਓ෺͕‫ࡱʹ͍ޓ‬ӨΧ. 5.

(6) Vol.2013-CG-153 No.18 Vol.2013-CVIM-189 No.18 2013/11/29. ৘ใॲཧֶձ‫ڀݚ‬ใࠂ IPSJ SIG Technical Report. (a). (b) ਤ 7. (c). Ұਓশࢹ఺ө૾ੜ੒ [60]ɽ(a) ೖྗଟࢹ఺ө૾ɼ(b) ࡾਓশࢹ఺ϨϯμϦϯάɼ(c) Ұਓ শࢹ఺ϨϯμϦϯάɽ. ϝϥ͔Β૬खΛःณͯ͠͠·͍ɼ޲͔͍߹͏໘͕ͲͷΧϝ ϥ͔Β΋‫؍‬ଌ͞Εͳ͍৔߹͕ੜ͡Δɽ͜ͷΑ͏ͳྖҬͰ͸ ‫ܗ‬ঢ়͕ෆ‫׬‬શͱͳΓɼ·ͨςΫενϟ͕ಘΒΕͳ͍ͨΊɼ ϨϯμϦϯά࣌ͷө૾඼࣭ͷྼԽ͕ආ͚ΒΕͳ͍ɽ ͜ͷ໰୊Λղܾ͢ΔҰͭͷख๏ͱͯ͠ɼͦΕͧΕͷಈ࡞ Λ‫ݸ‬ผʹ̏࣍‫ݩ‬ϏσΦࡱӨ͠ɼ‫ͦʹޙ‬ΕΒΛ౷߹͢ΔΞϓ ϩʔν͕ߟ͑ΒΕΔʢਤ 9ʣ͕ɼ͜ͷ৔߹͸ͦΕͧΕͷਓ ෺͕͔͋ͨ΋૬ख͕ଘࡏ͢Δ͔ͷΑ͏ʹৼΔ෣͏ඞཁ͕͋ ΔͨΊʹɼಈ࡞λΠϛϯά΍ҐஔͷͣΕ͕ൃੜ͢Δɽ ͦ ͜ Ͱ զ ʑ ͸ Augmented Motion History Volume. (aMHV) ͱ‫ݩ࣍̏Ϳݺ‬ϏσΦதͷӡಈ‫ه‬ड़๏ͱɼaMHV ಉ ࢜ͷ૊Έ߹Θͤํʹ‫͍ͨͮج‬ΠϯλϥΫγϣϯΠϕϯτͷ ෼ྨɼͦͯ͠ aMMV ͷ૊Έ߹ΘͤʹԠͯ͡ద੾ʹಈ࡞λ ΠϛϯάɾҐஔͷͣΕΛमਖ਼͠ͳ͕Β౷߹͢Δख๏Λ։ൃ ͨ͠ [72]ɽ͜ͷख๏ͷಛ௃͸ɼਤ 10(a), (b) ͷΑ͏ʹࠎ֨ ӡಈʹΑΔର৅ද໘‫ܗ‬ঢ়ͷӡಈ‫ه‬ड़͕ࠔ೉ͳ৔߹Ͱ͋ͬͯ ΋ɼ̏࣍‫ݩ‬ϏσΦ͕΋ͱ΋ͱ࣋ͭ̏࣍‫ݩ‬ද໘‫ܗ‬ঢ়ͷΈΛ༻ ͍ͨ aMHV ʹΑͬͯӡಈ‫ه‬ड़͢Δ఺ɼͦͯ͠ aMHV Λ ॲཧ୯Ґͱͨ͠ฤूΞϧΰϦζϜΛఆٛͨ͠఺Ͱ͋Δɽ ͜ͷख๏ʹΑΔฤू݁ՌΛਤ 10 ʹࣔ͢ɽಉਤ (a) ͓Αͼ. (b) ͕ଟࢹ఺ө૾ͷҰྫͰ͋Γɼಉਤ (c)ʙ(f) ͕‫ݸ‬ผʹੜ ੒͞Εͨ̏࣍‫ݩ‬ϏσΦΛ୯७ʹ߹੒ͨ݁͠ՌͰ͋Δɽ͜͜ Ͱ (d) ͓Αͼ (e) Ͱ͸౛ಉ͕࣮࢜ࡍ͸ଧͪ߹͍ͬͯΔ͸ͣ ͕ɼ߹੒݁ՌͰ͸ۭ͕ܺଘࡏ͓ͯ͠Γɼ·ͨ (f) Ͱ͸Ұํ ͕ଞํΛ੾͍ͬͯΔ͸͕ͣɼ߹੒݁ՌͰ͸౛͕ಧ͍͍ͯͳ ͍ɽ͜Εʹରͯ͠ [72] ʹΑΔฤूͰ͸ɼಉਤ (g)ʙ(j) ʹࣔ ͢Α͏ʹɼ͍ͣΕ΋ಈ࡞ͷҙਤ௨Γͷ݁Ռ͕ಘΒΕ͍ͯΔɽ ·ͨ͜͏ͯ͠ಘΒΕͨฤू݁ՌΛલड़ͷख๏ [60] ʹΑΓ ͦΕͧΕͷԋऀͷࢹ఺͔ΒϨϯμϦϯάͨ͠ྫΛਤ 11 ʹ ࣔ͢ɽ‫͍߹͍͔޲ʹ͍ޓ‬ɼ૬‫ʹޓ‬Χϝϥ͔Β૬खΛःณ͢. c 2013 Information Processing Society of Japan . ਤ 12. ਫத෺ମͷࢹମੵަࠩ๏ʹΑΔ࣮࣌ؒ‫ܗ‬ঢ়෮‫[ ݩ‬73]ɽࠨɿࡱ Ө‫ڥ؀‬ɼதԝɿೖྗը૾ɼӈɿ̏࣍‫ܗݩ‬ঢ়ɽ. Δঢ়‫͋Ͱگ‬Δ͕ɼద੾ʹςΫενϟ͕ੜ੒Ͱ͖͍ͯΔ͜ͱ ͕֬ೝͰ͖Δɽ. 4. ·ͱΊ ຊߘͰ͸̏࣍‫ݩ‬ϏσΦੜ੒ͷ‫ج‬ຊతͳΞϧΰϦζϜ͓Α ͼΞϓϦέʔγϣϯΛɼؔ࿈‫঺ʹڞͱڀݚ‬հͨ͠ɽࠓ‫ޙ‬ͷ ՝୊͸ (1) ΫϩϚΩʔഎ‫Ͳͳܠ‬Λ࣋ͨͳ͍࣮ੈքͰͷ̏࣍ ‫ݩ‬ϏσΦੜ੒Λ࣮‫͢ݱ‬Δ͜ͱͱɼ(2) ਤ 4 ͓Αͼਤ 5 ʹࣔ͠ ͨΑ͏ʹɼ‫ࡏݱ‬ͷٕज़Ͱ͸ѻΘΕ͍ͯͳ͔ͬͨޫֶ‫ݱ‬৅Ͱ ͋Δ۶ંɾ൓ࣹɾࢄཚͳͲΛ໌ࣔతʹϞσϧԽ͠ɼ̏࣍‫ݩ‬Ϗ σΦͱͯ͠ࡱӨՄೳͳର৅ͷΫϥεΛΑΓ޿͘͢Δ͜ͱ͕ ‫͛ڍ‬ΒΕΔɽͦͷͨΊ‫ࡏݱ‬චऀΒ͸ΞΫΞϏδϣϯͱ୊͠ ͯɼ͜ͷΑ͏ͳޫֶ‫ݱ‬৅͕ΑΓ‫ݦ‬ஶʹ‫؍‬ଌ͞ΕΔਫத෺ମ ͷ̏࣍‫ܗݩ‬ঢ়ɾӡಈ෮‫ʹݩ‬औΓ૊Έ࢝Ί͓ͯΓ [74][75][73] ʢਤ 12ʣ ɼࠓ‫ޙ‬͸൒ಁ໌෺ମͳͲ΋ѻ͑ΔΑ͏ʹ‫ڀݚ‬ΛਐΊ Δ͜ͱΛ‫ܭ‬ը͍ͯ͠Δɽ ँࣙɹ೔ࠒΑΓৗʹ͝ࢦಋΛ௖͍͍ͯΔদࢁོ࢘‫ڭ‬तΛ͸ ͡Ίɼ‫౎ژ‬େֶদࢁ‫֤܎ؔࣨڀݚ‬Ґʹ৺ΑΓ‫ँײ‬ਃ্͛͠ ·͢ɽ·ͨຊߘͷ಺༰͸෹ Inria ͱͷ JSPS ೋࠃؒަྲྀࣄ ‫ڞۀ‬ಉ‫ڀݚ‬ɼNTT ϝσΟΞΠϯςϦδΣϯε‫ͱॴڀݚ‬ͷ ‫ڞ‬ಉ‫ڀݚ‬ɼจՊলҕୗࣄ‫ۀ‬ʮେ‫ܕ‬༗‫ܗ‬ɾແ‫ܗ‬จԽࡒͷߴਫ਼ ౓σδλϧԽιϑτ΢ΣΞͷ։ൃʯ ɼJSPS Պ‫ݚ‬අʢ՝୊൪. 6.

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