観測スケールを考慮したメタリック塗装の表面下法線分布解析
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(2) Vol.2015-CG-161 No.15 Vol.2015-CVIM-199 No.15 2015/11/7. ใॲཧֶձڀݚใࠂ IPSJ SIG Technical Report. ࣹͷ࠶ݱͰ͖Δ͕ɺͦͷؒͷதؒࢹతͳঢ়ଶߟྀ͠. Clear paint Pearl mica coating Mica. ͨϞσϧͰͳ͍ɽͭ·ΓɼϝλϦοΫృʹ·ؚΕΔΑ ͏ͳ͋Δఔͷେ͖͞Λ࣋ͭۚଐϑϨʔΫͷҰͭҰͭɼ. Base color paint Under coat Iron plate. ϔΞϥΠϯՃ͞ΕͨۚଐதͷইͷҰͭҰͭ·Ͱ࠶͢ݱ Δ͜ͱ͕Ͱ͖ͳ͍ɽͦͷͨΊɼ͜ΕΒͷࣹϞσϧʹ؍ଌ σʔλΛͯΊΔ͚ͩͰɼϝλϦοΫృͷ࣭ײΛఆ. ਤ 1 ύʔϧϚΠΧృͷߏ. ྔԽ͢Δ͜ͱ͍͠ͱ͍͑Δɽ. 2.2 ϝλϦοΫృͷ࣭ײఆྔԽख๏. PET layer Printed pattern layer Adhesive layer Metallic flakes. ϝλϦοΫృΛԕ͔͘Βʹ͖ͱͨݟϑϨʔΫʹΑΔ ΩϥΩϥͱࣹͨ͋͠·Γ͡ײΒΕͳ͘ɼۙ͘Ͱͱͨݟ ͖ʹϑϨʔΫͷΩϥΩϥࣹ͕ͨ͠͡ײ͘ڧΒΕΔɽ͜. PVC or OLEFIN film layer. ͷΑ͏ʹɼϝλϦοΫృΛධՁ͢Δͱ͖ʹɼϚΫϩͳ ਤ 2. ޫًͱײϛΫϩͳޫًʹײ͚ͯධՁ͢Δඞཁ͕͋Δ [3]ɽ. Ճ০ϑΟϧϜͷߏ. ϚΫϩͳޫًͱײɼൺֱతԕ͔͘Β͞؍ΕΔۚଐͰײ ͋Γɼ֯؍ͷมԽͰ৭ௐ͕มԽͯ͑͠ݟΔɽ·ͨɼϛΫ ϩͳޫًͱײ͔ۙ͘Β͞؍ΕΔͱ͖ͷΩϥΩϥͱޫΔ ༷ࢠͷۚଐ͋ͰײΔɽ͜ͷϛΫϩͳεέʔϧʹண͢Δͱɼ ޫ͍ۙʹݯޫΛ༻ͨ͠ͱ͖ʹϛΫϩͳޫًײͷੑ ࣭͕ݱ͘ڧΕɼෳͷࣹϐʔΫ͕؍ଌ͞ΕΔɽ͜ͷࣹ. (a) ؍ଌମ. ϐʔΫɼϝλϦοΫృྉʹ༻͍ΒΕ͍ͯΔۚଐϑϨʔΫ. ਤ 3. (b) ؍ଌը૾. (c) ߴ͞ը૾. ϨʔβʔݦඍڸΛ༻͍ͨ؍ଌ. ͷܗঢ়ཻࢠܘɼϑϨʔΫͷ͖ʹԠͯ͡มԽ͢Δɽ͜Ε Βͷੑ࣭ʹ͖ͮجɼैདྷͷϝλϦοΫృͷ࣭ײఆྔԽʹ ɼେ͖͚ͯ͘ೋͭͷख๏͕ଘࡏ͢Δɽ ҰͭɼϝλϦοΫృʹಛ༗ͳࣹͷϐʔΫΛղੳ ͢Δํ๏Ͱ͋ΔɽాΒ [4] ɼݦඍޫܭΛ༻͍ࣹͯ ڧΛऔಘ͠ɼͦͷϐʔΫͷࢁͱ୩ͷࠩΛൺֱ͢Δ͜ͱͰɼ. 3. ϝλϦοΫృʹ͓͚ΔࣹͷΈ 3.1 ϝλϦοΫృͷߏ ҰൠʹɼϝλϦοΫృྉʹΞϧϛχϜͳͲͷۚଐϑ. ۚଐϑϨʔΫʹΑΔεύʔΫϦϯάޮՌΛࢉग़͢Δख๏Λ. ϨʔΫ͕ࠞͥΒΕ͍ͯΔɽͦͯ͠ɼϑϨʔΫͷܗঢ়େ͖. ఏҊͨ͠ɽ·ͨɼϨʔβʔࣜϝλϦοΫײଌఆ[ ث5] ։. ͞ɼ͖ʹΑͬͯɼ͕ํ͑ݟҟͳΔɽϑϨʔΫɼ΄΅ಉ. ൃ͞Ε͓ͯΓɼਖ਼ࣹ͔Βগͣ͠Εͨํͷ؍ଌͷڧ. ͡ํʹ໘Λ͚ͳ͕Β͋ΔఔͷΒ͖ͭΛ࣋ͨͤͯ. ͔ΒϝλϦοΫײΛද͢ύϥϝʔλΛਪఆ͍ͯ͠Δɽଞʹ. ͍ΔͨΊɼਖ਼ࣹํϑϨʔΫͷ͖ʹґଘ༷ͯ͠ʑͳ. ɼਗ਼ҪΒ [6] ɼࡱӨ͞Εͨը૾ͷج४໘ͷۚଐϑϨʔ. ֯ͱͳΓɼैࣹͬͯޫ༷ʑͳํʹϐʔΫΛͭ͜. ΫʹΑΔߴً෦ͷ໌Δ͞໘ੵͷฏۉࢄͳͲͷύϥ. ͱʹͳΔɽࣗಈंͷృͰ༻͍ΒΕ͍ͯΔύʔϧϚΠΧృ. ϝʔλΛઆ໌มͱͨ͠ॏճʹࣜؼΑͬͯɼࢹͰͷཻࢠ. ਤ 1 ͷΑ͏ͳߏΛ͍ͯ͠Δɽ͜ͷృɼද໘Լʹ. ײΛఆྔԽ͢Δख๏ΛఏҊͨ͠ɽ͜ΕΒͷख๏ࢹධՁ. ඍࡉۚଐཻࢠӢΛࠞೖ͢Δ͜ͱͰෳࡶͳࣹ͕͜ى. ͱͷ૬͕ؔ͋Δ͜ͱ͕֬ೝ͞Ε͍ͯΔ͕ɼࣹͷϐʔΫͱ. ΓɼಠಛͳਂΈߴײڃΛද͍ͯ͠ݱΔɽՈిͳͲʹ. ͍͏ը૾ಛΛѻ͍ͬͯΔͨΊɼཧతͳߏΛද͢ύϥ. ༻͍ΒΕ͍ͯΔՃ০ϑΟϧϜਤ 2 ͷΑ͏ʹɼࣅͨΑ͏ͳ. ϝʔλͰͳ͍ɽͦͷͨΊɼࡱӨํ๏ʹڥґଘ͢Δͱ. ߏΛ࣋ͭɽ. ͍͏͕͋Δɽ. ·ͨɼਤ 3(a) ͷՃ০ϑΟϧϜΛಁ໌ମͷද໘ɾཱମߏΛ. ೋͭϝλϦοΫృͷཧతͳߏΛਪఆ͢Δํ๏. ܭଌ͢Δ͜ͱ͕Մೳͳܗঢ়ղੳϨʔβʔݦඍ( ڸKEYENCE. Ͱ͋Δɽྫ͑ɼڞযϨʔβʔݦඍڸΛ༻͍Δ͜ͱͰϝ. VK-X250) Λ༻͍ͯ؍ଌͨ͠ɽ͢Δͱɼਤ 3(b) ͷΑ͏ͳߏ. λϦοΫృதͷۚଐϑϨʔΫͷ๏ઢΛݸผʹऔಘ͢Δ͜. ͕ղੳ͞Εͨɽը૾தͷԁ൫ঢ়ͷମ͕ද໘ԼͷϑϨʔ. ͱ͕Ͱ͖ΔɽSung Β [7] ɼͦͷ๏ઢΛେྔʹܭଌ͢Δ͜. ΫͰ͋ΓɼϑϨʔΫͷܗঢ়֓Ͷԁ൫ঢ়Ͱ͋Δͱ͍͑Δɽ. ͱͰɼϝλϦοΫృͷϑϨʔΫͷ๏ઢΛਪఆ͠ɼ. ·ͨɼ͜ͷը૾ͷߴ͞ใΛΧϥʔϚοϓͰදࣔͨ݁͠Ռ. ࣹಛੑͷਪఆʹԠ༻͢Δख๏ΛఏҊͨ͠ɽ͜ͷख๏. ͕ਤ 3(c) Ͱ͋Δɽ͜ͷը૾͔ΒɼҰͭҰͭͷϑϨʔΫಛ. ཧతʹਖ਼֬ͳύϥϝʔλΛਪఆͰ͖Δ͕ɼݦඍڸΛ༻͍Δ. ఆͷํʹ͖Λ͍࣋ͬͯΔ͜ͱ͕֬ೝͰ͖ΔɽҎ্ͷ͜. ͨΊɼܭଌʹखؒίετ͕͔͔ΔͳͲͷ͕͋Δɽ. ͱ͔ΒɼҰͭҰͭͷϑϨʔΫҟͳΔܘͷԁ͋ͰܗΓɼ ༷ʑͳ֯ʹؚ͍ͯ༗͞Ε͍ͯΔ͜ͱ͕͔Δɽ. c 2015 Information Processing Society of Japan . 2.
(3) Vol.2015-CG-161 No.15 Vol.2015-CVIM-199 No.15 2015/11/7. ใॲཧֶձڀݚใࠂ IPSJ SIG Technical Report. Surface normal. Subsurface normal. Surface normal distribution Subsurface normal distributions. ਤ 4. ද໘๏ઢͱද໘Լ๏ઢ. Surface. 1 pixel ਤ 6. 1. ද໘Լ๏ઢͷ. 2 3. 1. 2. 3. ri. ρi. ਤ 7 ϑϨʔΫҰͭͷ๏ઢ. 3.4 ද໘Լ๏ઢͷϞσϧ ਤ 5. ؍ଌεέʔϧʹԠͨ͡ϝλϦοΫృͷํ͑ݟͷΠϝʔδ. ϝλϦοΫృͷ๏ઢߏʹ͍ͭͯɼද໘๏ઢͱද໘Լ ๏ઢΛߟྀͯ͠ਤ 6 ͷΑ͏ͳ๏ઢͷϞσϧΛఏҊ͢. 3.2 ද໘๏ઢͱද໘Լ๏ઢ. ΔɽҰൠʹඍখ໘๏ઢͷΨεͱԾఆ͢Δ͜ͱ. Ұൠʹɼମ͋Δʹ͓͍ͯɼ།Ұͷ๏ઢΛ࣋ͪɼҰ. ͕Ͱ͖Δɽ͔͠͠ɼϝλϦοΫృͷද໘Լ๏ઢ 1 ըૉ. ͭͷࣹϐʔΫΛ࣋ͭɽ͔͠͠ɼύʔϧϚΠΧృՃ০. ʹෳͷ๏ઢΛ࣋ͭͨΊɼҰͭͷ͚ͩͰද͢͜ͱ. ϑΟϧϜͷΑ͏ͳମɼද໘ͷ๏ઢҰͭʹఆ·Δ͕ɼ. ͕Ͱ͖ͳ͍ɽͦͷͨΊɼද໘Լ๏ઢΛෳͷΨεͷ. ද໘ԼͷۚଐϑϨʔΫͷӨͰڹࣹϐʔΫ͕ෳଘࡏ͢. ઢܗॏͶ͋ΘͤͰද͞ΕΔࠞ߹ΨεΛ༻͍ͯද͢ݱ. ΔɽࣹϐʔΫͷํɼମද໘ͷ๏ઢํʹґଘ͢Δ. Δɽ͢ͳΘͪɼ1 ըૉʹ K ݸͷද໘Լ๏ઢΛؚΉͱ͖ʹɼ. ͨΊɼ͜ΕΒͷମͷࣹΛऔΓѻ͏ࡍʹද໘Լͷۚଐ. ਤ 7 ͷΑ͏ͳ K ͦݸΕͧΕͷද໘Լ๏ઢΛΨεͷ. ϑϨʔΫ͕ͲͷํΛ͍͍ͯΔͷ͔Λߟྀ͢Δඞཁ͕͋. Ͱද͢ɽͦΕͧΕͷΨεฏ ۉμ ͱࢄ Σ Ͱදݱ. Δɽͦ͜ͰຊจͰɼਤ 4 ʹࣔ͢Α͏ʹɼද໘Լʹ͋Δ. ͞ΕΔɽ·ͨɼϑϨʔΫ͕େ͖͍΄Ͳࣹڧͳ͘ڧΔ. ϑϨʔΫͳͲͷ๏ઢͷ͜ͱΛʮද໘Լ๏ઢʯͱఆٛ͢Δɽ. ͷͰ [8]ɼ ܘri ͷϑϨʔΫͷ໘ੵΛߟྀ͢Δɽ·ͨɼ. ͜ͷද໘Լ๏ઢͷӨͰڹɼΧϝϥͰࡱӨͨ͠ͱ͖ͷ 1 ըૉ. ମද໘ͷࣹΛ ρ1 ͱ͠ɼද໘ԼͷۚଐϑϨʔΫͷࣹ. Ͱෳͷ๏ઢΛؚΉ͜ͱʹͳΔɽ·ͨɼຊจͰऔΓ. Λ ρ2i ͱ͢Δɽ͢ΔͱɼϝλϦοΫృͷ๏ઢ N . ѻ͏Α͏ͳɼද໘Լ๏ઢͷӨͰڹը૾ͷ̍ըૉʹෳͷ. ࣜ (1) ͷΑ͏ʹϞσϧԽͰ͖Δɽ. ๏ઢ͕ରԠ͢ΔߏΛʮଟॏ๏ઢߏʯͱ͢ͱͱ͜ͿݺΔɽ. N = ρ1 N (μ, Σ) + 3.3 ؍ଌεέʔϧʹΑΔࣹಛੑͷมԽ ϝλϦοΫృͷΑ͏ͳଟॏ๏ઢߏɼਤ 5 ͷΑ͏ʹɼ. K . ri2 ρ2i N (μi , Σi ). (1). i=1. ͔͠͠ɼޙड़͢Δຊख๏Ͱɼ؍ଌ͔Β๏ઢΛਪఆ. ؍ଌεέʔϧʹԠ͕ͯ͡ํ͑ݟେ͖͘ҟͳΔɽదͳڑ. ͢ΔͨΊɼۚଐϑϨʔΫͷࣹͱαΠζΛผʑʹਪఆ͢. ͔Β؍ଌͨ͠ͱ͖ɼϝλϦοΫͷޫً͡ײ͕ײΒΕΔɽ. ΔͷࠔͰ͋ΔɽͦͷͨΊɼۚଐϑϨʔΫͷࣹͱα. ͔͠͠ɼ؍ଌڑΛۙͨ͘͠ΓɼഒΛߴͯ͘͠؍ଌͨ͠. ΠζΛҰͭͷͱͯ͠ѻ͏ɽ·ͨɼମͷද໘๏ઢͱಉ. ͱ͖ʹɼද໘Լʹ·ؚΕΔݸผͷϑϨʔΫʹண͍ͯ͠. ͡ํΛ͍͍ͯΔද໘Լ๏ઢΛผ͢Δ͜ͱ͍͠ɽ. Δ͜ͱʹͳΓɼޫًײ͋·Γ͡ײΒΕͳ͘ͳΔɽʹٯɼ. ͔͠͠ɼҰൠతʹϝλϦοΫృͷۚଐϑϨʔΫମද. ؍ଌڑΛԕͨ͘͠ΓɼഒΛͯ͘͠؍ଌͨ͠ͱ͖ʹɼ. ໘ͱ΄΅ಉ͡ํʹ໘͕͘Α͏ʹઃ͞ܭΕ͍ͯΔͨΊɼ. ແͷϑϨʔΫ͕ରԠͯ͠Ұͭͷૈ͍ڸ໘ࣹͷΑ͏ʹͳ. ମද໘ํͱಉ͡ํΛ͍͍ͯΔද໘Լ๏ઢଘࡏ͢. ΔͨΊɼޫًײ͋·Γ͡ײΒΕͳ͘ͳΔɽ͜ͷΑ͏ʹɼ. ΔͱԾఆͰ͖ΔɽͦͷͨΊɼද໘๏ઢͱಉ͡ํΛ͍ͯ. ϝλϦοΫృΛධՁ͢ΔࡍʹɼϝλϦοΫͷޫً͕ײ. ͍Δද໘Լ๏ઢҰͭͷ๏ઢͱͯ͠ѻ͏ɽΑͬͯɼຊจ. ͡ײΒΕΔదͳ؍ଌεέʔϧΛઃఆ͢Δඞཁ͕͋Δɽ. ͰऔΓѻ͏ද໘Լ๏ઢͷϞσϧΛࣜ (2) ͱఆٛ͢Δɽ. c 2015 Information Processing Society of Japan . 3.
(4) Vol.2015-CG-161 No.15 Vol.2015-CVIM-199 No.15 2015/11/7. ใॲཧֶձڀݚใࠂ IPSJ SIG Technical Report Camera. LED. zenith angle : T azimuth angle : I. ਤ 9. ࠞ߹ΨεͰѻ͏࠲ඪܥ. Rotary tables. ϧΰϦζϜΛ༻͍ͯɼද໘Լ๏ઢͷʹࠞ߹Ψε. ਤ 8. ΛͯΊΔɽ. N=. K . ܭଌஔ. ࠞ߹ΨεΛͯΊΔࡍʹɼߏ͢ΔΨε. Ci N (μi , Σi ). (2). ͷΛઃఆ͢Δඞཁ͕͋Δɽͦͷߏ͕ଟ͚Εશͯ ͷσʔλΛΧόʔ͢Δ͜ͱ؆୯ʹͳΔ͕ɼաద߹ʹͳͬ. i=1. 4. ද໘Լ๏ઢͷղੳ. ͯ͠·͍ɼͳද͏·ͯͬ͠ͳʹݱɽͦͷͨΊɼϞσϧ. 4.1 ๏ઢํͷਪఆ. Ϋࣹͷ߹ɼҰͭͷϑϨʔΫʹΑΔࣹɼҰͭͷࣹ. ʹର͢ΔదͳߏΛܾఆ͢Δඞཁ͕͋ΔɽϝλϦο. ද໘Լ๏ઢΛਪఆ͢ΔͨΊʹɼද໘Լ๏ઢͷΛ. ϐʔΫΛ࣋ͭɽ͜ͷ؍ଌʹ͖ͮجɼ؍ଌ͞Εࣹͨσʔλ. ٻΊΔඞཁ͕͋Δɽ؆୯ԽͷͨΊʹڸ໘ࣹͷΦϑεϖ. ͷதͷࣹϐʔΫͷΛɼද໘Լ๏ઢͷͷߏͰ͋. ΩϡϥʔΛແࢹ͢Δͱɼڸ໘ࣹΛੜ͡Δମͷ๏ઢํ. ΔͱԾఆ͢Δɽ. ޫͱํݯࣹํͷೋํͱҰக͢Δɽ͢ͳΘ ͪɼ๏ઢํɼࢹઢϕΫτϧ v ͱޫݯϕΫτϧ l ͷ 2 ํΛࣔ͢ϋʔϑϕΫτϧ h ͱͳΔɽϋʔϑϕΫτϧ h ࣍ࣜͰٻΊΔ͜ͱ͕Ͱ͖Δɽ. 4.3 ද໘Լ๏ઢͷ౷ྔܭͷࢉग़ ͜͜Ͱɼਪఆͨ͠ද໘Լ๏ઢͱ࣮ࡍͷϑϨʔΫͷ ঢ়ଶͱͷؔੑʹ͍ͭͯड़ΔɽఏҊϞσϧͰɼҰͭͷ. v+l h= |v + l|. (3). ͭ·Γɼମʹର༷ͯ͠ʑͳํ͔ΒޫΛরࣹ͠ɼ؍ଌ͞. ද໘Լ๏ઢΛҰͭͷΨεʹͯΊ͍ͯΔɽͦ ͷͨΊɼࠞ߹Ψεͷߏ؍ଌըૉͷϑϨʔΫ ͷʹݸରԠ͍ͯ͠Δɽ. Εࣹͨޫͷ͚ڧ͕ڧΕͲ΄͍ڧɼͦͷϋʔϑϕΫτ. ·ͨɼ֤๏ઢͷࢄͷɼۚଐϑϨʔΫͷද໘ૈ. ϧํʹ๏ઢ͕͋ΔՄೳੑ͕ߴ͍ͱ͍͑ΔɽͦͷͨΊɼ؍. ͞Λද͢ɽۚଐϑϨʔΫͷද໘͕ૈ͚ΕɼରԠ͢Δ֤๏. ଌࣹͨ͠ͷڧΛɼޫݯϕΫτϧͱࢹઢϕΫτϧΛ༻͍. ઢͷࢄେ͖͘ͳΓɼද໘͕Β͔Ͱ͋Ε๏ઢ. ͯϋʔϑϕΫτϧํʹͯΊΕɼද໘Լ๏ઢͷ. ͷࢄখ͘͞ͳΔɽ͞Βʹɼ֤͕ํͰ͋Δ͔Λ. Λࢉग़͢Δ͜ͱ͕Ͱ͖Δɽ. ௐΔ͜ͱͰɼҟํੑΛఆྔԽͰ͖Δɽ͜ͷࡍɼ֤ਖ਼ن. ͦͷͨΊͷܭଌํ๏ͱͯ͠ɼΧϝϥͱ؍ଌମݻఆ͠ɼ. ͷҟํੑɼਖ਼نͷ࣠ͱ࣠ͷൺͰද͢ݱΔ͜. ޫݯͷΈΛճసͤ͞Δɽ͢ͳΘͪɼਤ 8 ʹࣔ͢Α͏ͳηο. ͱ͕ग़དྷΔɽ࣠ͱ࣠ͷൺɼਖ਼نͷڞࢄߦྻ. ςΟϯάͰޫ( ํݯθ, φ) ͝ͱʹࣹޫΛܭଌ͢Δɽ͜ͷ. ͷ 2 ͭͷݻ༗ͷൺΛٻΊΕΑ͍ɽ. ࡍɼ֦ࢄࣹޫڸ໘ࣹޫʹൺͯेʹখ͍ͨ͞Ίɼ. ϑϨʔΫͷํͳͲɼํʹؔ͢Δσʔλ୯७ʹ֯ ͷࢉज़ฏۉΛٻΊͯਖ਼͍͠ฏۉతͳํٻΊΔ͜ͱ. ແࢹͰ͖ΔͱԾఆ͢Δɽ. Ͱ͖ͳ͍ [10]ɽͦͷͨΊɼํ౷ֶܭͷ֓೦ʹ͕ͨͬͯ͠. 4.2 EM ΞϧΰϦζϜΛ༻͍ͨද໘Լ๏ઢͷਪఆ ਪఆͨ͠ද໘Լ๏ઢͷΛࠞ߹ΨεʹͯΊ. ํͷฏͱۉࢄΛٻΊΔඞཁ͕͋ΔɽํͷฏۉΛٻΊ ΔͨΊʹɼ֯ΛͦΕͧΕͷ֯ํͷ୯ҐϕΫτϧʹ. Δ͜ͱͰද໘Լ๏ઢΛਪఆ͢Δɽͨͩ͠ɼϋʔϑϕΫ. มͯ͠ɼ୯ҐϕΫτϧͷฏํۉΛٻΊΕΑ͍ɽ·ͣɼ. τϧͷํΛํͱ֯ڼҐ֯ (θh , φh ) ͱ͢Δͱɼφh = 0◦ ͱ. N ݸͷ֯ํͷฏํۉΛٻΊΔͳΒɼ֯ํʹର. φh = 360 ͕ಉ֯͡ʹͳΓɼ·ͨɼθh = 0 Ͱ θh Λม. ͯ͠ͷ୯ҐϕΫτϧ n Λ༻͍ͯɼฏ߹ۉϕΫτϧ࣍ࣜ. Խͤͯ͞ಉ֯͡ʹͳΔͳͲɼѻ͍͕ࡶʹͳΔɽͦ͜. Ͱද͞ΕΔɽ. ◦. ◦. N 1 n ¯= ni N. Ͱɼਤ 9 ʹࣔ͢Α͏ʹɼٿΛఱํ͔Β͖ͱͨݟͷ 2 ࣍ ݩฏ໘Ͱߟ͑ͨͱ͖ͷ࠲ඪʹܥมͯ͠ѻ͏ɽ ࠷ਪఆͷख๏ͱͯ͠ɼෆશσʔλ͔Β࠷ਪఆΛ. (4). i=1. ͜ͷϕΫτϧͷํ͕ N ݸͷ֯ํͷฏ͋ͰํۉΔɽ. ٻΊΔख๏Ͱ͋Δ EM ΞϧΰϦζϜ (ظ࠷େԽ๏)[9]. ·ͨɼํͷࢄ circular variance[11] Λ༻͍Δ͜ͱͱ. ͕ར༻͞ΕΔ͜ͱ͕ଟ͍ɽͦͷͨΊɼຊͰڀݚɼEM Ξ. ͠ɼ࣍ࣜͰදͤΔɽ. c 2015 Information Processing Society of Japan . 4.
(5) Vol.2015-CG-161 No.15 Vol.2015-CVIM-199 No.15 2015/11/7. ใॲཧֶձڀݚใࠂ IPSJ SIG Technical Report. Camera. Reflection LED. Target object Rotary tables. PC. ਤ 10. ਤ 11. ࣮ݧஔ. ϝλϦοΫృͷܭଌମɽ্ஈࠨ͔Βॱʹ 5ɼ20ɼ40ɼ55ɼ. 90μm ͷΞϧϛϑϨʔΫؚ͕༗ྔ 1%ɼԼஈࠨ͔Βॱʹ 30ɼ 40ɼ60ɼ90μm ͷΞϧϛϑϨʔΫؚ͕༗ྔ 2%ͰຒΊࠐ·Ε ͍ͯΔɽ. Var(n) = 1 − |¯ n|. (5) ϳ ŽŶƚĞŶƚ;йͿͲ&ůĂŬĞƐŝnjĞ;ƵŵͿ. ͜ͷ͕ 1 ʹ͚ۙΕࢄ͕େ͖͘ɼ0 ʹ͚ۙΕࢄ͕ λΛదʹѻ͏͜ͱ͕Ͱ͖Δɽ ͜ΕΒͷཧతಛྔʹؔͯ͠ɼͦΕͧΕͷ౷ܭతͳฏ ۉͱࢄ͕͔Εɼ࣭ײΛఆྔԽ͢Δ͜ͱ͕Ͱ͖Δɽ ·ͨɼଟॏ๏ઢߏʹಛ༗ͳΩϥΩϥࣹͨ͠ʹɼද໘ Լ๏ઢͷͦͱݸͷ๏ઢํͷࢄ͕େ͖͘ىҼ͢Δͱ ༧Ͱ͖ΔɽͦͷͨΊɼ͜ΕΒೋͭͷύϥϝʔλʹண͢. EƵŵďĞƌŽĨŶŽƌŵĂůƐ. খ͍͞ͱ͍͑Δɽ͜ΕʹΑΓɼํʹؔ͢Δ౷ܭతͳσʔ. ϲ. ϭйͲϱƵŵ ϭйͲϮϬƵŵ ϭйͲϰϬƵŵ ϭйͲϱϱƵŵ ϭйͲϵϬƵŵ ϮйͲϯϬƵŵ ϮйͲϰϬƵŵ ϮйͲϲϬƵŵ ϮйͲϵϬƵŵ. ϱ ϰ ϯ Ϯ ϭ Ϭ Ϭ. ϮϬϬ. ͖Δɽ. ϰϬϬ. ϲϬϬ. ϴϬϬ. ϭϬϬϬ. ϭϮϬϬ. ϭϰϬϬ. WŝdžĞůƐŝnjĞƵŵ. Δ͜ͱͰɼମ͕ͲΕ͚ͩΩϥΩϥ͍ͯ͠Δͷ͔ఆྔԽͰ ਤ 12. ըૉαΠζ͝ͱͷ๏ઢɽʮؚ༗ྔʢ%ʣ-ϑϨʔΫͷେ͖͞ ʢμmʣ ʯͷϓϨʔτΛ༻͍͍ͯΔɽ. 5. ࣮ݧ 5.1 ࣮ڥݧ. 5.2 దͳࡱӨεέʔϧͷ֬ೝ. ϝλϦοΫృͷΑ͏ʹ༷ʑͳํʹ๏ઢ͕ଘࡏ͢Δ. ଟॏ๏ઢߏΛ࣋ͭମɼࡱӨεέʔϧʹԠͯ͡ɼ1. ମͷ๏ઢΛਪఆ͢ΔͨΊʹɼରମʹରͯ͠ٿ. ըૉͰͷࣹͷৼΔ͍͕େ͖͘ҟͳΔɽͦͷͨΊɼద. ঢ়ʹޫΛরࣹ͢Δඞཁ͕͋ΔɽͦͷͨΊɼ࣮ݧஔͱͯ͠. ͳࡱӨεέʔϧͰղੳ͢ΔࣄॏཁͱͳΔɽ. ਤ 10 Ͱࣔ͢Α͏ͳɼٿঢ়ʹޫ( ݯਐిࢠࣜגۀձ. దͳࡱӨεέʔϧΛௐΔͨΊɼ1 ըૉͷεέʔϧΛ. ࣾ W3VP-8) Λಈ͔ͯ͠ࡱӨͰ͖ΔγεςϜΛ࡞ͨ͠ɽ. ༷ʑʹมԽͤͯ͞ܭଌͨ͠ࡍͷࣹϐʔΫͷΛٻΊΔɽ. ϑϨʔΫʹΑΔΩϥΩϥࣹͨ͠Λऔಘ͍ͨͨ͠Ίɼޫݯ. ͨͩ͠ɼࡱӨεέʔϧͷมߋ࣮ࡍʹΧϝϥͷࡱӨഒΛ. ʹޫ ͍ۙʹݯLED Λ࠾༻ͨ͠ɽͳ͓ɼମͱޫ·ݯ. มԽͤ͞ΔͷͰͳ͘ɼͰ͖Δ͚ͩߴഒͰࡱӨͨ͠ը. Ͱͷڑ 50cm ͨ͠ɽଟॏ๏ઢߏΛ࣋ͭମͷৄࡉ. ૾ʹμϯαϯϓϦϯάॲཧΛద༻͢Δ͜ͱͰ̍ըૉͷ. ͳࣹͷมԽΛ؍ଌ͢ΔͨΊɼΧϝϥϞϊΫϩΧϝϥ. εέʔϧΛԾతʹมԽͤ͞Δɽຊ࣮Ͱݧয͕ڑ. (PointGrey GS3-U3-28S4M-C) Λ༻͢ΔɽΧϝϥͷҐஔ. 75mm ͷϨϯζʹΤΫεςϯγϣϯɾνϡʔϒΛऔΓ͚. ମͷ๏ઢํͰɼද໘ͷڸ໘ࣹͷӨڹΛେ͖͘ड. Δ͜ͱͰɼۃΊͯߴഒͰͷࡱӨΛߦͬͨɽͦͷ݁Ռɼ1. ͚ͯ͠·͍ඍࡉߏͷ๏ઢͷࣹ͕ܭଌ͠ʹ͍͘ͷͰɼڼ. ըૉͷαΠζ͕ 7μm ͰࡱӨ͢Δ͜ͱ͕Ͱ͖ͨɽର. ֯Λ 45◦ ͣΒͨ͠ (45, 0) ͷҐஔ͔ΒࡱӨ͢Δɽ͜ͷͱ͖ɼ. ମͱͯ͠ɼਤ 11 ʹࣔ͢ɼΞϧϛϑϨʔΫ͕ຒΊࠐ·Εͨ. ଟॏ๏ઢߏͰྡΓ߹ͬͨըૉͰ๏ઢํ͕ҟͳΔ͜. ΞΫϦϧथࢷϓϨʔτ (JIDA ελϯμʔυαϯϓϧζɾ2). ͱʹΑࣹ͕ͬͯҟͳΔͷͰɼ10×10 ͷྡ 100 ըૉͷ. Λ༻͍ͨɽ. ࣹޫΛܭଌ͢ΔɽΧϝϥͷઃఆ ISO ײ 100ɼF . ͦͷ݁ՌɼըૉαΠζ͝ͱͷ๏ઢ͕ਤ 12 ͷΑ͏ʹͳͬ. 11ɼγϟολʔ؍ଌ݁Ռʹ߹Θͤͯదʹઃఆ͢. ͨɽ͜ͷ݁Ռ͔Βɼ؍ଌεέʔϧʹԠͨ͡ 1 ըૉͷࣹͷ. ΔɽΧϝϥͷ༗ޮϏοτ 14bit Ͱ͋ΔɽຊγεςϜʹ. ৼΔ͍ͷมԽΛ֬ೝͰ͖ΔɽըૉαΠζ͕খ͍͞ͱ͖ʹ. ◦. ΑΓɼ֯ θ ͱ φ ΛͦΕͧΕ 3 ͣͭճసࣹͤͯ͞ޫΛ. ๏ઢ͕ҰͭʹͳΒͳ͍ͷɼද໘๏ઢͱද໘Լ๏ઢ͕ࠞ. ܭଌ͢Δɽ. ࡏ͍ͯ͠ΔͨΊͰ͋Δͱ༧Ͱ͖ɼ࣮ࡍͷද໘Լ๏ઢද. c 2015 Information Processing Society of Japan . 5.
(6) Vol.2015-CG-161 No.15 Vol.2015-CVIM-199 No.15 2015/11/7. ใॲཧֶձڀݚใࠂ IPSJ SIG Technical Report. ໘๏ઢͷҰͭΛҾ͍ͨʹͳΔͱ༧Ͱ͖ΔɽҎޙɼղ. Ϭ͘Ϭϯ. ੳͷࡍʹɼ࠷ϝλϦοΫͷޫً͡ײ͕ײΒΕΔ 1 ըૉ ͋ͨΓͷද໘Լ๏ઢ͕ଟ͍ըૉαΠζͰͦΕͧΕղੳΛ. ϮйͲϵϬƵŵ. Ϭ͘ϬϮϱ. ʹͳΔɽ ࣭ײਓؒͷͨݟͰஅ͞ΕΔͨΊɼධՁج४ͱͯ͠ ඪ४తͳਓؒͷࢹྗΛߟྀ͢Δඞཁ͕͋ΔɽࢹྗࠪݕΛج ४ʹͨ͠ͱ͖ɼࢹྗ 1.0 ͷਓؒ 5m ͷ͔ڑΒϥϯυϧτ ͷ 1.45mm ͷΕΛೝࣝ͢Δ͜ͱ͕Ͱ͖Δɽͭ·Γɼ. 5m ͷ͚͓ʹڑΔਓؒͷͷղ૾ 17.52ppi ͱ͍͏͜. ŝƌĐƵůĂƌǀĂƌŝĂŶĐĞ. ߦ͏ɽͦΕΒΛฏ͢ۉΔͱɼ1 ըૉ͕ 170μm ͷεέʔϧ Ϭ͘ϬϮ Ϭ͘Ϭϭϱ. ϮйͲϰϬƵŵ ϮйͲϯϬƵŵ. Ϭ͘Ϭϭ. ϭйͲϮϬƵŵ Ϭ͘ϬϬϱ ϭйͲϱƵŵ. ͱʹͳΔɽ͜ͷߟ͑ʹͱͮ͘جɼ1 ըૉͷαΠζ͕ 170μm ͱ͍͏εέʔϧɼਓ͕ؒ 58cm ͔ΒମΛ͖ͱͨݟͷ. ϭйͲϱϱƵŵ ϭйͲϵϬƵŵ ϭйͲϰϬƵŵ. Ϭ Ϭ. ؍ଌεέʔϧʹରԠ͢ΔͷͰɼ࣭ײධՁʹଥͳεέʔ ϧͰ͋Δͱ͍͑Δɽ. 5.3 ελϯμʔυαϯϓϧΛ༻͍ͨධՁ. ϮйͲϲϬƵŵ. ਤ 15. ϭ Ϯ ϯ ϰ ϱ EƵŵďĞƌŽĨƐƵďƐƵƌĨĂĐĞŶŽƌŵĂůƐŝŶϭƉdž. ϲ. 1 ըૉͷද໘Լ๏ઢͱ๏ઢํͷࢄͷؔ. ࣮ʹݧɼਤ 11 ʹࣔ͢ΞϧϛϑϨʔΫ͕ຒΊࠐ·Εͨ ΞΫϦϧथࢷϓϨʔτ༻͍ࣹͯͷܭଌΛߦͬͨɽೖࣹ֯. ࣍ʹɼۚଐϑϨʔΫͷද໘ૈ͞Λද͢ɼڞࢄߦྻͷݻ. ͷํʹਖ਼نԽͨ͠؍ଌًΛϓϩοτͨ͠ٿͷਤ. ༗ λ1 , λ2 (λ1 > λ2 ) ͷฏۉͱɼͦͷൺͷฏ͍ͯͭʹۉ. Λɼදతͳ݁Ռͱͯ͠ 1%-40μmɼ1%-90μmɼ2%-90μm. ௐͨɽϑϨʔΫͷද໘ૈ͞ͷҟํੑʹؔͯ͠ɼϑϨʔ. ͷ݁ՌͷΈൈਮͯ͠ਤ 13 ʹࣔ͢ɽ͜ͷ݁Ռ͔Βɼଟॏ๏. ΫαΠζͱؚ༗ྔ͕ଟ͘ͳΔʹͭΕͯํʹۙͮ͘ɽ͜Ε. ઢମෳͷࣹͷϐʔΫΛ࣋ͭ͜ͱ͕֬ೝͰ͖Δɽͳ. ɼϑϨʔΫ͕ີʹͳΔ΄Ͳ๏ઢີʹͳΔͨΊɼෳ. ͓ɼ͜ͷ؍ଌ݁ՌྡըૉͰେ͖͘ҟͳΔɽ. ͷํͳਖ਼نͰͯΊΔͷ͕ྑ͍݁Ռʹͳ͍ͬͯ. ·ͨɼ͜ͷ؍ଌΛ༻͍ͯද໘Լ๏ઢͷΛਪఆͨ͠ ݁ՌΛਤ 14 ʹࣔ͢ɽશମతʹఱํʹ๏ઢ͕͍͍ͯ. Δͱ༧Ͱ͖Δɽ ࣍ʹɼ1 ըૉͷද໘Լ๏ઢͱ๏ઢํͷࢄ͔ΒɼͲ. Δ͕ɼͦͷํੑʹόϥ͖͕ͭݟΒΕΔɽ·ͨɼ݁Ռ. ͷ͘Β͍ΩϥΩϥ͍ͯ͠Δͷ͔ͷؔΛਤ 15 ʹࣔ͢ɽ࣮. ྡըૉͰද໘Լ๏ઢେ͖͘ҟͳΔɽ. ମͷͨݟͱ݁Ռͷൺֱ͔Βɼάϥϑதͷӈ্ʹϓϩο. ਪఆͨ͠ද໘Լ๏ઢͷ݁Ռ 100 ըૉͷσʔλΛݩ. τ͞ΕΔ΄ͲɼΩϥΩϥײΛ͡ײ͘ڧΔ͜ͱ͕֬ೝͰ͖Δɽ. ʹɼରମͷཧతͳ౷ྔܭΛٻΊͨ݁ՌΛද 1 ʹࣔ. ͜ͷ݁Ռ͔ΒɼϝλϦοΫృͳͲͷଟॏ๏ઢମͷΩϥ. ͢ɽ·ͣɼ1 ըૉͷ๏ઢͷฏۉɾඪ४ภࠩʹ͍ͭͯௐ. Ωϥͱً͘ಠಛͳࣹͷఆྔԽ͕࣮͕ͱ͖ͨ͜ͰݱΘ͔Δɽ. ͨɽ1%-40μm ͱ 1%-90μm Λൺֱ͢Δͱɼಉ͡େ͖͞ͷ ըૉʹ·ؚΕΔ๏ઢɼϑϨʔΫαΠζ͕େ͖͍ํ͕. 6. ϔΞϥΠϯՃͷద༻. গͳ͍݁Ռͱͳͬͨɽ͔͠͠ɼਤ 12 ͷ݁ՌͷΑ͏ʹɼϑ. 6.1 ϔΞϥΠϯՃͷੑ࣭. ϨʔΫͷେ͖͞ͱ୯Ґ໘ੵʹ·ؚΕΔϑϨʔΫͷ๏ઢͷ. ύʔϧϚΠΧృՃ০ϑΟϧϜ͚ͩͰͳ͘ɼಠಛͳ. ʹݸɼ໌നͳ૬ؔ֬ೝͰ͖ͳ͍ɽ·ͨɼ1%-40μm ͱ. ๏ઢΛ࣋ͭମͱͯ͠ɼϔΞϥΠϯՃ͞Εͨۚଐɼ. 2%-40μm 1%-90μm ͱ 2%-90μm Λൺֱ͢Δͱɼؚ༗ྔ. զʑͷͷճΓʹଟ͘ݟΒΕΔɽۚଐ൘ͷද໘্͛ํ๏. ͷগͳ͍ϓϨʔτͷํ͕๏ઢ͕খ͘͞ͳ͕ͬͨɼͦͷඪ. ͷ͏ͪɼۚଐද໘ʹͷໟͷΑ͏ʹࡉ͔͍ϥΠϯ͕ઢత. ४ภࠩେ͖͍݁ՌͱͳΓɼ؍ଌ͝ͱͷ͕ࠩେ͖͍݁Ռ. ʹݚຏ͞Ε্ͨ͛ͷ͜ͱΛϔΞϥΠϯՃͱͿݺɽϔΞ. ͱͳͬͨɽ. ϥΠϯՃɼମΛ؍ଌ໘ͷ๏ઢΛ࣠ʹճసͤͨ͞ͱ͖. ࣍ʹɼද໘Լ๏ઢ͕ͲͷํΛ͍͍ͯΔͷ͔ʹ͍ͭͯ. ʹ໌Δ͕͞มԽ͢Δҟํੑࣹ͕؍ଌ͞ΕΔମͰ͋Δɽ. ͷฏͱํۉɼํͷࢄʹ͍ͭͯௐͨɽฏͭʹํۉ. ϔΞϥΠϯՃ͞ΕͨۚଐͰɼϒϥγํʹԠࣹͯ͡. ͍ͯɼ֯ڼɾํҐ֯Λ༻͍ͯ (θ, φ) [deg] Ͱද͢ɽͦͷ݁. ͕ઢରশʹͳΔɽ. ՌɼͲͷϓϨʔτද໘Լ๏ઢฏͯ͠ۉఱํΛ͍. ϔΞϥΠϯՃϝλϦοΫృͱಉ༷ʹɼ؍ଌεέʔ. ͍ͯΔ͜ͱ͕֬ೝͰ͖Δɽ·ͨɼϑϨʔΫͷؚ༗ྔ͕ଟ͍. ϧʹԠ͕ͯ͡ํ͑ݟେ͖͘ҟͳΔɽखͰ࣋ͬͯݟΔΑ͏ͳ. ΄Ͳ๏ઢํͷࢄ͕େ͖͍݁ՌͱͳͬͨɽϑϨʔΫαΠ. ௨ৗͷ؍ଌεέʔϧͰɼଟͷϔΞϥΠϯͷই͕͑ݟɼ. ζʹؔͯ͠໌֬ͳ૬ؔ֬ೝͰ͖ͳ͍͕ɼ1%ͷؚ༗ྔͷ. ڸ໘্͛ͱҟͳΓۚଐͷ࣭ײΛ͡ײ͘ڧΒΕΔɽ؍ଌڑ. ͷ͚ͩʹண͢ΔͱɼαΠζ͕େ͖͘ͳΔ΄Ͳ๏ઢࢄ. Λۙͨ͘͠ΓɼഒΛߴͯ͘͠؍ଌͨ͠ͱ͖ʹɼ1 ͭ. ͕େ͖͘ͳΔ͕֬ೝͰ͖Δɽ. 1 ͭͷইʹண͍ͯ͠Δ͜ͱʹͳΓɼইͷஅ໘ํʹ๏ઢ. c 2015 Information Processing Society of Japan . 6.
(7) Vol.2015-CG-161 No.15 Vol.2015-CVIM-199 No.15 2015/11/7. ใॲཧֶձڀݚใࠂ IPSJ SIG Technical Report. (a) 1%-40μm ਤ 13. (b) 1%-90μm. (c) 2%-90μm. ؍ଌًɽٿΛఱํ͔ΒͨݟਤͰ͋Γɼೖࣹํ࠲ඪʹ؍ଌΛͯΊͯ ͍Δɽ. (a) 1%-40μm ਤ 14. (b) 1%-90μm. (c) 2%-90μm. ද໘Լ๏ઢɽਤ 9 ʹࣔ͢࠲ඪͰܥද͓ͯ͠ݱΓɼٿΛఱํ͔ΒͨݟਤͰ͋Δɽ. ͕ଘࡏ͢Δɽʹٯɼ؍ଌڑΛԕͨ͘͠ΓɼഒΛ ͯ͘͠؍ଌͨ͠ͱ͖ɼແͷই͕ରԠͯ͠ɼই͕ͳ͑ݟ ͍ҟํੑࣹ͕؍ଌ͞ΕΔɽ. 6.3 ϔΞϥΠϯՃͷ๏ઢͷ౷ྔܭͷࢉग़ ͜͜Ͱɼਪఆͨ͠๏ઢͱϔΞϥΠϯՃͷද໘ঢ় ଶͱͷؔੑʹ͍ͭͯड़ΔɽϔΞϥΠϯͷই͕͍ڧ ߹ɼইͷࣼ໘ͷํʹରͯ͠ෳͷߏͷ͕ੜ͡Δɽ. 6.2 ϔΞϥΠϯՃͷ๏ઢਪఆ. ͦͷͨΊɼͷߏϔΞϥΠϯͷইͷͱ͞ڧରԠ͢. ϝλϦοΫృͰɼۚଐϑϨʔΫ͕༷ʑͳํΛ͍. Δɽ·ͨɼ๏ઢͷࢄ͕ϔΞϥΠϯՃͷද໘ૈ͞ʹ. ͍ͯΔӨͰڹϑϨʔΫͷ๏ઢͷ͕ϑϨʔΫʹΑΔࣹ. ରԠ͢ΔɽಛʹɼϔΞϥΠϯՃࣹʹҟํੑΛੜ͡Δ. ϐʔΫͷͱରԠ͍ͯ͠ΔͷͰɼࣹϐʔΫͷͰ๏ઢ. ͨΊɼ๏ઢͷҟํੑΛٻΊΔ͜ͱͰɼࣹͷҟํੑΛ. ͷΛܾఆͨ͠ɽ͔͠͠ɼϔΞϥΠϯՃͰইͷେ͖. ٻΊΔ͜ͱ͕ग़དྷΔɽ. ͕͞ҰఆͰͳ͘ɼେ͖ͳই͔Βখ͞ͳই·Ͱ·ؚΕ͍ͯ ΔͨΊɼ๏ઢͷΛϝλϦοΫృͱಉ༷ʹܾఆ͢. ͜ΕΒͷཧతಛྔʹؔͯ͠ɼͦΕͧΕͷ౷ܭతͳฏ ۉͳͲ͔Εɼ࣭ײΛఆྔԽ͢Δ͜ͱ͕Ͱ͖Δɽ. Δ͜ͱͰ͖ͳ͍ɽͦͷͨΊɼ๏ઢͷਪఆख๏ϝλ ϦοΫృͱಉ͡Ͱ͋Δ͕ɼࠞ߹Ψεͷߏͷܾ. 6.4 ϔΞϥΠϯՃͷղੳ݁Ռ. ఆํ๏Λมߋ͢Δɽࠞ߹ΨεͷߏΛ૯ΓͰධ. ରମʹਤ 16 ʹࣔ͢ϔΞϥΠϯՃ͞ΕͨۚଐΛ. Ձ͠ɼϞσϧʹର͢ΔదͳߏΛܾఆ͢ΔͨΊͷࢦඪ. ࡾͭ༻͍ͨɽࠨ্ͷۚଐଞͷೋͭʹൺͯϔΞϥΠϯ͕. ͱͯ࣍ࣜ͠Ͱද͞ΕΔ BICʢϕΠζใྔʣΛ༻͍Δɽ. ऑ͘ɼԼͷۚଐଞͷೋͭʹൺͯϔΞϥΠϯ͕͍ڧɽӈ ্ͷۚଐࠨ্ͷۚଐͷཪ໘Λۚ͢ΓͰݚຏ͢Δ͜ͱ. BIC = −2 ln(L) + K ln(N ). ͰɼதؒతͳϔΞϥΠϯঢ়ଶΛ࡞ͨ͠ɽ͜ΕΒࡾͭͷϔ. (6). ΞϥϯՃ͞ΕͨۚଐΛ༻͍ͯղੳΛߦ͏ɽ ·ͣɼεέʔϧΛมԽͤͨ͞ࡍͷ 1 ըૉͷ๏ઢ. ͜͜ͰɼL ࠷େɼK ύϥϝʔλɼN ඪຊΛ. Λਤ 17 ʹࣔ͢ɽϔΞϥΠϯͷই͕͚ڧΕͲ΄͍ڧɼ1 ը. ද͢ɽ͜ͷ BIC ͷ͕খ͍͞ͷ͕࠷దͳύϥϝʔλͰ. ૉͷ๏ઢ͕ଟ͍ɽεέʔϧΛมԽͤͨ͞ࡍͷ๏ઢ. ͋Γɼࠞ߹ΨεͷߏΛٻΊΔ͜ͱ͕Ͱ͖Δɽ. ͷมԽ͕গͳ͍ͷɼ༷ʑͳεέʔϧͷই͕ࠞࡏͯ͠. c 2015 Information Processing Society of Japan . 7.
(8) Vol.2015-CG-161 No.15 Vol.2015-CVIM-199 No.15 2015/11/7. ใॲཧֶձڀݚใࠂ IPSJ SIG Technical Report ද 1 ϑϨʔΫ. ϝλϦοΫృͷղੳ݁Ռ. 1%-5μm. 1%-20μm. 1%-40μm. 1%-55μm. 1%-90μm. 2%-30μm. 2%-40μm. 2%-60μm. 2%-90μm. ฏۉ๏ઢ. 1.04. 2.09. 5.45. 3.88. 4.47. 4.22. 4.76. 5.35. 4.38. ๏ઢඪ४ภࠩ. 0.19. 0.91. 1.43. 0.81. 1.26. 1.02. 1.69. 1.12. 1.46. ฏۉ๏ઢ (θ, φ) [deg]. (1.1, 269.9). (2.9, 282.0). (1.8, 291.4). (3.5, 264.9). (1.3, 345.2). (3.5, 288.2). (3.4, 318.1). (1.9, 274.9). (3.3, 355.4). ๏ઢࢄ λ¯1 λ¯2 . 0.01×10−2. 0.24×10−2. 0.33×10−2. 0.54×10−2. 0.48×10−2. 0.72×10−2. 1.01×10−2. 0.47×10−2. 2.55×10−2. 0.23. 0.30. 0.14. 0.26. 0.17. 0.14. 0.21. 0.15. 0.13. 0.15. 0.22. 0.14. 0.24. 0.15. 0.13. 0.17. 0.15. 0.12. 0.81. 0.75. 0.80. 0.65. 0.90. 0.90. 0.87. 0.98. 0.94. λ2 λ1. Weak hairline. Ө͕ͱ͍͜ͳ͠ڹ͔ͬͨɽͦΕɼۚଐϑϨʔΫͷΑ͏. Manual hairline. ͳେ͖ͳମ͕ࣹʹӨڹΛ༩͑Δ߹ͰεέʔϧมԽ ʹରͯ͠େ͖͘Ө͢ڹΔ͕ɼϔΞϥΠϯՃͰɼইͷ தʹ͞Βʹඍখͳই͕ଘࡏ͢ΔͨΊεέʔϧมԽʹର͠ ͯ͋·Γଟ͘Өͱ͍ͳ͠ڹ༧Ͱ͖Δɽ·ͨɼϔΞϥΠ. Strong hairline. ϯͷইͷ͞ڧִؒͷҧ͍๏ઢʹӨڹΛ༩͑Δ͜ ͱ͕֬ೝͰ͖ͨɽͦͷͨΊɼ๏ઢΛղੳ͢Δ͜ͱͰϔ ΞϥΠϯՃͷ࣭ײΛಡΈऔΕΔͱ༧Ͱ͖Δɽ. 7. Ή͢ͼ ਤ 16. ຊͰڀݚɼද໘ԼͷϑϨʔΫͳͲʹΑͬͯ๏ઢͷ. ϔΞϥΠϯՃͷܭଌମ. ͕ಠಛʹมԽ͢Δද໘Λରͱ͠ɼද໘Լͷ๏ઢΛ౷ ܭతʹղੳ͢Δ͜ͱͰϝλϦοΫృͷ࣭ײఆྔԽΛߦͬ. EƵŵďĞƌŽĨŶŽƌŵĂůĚŝƐƚƌŝďƵƟŽŶ. ͨɽද໘Լ๏ઢΛޫͷࣹ͔Βਪఆ͠ɼͦͷ౷͔ྔܭ. ϳ ϲ. Β 1 ըૉͷ๏ઢͱͦͷํͷฏͱۉࢄΛٻΊΔ͜ͱ. ϱ ϰ. tĞĂŬŚĂŝƌůŝŶĞ. ϯ. DĂŶƵĂůŚĂŝƌůŝŶĞ. Ϯ. ^ƚƌŽŶŐŚĂŝƌůŝŶĞ. ϭ. ͕Ͱ͖ͨɽ·ͨɼ1 ըૉͷαΠζ͝ͱͷ๏ઢΛٻΊΔ͜ ͱͰɼదͳ؍ଌεέʔϧͰͷධՁΛߦ͏͜ͱ͕Ͱ͖ͨɽ ͦͷ݁Ռɼ1 ըૉͷ๏ઢͱͦͷํͷࢄΩϥΩϥ. Ϭ Ϭ. ϮϬϬ. ϰϬϬ. ϲϬϬ. ϴϬϬ. ϭϬϬϬ. ϭϮϬϬ. ϭϰϬϬ. ϭϲϬϬ. ͱ࣭ͨ͠ײΛද͢ݱΔύϥϝʔλͱͯ͠༗ޮͰ͋Δ͜ͱΛ. WŝdžĞůƐŝnjĞƵŵ. ֬ೝͨ͠ɽ ਤ 17. ըૉαΠζ͝ͱͷ๏ઢ. ·ͨɼಉ༷ʹϔΞϥΠϯՃͷ๏ઢΛղੳ͢Δ͜ͱ ͰɼεέʔϧมԽʹର͢Δ๏ઢͷৼΔ͍ͷมԽΛٻ Ίͨɽͦͷ݁ՌɼϔΞϥΠϯͷইͷִ͕ؒͱ͞ڧ๏ઢ. /ƐŽƚƌŽƉŝĐǀĂůƵĞ ϭ Ϭ͘ϵ Ϭ͘ϴ Ϭ͘ϳ Ϭ͘ϲ Ϭ͘ϱ Ϭ͘ϰ Ϭ͘ϯ Ϭ͘Ϯ. ʹӨڹΛ༩͑Δ͜ͱΛ֬ೝͨ͠ɽ ຊͰڀݚ࣭ײΛද͢ݱΔಛͷݕग़Λߦ͍ͬͯΔ͕ɼ tĞĂŬŚĂŝƌůŝŶĞ DĂŶƵĂůŚĂŝƌůŝŶĞ ^ƚƌŽŶŐŚĂŝƌůŝŶĞ. ࠓޙɼ͜Ε͕ϝλϦοΫృʹಛ༗ͳਂΈߴͲͳײڃ ͷਓؒͷ֮ͱͲͷΑ͏ʹରԠ͢Δͷ͔ௐ͍ࠪͨ͠ɽ· ͨɼϔΞϥΠϯՃ͞Εͨۚଐͷ࣭ײఆྔԽͷͨΊʹඞཁ. Ϭ. ϮϬϬ. ϰϬϬ. ϲϬϬ. ϴϬϬ. ϭϬϬϬ. ϭϮϬϬ. ϭϰϬϬ. ϭϲϬϬ. WŝdžĞůƐŝnjĞƵŵ. ਤ 18. ըૉαΠζ͝ͱͷ๏ઢͷҟํੑ. ͍ΔͨΊͰ͋Δͱ༧Ͱ͖Δɽ. ͳಛΛ͞Βʹ૿ͤΔΑ͏ʹղੳΛਐΊ͍͖͍ͯͨɽ ࢀߟจݙ [1]. ·ͨɼεέʔϧΛมԽͤͨ͞ࡍͷ๏ઢͷҟํੑΛਤ. 18 ʹࣔ͢ɽਓҝతʹϔΞϥΠϯΛ͚ͭͨۚଐଞͷۚଐʹ. [2]. ൺͯϔΞϥΠϯͷই͕ଟ͘ɼϔΞϥΠϯͷִ͕͍ؒڱɽ ͜ͷ݁Ռ͔ΒɼϔΞϥΠϯͷִ͕ؒͲ΄͍ڱҟํੑ͕͍ڧ. [3]. ͜ͱ͕͔ΔɽεέʔϧΛมԽͤͯ͞ɼ๏ઢͷҟํ ੑେ͖͘มԽ͠ͳ͍ɽ Ҏ্ͷ͜ͱ͔ΒɼϝλϦοΫృεέʔϧͷҧ͍͕ද ໘Լʹେ͖͘Ө͢ڹΔ͕ɼϔΞϥΠϯՃʹ͋·Γ. c 2015 Information Processing Society of Japan . [4]. Torrance, K. E. and Sparrow, E. M.: Theory for OffSpecular Reflection From Roughened Surfaces, J. Opt. Soc. Am., Vol. 57, No. 9, pp. 1105–1112 (1967). Ward, G. J.: Measuring and Modeling Anisotropic Reflection, SIGGRAPH Comput. Graph., Vol. 26, No. 2, pp. 265–272 (1992). ޱ༸Ұɼߴًڮɼࢁɹ৳ɿϝλϦοΫΧϥʔʹ͓͚ Δ࣭ํݱ࠶ײ๏ɼృྉͷڀݚɼNo. 145, pp. 14–21 (2006). ాஉɼਗ਼ਫলࡾɼय़༝ɼү୩ग़உɼాɹొɼ ࠤʑྑɼాลরඒɼߴڮɹɼٶԼ߂ɼ܂ɹɼ ্ݩɼฏҪහɿϝλϦοΫײͷܭଌํ๏ɼ৭ࡐڠ ձࢽɼVol. 43, No. 8, pp. 375–383 (1970).. 8.
(9) ใॲཧֶձڀݚใࠂ IPSJ SIG Technical Report. [5]. [6] [7]. [8]. [9]. [10]. [11]. Vol.2015-CG-161 No.15 Vol.2015-CVIM-199 No.15 2015/11/7. ɹపɼࣉलɿϝλϦοΫృບͷఆྔతධՁ͓Α ͼଌఆஔʹ͍ͭͯɼୈ 10 ճృྉɾృٕज़૯߹ൃڀݚ දձཁࢫूɼp. 42 (1992). ਗ਼Ҫܭɼࢁຊ৴࣍ɼɹऩɿϝλϦοΫ৭ͷཻࢠײͷ ଌఆɼຊ৭࠼ֶձࢽɼVol. 30, No. 1, pp. 9–15 (2006). Sung, L. P., Nadal, M. E., McKnight, M. E., Marx, E. and Laurenti, B.: Optical reflectance of metallic coatings: Effect of aluminum flake orientation, Journal of Coatings Technology, Vol. 74, No. 932, pp. 55–63 (2002). Levin, A., Glasner, D., Xiong, Y., Durand, F., Freeman, W., Matusik, W. and Zickler, T.: High Spatial Resolution BRDFs with Metallic powders Using Wave Optics Analysis (2013). Dempster, A. P., Laird, N. M. and Rubin, D. B.: Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society, Series B, Vol. 39, No. 1, pp. 1–38 (1977). Bishop, C. M.: Pattern Recognition and Machine Learning (Information Science and Statistics), Springer-Verlag New York, Inc., Secaucus, NJ, USA (2006). Mardia, K. V.: Statistics of Directional Data, Probability and Mathematical Statistics a Series of Monographs and Textbooks, Academic Press (1972).. c 2015 Information Processing Society of Japan . 9.
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