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(1)Vol.2015-CG-161 No.15 Vol.2015-CVIM-199 No.15 2015/11/7. ৘ใॲཧֶձ‫ڀݚ‬ใࠂ IPSJ SIG Technical Report. ‫؍‬ଌεέʔϧΛߟྀͨ͠ ϝλϦοΫృ૷ͷද໘Լ๏ઢ෼෍ղੳ ஑ຊ ঵1. ޲઒ ߁ത2. দԼ ߁೭1. ‫ٱ‬อ ਘ೭2. ീ໦ ߁࢙1. ֓ཁɿۙ೥ɼ࢈‫ۀ‬քͰ͸੡඼ͷࠩผԽͷͨΊʹߴ‫ײڃ‬Λ࣋ͨͤΔͨΊͷՃ০ٕज़͕ൃୡ͠ɼ࣭‫ײ‬ΛఆྔԽ ͢Δ͜ͱ͕ࠔ೉ͳද໘ͷ‫͖ͨͯ͑૿͕͑ݟ‬ɽྫ͑͹ɼࣗಈं΍Ոి੡඼ʹ༻͍ΒΕΔϝλϦοΫృ૷Ͱ͸ɼ ృບதͷඍࡉͳۚଐϑϨʔΫͷ൓ࣹʹΑͬͯߴ‫ײڃ‬Λग़͍ͯ͠Δ͕ɼͦͷΩϥΩϥͱ࣭ͨ͠‫ײ‬ΛఆྔԽ͢ Δ͜ͱ͸೉͍͠ɽͦ͜Ͱຊ࿦จͰ͸ɼ͜ΕΒͷΑ͏ʹද໘ԼͷϑϨʔΫͳͲʹΑͬͯ൓ࣹޫ͕ಠಛʹมԽ ͢Δද໘Λର৅ͱ͠ɼද໘Լͷ๏ઢ෼෍Λ౷‫ܭ‬తʹղੳ͢Δ͜ͱͰϝλϦοΫృ૷ͷ࣭‫ײ‬ఆྔԽΛߦ͏ɽ ͦͷࡍɼϝλϦοΫృ૷͸‫؍‬ଌ‫ʹ཭ڑ‬Ԡͯ͡൓ࣹͷৼΔ෣͍͕ҟͳΔͨΊɼద੾ͳ‫؍‬ଌεέʔϧΛධՁ͢ Δɽͦͯ͠ɼ൓ࣹσʔλ͔Βਪఆͨ͠๏ઢ໬౓ʹɼࠞ߹Ψ΢εϞσϧΛ౰ͯ͸ΊΔ͜ͱͰද໘Լͷ๏ઢ෼ ෍Λղੳ͢Δɽ·ͨɼղੳͨ͠ද໘Լͷ๏ઢ෼෍͔Βɼ୯Ґ໘ੵ಺ͷϑϨʔΫͷ๏ઢ਺΍๏ઢํ޲ͳͲͷ ౷‫ྔܭ‬Λ‫ٻ‬Ίɼ࣭‫ײ‬ͷఆྔԽΛߦ͏ɽ͞Βʹɼಠಛͳ๏ઢ෼෍Λ࣋ͭ෺ମͱͯ͠ɼϔΞϥΠϯՃ޻͞Εͨ ۚଐʹ͍ͭͯ΋ಉ༷ʹɼ๏ઢ෼෍Λ౷‫ܭ‬తʹղੳ͢Δ͜ͱͰ࣭‫ײ‬ͷఆྔԽΛߦ͏ɽ. 1. ·͕͖͑. ͦ͜Ͱɼຊ࿦จͰ͸ɼද໘Լʹ༷ʑͳํ޲Λ޲͍ͨۚଐ ϑϨʔΫΛ‫ؚ‬ΉϝλϦοΫృ૷ͳͲͷಠಛͷ࣭‫ײ‬Λ࣋ͬͨ. ࢈‫ۀ‬քͰ͸֎૷ʹʮՃ০ʯͱ‫ݺ‬͹ΕΔಛघͳృ૷Λࢪ͠. ද໘Λର৅ͱ͠ɼͦͷ൓ࣹσʔλ͔Βද໘ԼͷۚଐϑϨʔ. ͨ੡඼͕਺ଟ͘ੜ࢈͞Ε͖͓ͯͯΓɼͦͷҰͭͱͯ͠ɼ ʮߴ. Ϋͷ๏ઢ෼෍Λ‫ٻ‬ΊΔɽ·ͨɼͦͷ݁Ռ͔Β୯Ґ໘ੵ౰ͨ. ‫ײڃ‬ʯΛ࣋ͨͤͨՃ০ٕज़Ͱ͋ΔϝλϦοΫృ૷͕‫͛ڍ‬Β. ΓͷϑϨʔΫͷ๏ઢ਺΍ϑϨʔΫͷ޲͖Λ౷‫ܭ‬తʹղੳ͢. ΕΔɽϝλϦοΫృ૷ʹ͸༷ʑͳछྨ͕ଘࡏ͠ɼࣗಈंͷ. Δ͜ͱͰɼ࣭‫ײ‬ͷఆྔԽΛ͢Δɽ·ͨɼಠಛͷ๏ઢ෼෍Λ. ֎૷ʹ͸ඍࡉͳӢ฼ͷཻࢠΛΫϦΞ૚ʹࠞͥͨύʔϧϚΠ. ෺ମʹ༩͑ΔՃ޻ͱͯ͠ɼϔΞϥΠϯՃ޻͕‫͛ڍ‬ΒΕΔɽ. Χృ૷Λ༻͍ͯߴ‫ײڃ‬Λԋग़͍ͯ͠Δɽ·ͨɼۙ೥ͷՈి. ϔΞϥΠϯՃ޻͞Εͨۚଐ΋ಉ༷ʹɼ๏ઢ෼෍Λղੳ͢Δ. ੡඼ͳͲʹ༻͍ΒΕ͍ͯΔۚଐϑϨʔΫΛ‫ؚ‬Ή૚Λ΋ͬͨ. ͜ͱͰɼ࣭‫ײ‬ͷఆྔԽΛߦ͏ɽ͜ͷख๏Ͱ͸ɼ൓ࣹޫͷۭ. Ճ০ϑΟϧϜʹ͓͍ͯ΋ɼಉ͡Α͏ͳߏ଄͕‫؍‬ଌ͞ΕΔɽ. ؒ෼෍Λ௚઀ղੳ͢ΔͷͰ͸ͳ͘ɼ๏ઢ෼෍ͱ͍͏෺ཧత. ͜ΕΒͷృ૷͸࢈‫ۀ‬քʹ͓͍ͯɼߴ‫ײڃ‬Λද‫͢ݱ‬Δ্Ͱॏ. ͳύϥϝʔλΛਪఆ͢ΔͨΊɼ‫ʹڥ؀‬ରͯ͠ෆมͰ͋Δɽ. ཁͰ͋ΔͨΊؔ৺͕ߴ͍΋ͷͷɼͦͷද໘ঢ়ଶͷ࣭‫ײ‬Λఆ ྔԽ͢Δ͜ͱ͸ैདྷख๏Ͱ͸ࠔ೉Ͱ͋Δɽ ਓ͕ؒ͋Δ෺ମΛ‫͔֮ࢹʹ͖ͱͨ͠࡯؍‬Β‫͡ײ‬Δ࣭‫ײ‬. 2. ؔ࿈‫ڀݚ‬ 2.1 ैདྷͷ൓ࣹϞσϧ͕औΓѻ͏ද໘ঢ়ଶ. ͸ɼͦͷ෺ମͷ൓ࣹಛੑͱਂ͍ؔΘΓΛ΋ͭɽྫ͑͹ɼ‫ڸ‬. ैདྷͷ൓ࣹϞσϧͰ͸ɼ෺ମͷද໘ʹ͸‫؍‬ଌεέʔϧʹ. ͷΑ͏ʹද໘͕‫׈‬Β͔ͳ΋ͷ͸‫ڸ‬໘൓ࣹ੒෼͕‫͍ͨڧ‬Ίͭ. ରͯ͠े෼ʹඍࡉͳϚΠΫϩϑΝηοτͱ‫ݺ‬͹ΕΔߏ଄Λ. ΍ͭ΍ͱ࣭ͨ͠‫ײ‬Λ‫͡ײ‬Δ͕ɼࢴͷΑ͏ʹද໘͕ૈ͍΋ͷ. ༗͢Δ΋ͷͱϞσϧԽ͞Ε͍ͯΔɽྫ͑͹ɼ‫ڸ‬໘൓ࣹΛද. ͸֦ࢄ൓ࣹ੒෼͕‫͍ͨڧ‬Ί͟Β͟Βͱ࣭ͨ͠‫ײ‬Λ‫͡ײ‬Δɽ. ‫͢ݱ‬Δ Torrance-Sparrow Ϟσϧ [1] ͸ɼ෺ମද໘Λ‫׬‬શ‫ڸ‬. ͜ͷΑ͏ʹɼ෺ମͷ൓ࣹಛੑ͸ɼ෺ମද໘ͷඍࢹత‫ܗ‬ঢ়ʹ. ໘൓ࣹ͢Δඍখ໘ͷू߹Ͱߏ੒͞ΕΔͱԾఆͨ͠ϞσϧͰ. ґଘ͢ΔɽͦͷͨΊɼ෺ମද໘ͷඍࢹత‫ܗ‬ঢ়Λৄࡉʹௐࠪ. ͋Δɽ͜ͷϞσϧ͸ɼর໌ํ޲ͱ‫؍‬ଌํ޲ͷ྆ํΛ‫ݻ‬ఆ͠ɼ. ͢Ε͹ɼͦͷ෺ମͷ࣭‫ײ‬ΛఆྔతʹධՁ͢Δ͜ͱ͕Մೳʹ. ର৅෺ମΛ๏ઢํ޲Λ࣠ʹճసͤͯ͞΋໌Δ͕͞มԽ͠ͳ. ͳΔͱߟ͑ΒΕΔɽ. ͍౳ํੑ൓ࣹΛԾఆ͍ͯ͠Δɽͦͷଞʹ΋ɼҟํੑͷ൓ࣹ. 1 2. ΛऔΓѻ͏͜ͱ͕Ͱ͖Δ Ward Ϟσϧ [2] Ͱ΋ɼද໘ͷߏ େࡕେֶ Osaka University ಸྑઌ୺Պֶٕज़େֶӃେֶ Nara Institute of Science and Technology. c 2015 Information Processing Society of Japan . ଄͸े෼ʹখ͍͞ͱԾఆͯ͠൓ࣹΛ࠶‫͍ͯ͠ݱ‬Δɽ͜ΕΒ ͷϞσϧ͸෺ମΛ‫ࢹڊ‬త΍ඍࢹతʹ‫͖ͱͨݟ‬ͷͦΕͧΕͷ. 1.

(2) Vol.2015-CG-161 No.15 Vol.2015-CVIM-199 No.15 2015/11/7. ৘ใॲཧֶձ‫ڀݚ‬ใࠂ IPSJ SIG Technical Report. ൓ࣹͷ࠶‫ݱ‬͸Ͱ͖Δ͕ɺͦͷؒͷதؒࢹతͳঢ়ଶ΋ߟྀ͠. Clear paint Pearl mica coating Mica. ͨϞσϧͰ͸ͳ͍ɽͭ·ΓɼϝλϦοΫృ૷ʹ‫·ؚ‬ΕΔΑ ͏ͳ͋Δఔ౓ͷେ͖͞Λ࣋ͭۚଐϑϨʔΫͷҰͭҰͭ΍ɼ. Base color paint Under coat Iron plate. ϔΞϥΠϯՃ޻͞ΕͨۚଐதͷইͷҰͭҰͭ·Ͱ͸࠶‫͢ݱ‬ Δ͜ͱ͕Ͱ͖ͳ͍ɽͦͷͨΊɼ͜ΕΒͷ൓ࣹϞσϧʹ‫؍‬ଌ σʔλΛ౰ͯ͸ΊΔ͚ͩͰ͸ɼϝλϦοΫృ૷ͷ࣭‫ײ‬Λఆ. ਤ 1 ύʔϧϚΠΧృ૷ͷߏ଄. ྔԽ͢Δ͜ͱ͸೉͍͠ͱ͍͑Δɽ. 2.2 ϝλϦοΫృ૷ͷ࣭‫ײ‬ఆྔԽख๏. PET layer Printed pattern layer Adhesive layer Metallic flakes. ϝλϦοΫృ૷Λԕ͔͘Β‫ʹ͖ͱͨݟ‬͸ϑϨʔΫʹΑΔ ΩϥΩϥͱͨ͠൓ࣹ͸͋·Γ‫͡ײ‬ΒΕͳ͘ɼۙ͘Ͱ‫ͱͨݟ‬ ͖ʹ͸ϑϨʔΫͷΩϥΩϥͨ͠൓ࣹ͕‫͡ײ͘ڧ‬ΒΕΔɽ͜. PVC or OLEFIN film layer. ͷΑ͏ʹɼϝλϦοΫృ૷ΛධՁ͢Δͱ͖ʹ͸ɼϚΫϩͳ ਤ 2. ޫً‫ͱײ‬ϛΫϩͳޫً‫ʹײ‬෼͚ͯධՁ͢Δඞཁ͕͋Δ [3]ɽ. Ճ০ϑΟϧϜͷߏ଄. ϚΫϩͳޫً‫ͱײ‬͸ɼൺֱతԕ͔͘Β‫͞࡯؍‬ΕΔۚଐ‫Ͱײ‬ ͋Γɼ‫֯࡯؍‬ͷมԽͰ৭ௐ͕มԽͯ͠‫͑ݟ‬Δɽ·ͨɼϛΫ ϩͳޫً‫ͱײ‬͸͔ۙ͘Β‫͞࡯؍‬ΕΔͱ͖ͷΩϥΩϥͱޫΔ ༷ࢠͷۚଐ‫͋Ͱײ‬Δɽ͜ͷϛΫϩͳεέʔϧʹண໨͢Δͱɼ ఺ޫ‫͍ۙʹݯ‬௚઀ޫΛ࢖༻ͨ͠ͱ͖ʹϛΫϩͳޫً‫ײ‬ͷੑ ࣭͕‫ݱ͘ڧ‬Εɼෳ਺ͷ൓ࣹϐʔΫ͕‫؍‬ଌ͞ΕΔɽ͜ͷ൓ࣹ. (a) ‫؍‬ଌ෺ମ. ϐʔΫ͸ɼϝλϦοΫృྉʹ༻͍ΒΕ͍ͯΔۚଐϑϨʔΫ. ਤ 3. (b) ‫؍‬ଌը૾. (c) ߴ͞ը૾. Ϩʔβʔ‫ݦ‬ඍ‫ڸ‬Λ༻͍ͨ‫؍‬ଌ. ͷ‫ܗ‬ঢ়΍ཻࢠ‫ܘ‬ɼϑϨʔΫͷ޲͖ʹԠͯ͡มԽ͢Δɽ͜Ε Βͷੑ࣭ʹ‫͖ͮج‬ɼैདྷͷϝλϦοΫృ૷ͷ࣭‫ײ‬ఆྔԽʹ ͸ɼେ͖͘෼͚ͯೋͭͷख๏͕ଘࡏ͢Δɽ Ұͭ໨͸ɼϝλϦοΫృ૷ʹಛ༗ͳ൓ࣹͷϐʔΫΛղੳ ͢Δํ๏Ͱ͋Δɽ෼ాΒ [4] ͸ɼ‫ݦ‬ඍޫ୔‫ܭ‬Λ༻͍ͯ൓ࣹ ‫౓ڧ‬Λऔಘ͠ɼͦͷϐʔΫͷࢁͱ୩ͷࠩΛൺֱ͢Δ͜ͱͰɼ. 3. ϝλϦοΫృ૷ʹ͓͚Δ൓ࣹͷ࢓૊Έ 3.1 ϝλϦοΫృ૷ͷߏ଄ ҰൠʹɼϝλϦοΫృྉʹ͸Ξϧϛχ΢ϜͳͲͷۚଐϑ. ۚଐϑϨʔΫʹΑΔεύʔΫϦϯάޮՌΛࢉग़͢Δख๏Λ. ϨʔΫ͕ࠞͥΒΕ͍ͯΔɽͦͯ͠ɼϑϨʔΫͷ‫ܗ‬ঢ়΍େ͖. ఏҊͨ͠ɽ·ͨɼϨʔβʔࣜϝλϦοΫ‫ײ‬ଌఆ‫[ ث‬5] ΋։. ͞ɼ޲͖ʹΑͬͯɼ‫͕ํ͑ݟ‬ҟͳΔɽϑϨʔΫ͸ɼ΄΅ಉ. ൃ͞Ε͓ͯΓɼਖ਼൓ࣹ͔Βগͣ͠Εͨํ޲ͷ‫؍‬ଌ஋ͷ‫౓ڧ‬. ͡ํ޲ʹ໘Λ޲͚ͳ͕Β΋͋Δఔ౓ͷ͹Β͖ͭΛ࣋ͨͤͯ. ͔ΒϝλϦοΫ‫ײ‬Λද͢ύϥϝʔλΛਪఆ͍ͯ͠Δɽଞʹ. ͍ΔͨΊɼਖ਼൓ࣹํ޲͸ϑϨʔΫͷ޲͖ʹґଘ༷ͯ͠ʑͳ. ΋ɼਗ਼ҪΒ [6] ͸ɼࡱӨ͞Εͨը૾ͷ‫ج‬४໘಺ͷۚଐϑϨʔ. ֯౓ͱͳΓɼैͬͯ൓ࣹޫ͸༷ʑͳํ޲ʹϐʔΫΛ΋ͭ͜. ΫʹΑΔߴً౓෦ͷ໌Δ͞΍໘ੵͷฏ‫ۉ‬΍෼ࢄͳͲͷύϥ. ͱʹͳΔɽࣗಈंͷృ૷Ͱ༻͍ΒΕ͍ͯΔύʔϧϚΠΧృ. ϝʔλΛઆ໌ม਺ͱͨ͠ॏճ‫ʹࣜؼ‬Αͬͯɼ໨ࢹͰͷཻࢠ. ૷͸ਤ 1 ͷΑ͏ͳߏ଄Λ͍ͯ͠Δɽ͜ͷృ૷͸ɼද໘Լʹ. ‫ײ‬ΛఆྔԽ͢Δख๏ΛఏҊͨ͠ɽ͜ΕΒͷख๏͸໨ࢹධՁ. ඍࡉۚଐཻࢠ΍Ӣ฼Λࠞೖ͢Δ͜ͱͰෳࡶͳ൓ࣹ͕‫͜ى‬. ͱͷ૬͕ؔ͋Δ͜ͱ͕֬ೝ͞Ε͍ͯΔ͕ɼ൓ࣹͷϐʔΫͱ. ΓɼಠಛͳਂΈ΍ߴ‫ײڃ‬Λද‫͍ͯ͠ݱ‬ΔɽՈి੡඼ͳͲʹ. ͍͏ը૾ಛ௃Λѻ͍ͬͯΔͨΊɼ෺ཧతͳߏ଄Λද͢ύϥ. ༻͍ΒΕ͍ͯΔՃ০ϑΟϧϜ΋ਤ 2 ͷΑ͏ʹɼࣅͨΑ͏ͳ. ϝʔλͰ͸ͳ͍ɽͦͷͨΊɼࡱӨํ๏΍‫ʹڥ؀‬ґଘ͢Δͱ. ߏ଄Λ࣋ͭɽ. ͍͏໰୊͕͋Δɽ. ·ͨɼਤ 3(a) ͷՃ০ϑΟϧϜΛಁ໌ମͷද໘ɾཱମߏ଄Λ. ೋͭ໨͸ϝλϦοΫృ૷ͷ෺ཧతͳߏ଄Λਪఆ͢Δํ๏. ‫ܭ‬ଌ͢Δ͜ͱ͕Մೳͳ‫ܗ‬ঢ়ղੳϨʔβʔ‫ݦ‬ඍ‫( ڸ‬KEYENCE. Ͱ͋Δɽྫ͑͹ɼ‫ڞ‬য఺Ϩʔβʔ‫ݦ‬ඍ‫ڸ‬Λ༻͍Δ͜ͱͰϝ. VK-X250) Λ༻͍ͯ‫؍‬ଌͨ͠ɽ͢Δͱɼਤ 3(b) ͷΑ͏ͳߏ. λϦοΫృ૷தͷۚଐϑϨʔΫͷ๏ઢΛ‫ݸ‬ผʹऔಘ͢Δ͜. ଄͕ղੳ͞Εͨɽը૾தͷԁ൫ঢ়ͷ෺ମ͕ද໘ԼͷϑϨʔ. ͱ͕Ͱ͖ΔɽSung Β [7] ͸ɼͦͷ๏ઢΛେྔʹ‫ܭ‬ଌ͢Δ͜. ΫͰ͋ΓɼϑϨʔΫͷ‫ܗ‬ঢ়͸֓Ͷԁ൫ঢ়Ͱ͋Δͱ͍͑Δɽ. ͱͰɼϝλϦοΫృ૷಺ͷϑϨʔΫͷ๏ઢ෼෍Λਪఆ͠ɼ. ·ͨɼ͜ͷը૾ͷߴ͞৘ใΛΧϥʔϚοϓͰදࣔͨ݁͠Ռ. ൓ࣹಛੑͷਪఆʹԠ༻͢Δख๏ΛఏҊͨ͠ɽ͜ͷख๏͸෺. ͕ਤ 3(c) Ͱ͋Δɽ͜ͷը૾͔ΒɼҰͭҰͭͷϑϨʔΫ͸ಛ. ཧతʹਖ਼֬ͳύϥϝʔλΛਪఆͰ͖Δ͕ɼ‫ݦ‬ඍ‫ڸ‬Λ༻͍Δ. ఆͷํ޲ʹ܏͖Λ͍࣋ͬͯΔ͜ͱ͕֬ೝͰ͖ΔɽҎ্ͷ͜. ͨΊɼ‫ܭ‬ଌʹखؒ΍ίετ͕͔͔ΔͳͲͷ໰୊͕͋Δɽ. ͱ͔ΒɼҰͭҰͭͷϑϨʔΫ͸ҟͳΔ൒‫ܘ‬ͷԁ‫͋Ͱܗ‬Γɼ ༷ʑͳ֯౓ʹ܏͍ͯ‫ؚ‬༗͞Ε͍ͯΔ͜ͱ͕෼͔Δɽ. 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๏ઢͷ෼෍Ϟσϧ ਤ 5. ‫؍‬ଌεέʔϧʹԠͨ͡ϝλϦοΫృ૷ͷ‫ํ͑ݟ‬ͷΠϝʔδ. ϝλϦοΫృ૷ͷ๏ઢߏ଄ʹ͍ͭͯɼද໘๏ઢͱද໘Լ ๏ઢΛߟྀͯ͠ਤ 6 ͷΑ͏ͳ๏ઢͷ෼෍ϞσϧΛఏҊ͢. 3.2 ද໘๏ઢͱද໘Լ๏ઢ. ΔɽҰൠʹඍখ໘๏ઢͷ෼෍͸Ψ΢ε෼෍ͱԾఆ͢Δ͜ͱ. Ұൠʹɼ෺ମ͸͋Δ఺ʹ͓͍ͯɼ།Ұͷ๏ઢΛ࣋ͪɼҰ. ͕Ͱ͖Δɽ͔͠͠ɼϝλϦοΫృ૷ͷද໘Լ๏ઢ͸ 1 ըૉ. ͭͷ൓ࣹϐʔΫΛ࣋ͭɽ͔͠͠ɼύʔϧϚΠΧృ૷΍Ճ০. ಺ʹෳ਺ͷ๏ઢΛ࣋ͭͨΊɼҰͭͷ෼෍͚ͩͰ͸ද͢͜ͱ. ϑΟϧϜͷΑ͏ͳ෺ମ͸ɼද໘ͷ๏ઢ͸Ұͭʹఆ·Δ͕ɼ. ͕Ͱ͖ͳ͍ɽͦͷͨΊɼද໘Լ๏ઢΛෳ਺ͷΨ΢ε෼෍ͷ. ද໘ԼͷۚଐϑϨʔΫͷӨ‫Ͱڹ‬൓ࣹϐʔΫ͕ෳ਺ଘࡏ͢. ઢ‫ܗ‬ॏͶ͋ΘͤͰද͞ΕΔࠞ߹Ψ΢ε෼෍Λ༻͍ͯද‫͢ݱ‬. Δɽ൓ࣹϐʔΫͷํ޲͸ɼ෺ମද໘ͷ๏ઢํ޲ʹґଘ͢Δ. Δɽ͢ͳΘͪɼ1 ըૉʹ K ‫ݸ‬ͷද໘Լ๏ઢΛ‫ؚ‬Ήͱ͖ʹɼ. ͨΊɼ͜ΕΒͷ෺ମͷ൓ࣹΛऔΓѻ͏ࡍʹ͸ද໘Լͷۚଐ. ਤ 7 ͷΑ͏ͳ K ‫ͦݸ‬ΕͧΕͷද໘Լ๏ઢΛΨ΢ε෼෍ͷ. ϑϨʔΫ͕Ͳͷํ޲Λ޲͍͍ͯΔͷ͔Λߟྀ͢Δඞཁ͕͋. ࿨Ͱද͢ɽͦΕͧΕͷΨ΢ε෼෍͸ฏ‫ ۉ‬μ ͱ෼ࢄ Σ Ͱද‫ݱ‬. Δɽͦ͜Ͱຊ࿦จͰ͸ɼਤ 4 ʹࣔ͢Α͏ʹɼද໘Լʹ͋Δ. ͞ΕΔɽ·ͨɼϑϨʔΫ͕େ͖͍΄Ͳ൓ࣹ‫౓ڧ‬͸‫ͳ͘ڧ‬Δ. ϑϨʔΫͳͲͷ๏ઢͷ͜ͱΛʮද໘Լ๏ઢʯͱఆٛ͢Δɽ. ͷͰ [8]ɼ൒‫ ܘ‬ri ͷϑϨʔΫͷ໘ੵΛߟྀ͢Δɽ·ͨɼ෺. ͜ͷද໘Լ๏ઢͷӨ‫Ͱڹ‬ɼΧϝϥͰࡱӨͨ͠ͱ͖ͷ 1 ըૉ. ମද໘ͷ൓ࣹ཰Λ ρ1 ͱ͠ɼද໘ԼͷۚଐϑϨʔΫͷ൓ࣹ. ಺Ͱ΋ෳ਺ͷ๏ઢΛ‫ؚ‬Ή͜ͱʹͳΔɽ·ͨɼຊ࿦จͰऔΓ. ཰Λ ρ2i ͱ͢Δɽ͢ΔͱɼϝλϦοΫృ૷ͷ๏ઢ෼෍ N ͸. ѻ͏Α͏ͳɼද໘Լ๏ઢͷӨ‫Ͱڹ‬ը૾಺ͷ̍ըૉʹෳ਺ͷ. ࣜ (1) ͷΑ͏ʹϞσϧԽͰ͖Δɽ. ๏ઢ͕ରԠ͢Δߏ଄Λʮଟॏ๏ઢߏ଄ʯͱ‫͢ͱͱ͜Ϳݺ‬Δɽ. N = ρ1 N (μ, Σ) + 3.3 ‫؍‬ଌεέʔϧʹΑΔ൓ࣹಛੑͷมԽ ϝλϦοΫృ૷ͷΑ͏ͳଟॏ๏ઢߏ଄͸ɼਤ 5 ͷΑ͏ʹɼ. K . ri2 ρ2i N (μi , Σi ). (1). i=1. ͔͠͠ɼ‫ޙ‬ड़͢Δຊख๏Ͱ͸ɼ‫؍‬ଌ஋͔Β๏ઢ෼෍Λਪఆ. ‫؍‬ଌεέʔϧʹԠͯ͡‫͕ํ͑ݟ‬େ͖͘ҟͳΔɽద੾ͳ‫཭ڑ‬. ͢ΔͨΊɼۚଐϑϨʔΫͷ൓ࣹ཰ͱαΠζΛผʑʹਪఆ͢. ͔Β‫؍‬ଌͨ͠ͱ͖͸ɼϝλϦοΫͷޫً‫͡ײ͕ײ‬ΒΕΔɽ. Δͷ͸ࠔ೉Ͱ͋ΔɽͦͷͨΊɼۚଐϑϨʔΫͷ൓ࣹ཰ͱα. ͔͠͠ɼ‫؍‬ଌ‫཭ڑ‬Λۙͨ͘͠Γɼഒ཰Λߴͯ͘͠‫؍‬ଌͨ͠. ΠζΛҰͭͷ܎਺ͱͯ͠ѻ͏ɽ·ͨɼ෺ମͷද໘๏ઢͱಉ. ͱ͖ʹ͸ɼද໘Լʹ‫·ؚ‬ΕΔ‫ݸ‬ผͷϑϨʔΫʹண໨͍ͯ͠. ͡ํ޲Λ޲͍͍ͯΔද໘Լ๏ઢΛ൑ผ͢Δ͜ͱ͸೉͍͠ɽ. Δ͜ͱʹͳΓɼޫً‫ײ‬͸͋·Γ‫͡ײ‬ΒΕͳ͘ͳΔɽ‫ʹٯ‬ɼ. ͔͠͠ɼҰൠతʹϝλϦοΫృ૷ͷۚଐϑϨʔΫ͸෺ମද. ‫؍‬ଌ‫཭ڑ‬Λԕͨ͘͠Γɼഒ཰Λ௿ͯ͘͠‫؍‬ଌͨ͠ͱ͖ʹ΋ɼ. ໘ͱ΄΅ಉ͡ํ޲ʹ໘͕޲͘Α͏ʹઃ‫͞ܭ‬Ε͍ͯΔͨΊɼ. ແ਺ͷϑϨʔΫ͕ରԠͯ͠Ұͭͷૈ͍‫ڸ‬໘൓ࣹͷΑ͏ʹͳ. ෺ମද໘ํ޲ͱಉ͡ํ޲Λ޲͍͍ͯΔද໘Լ๏ઢ͸ଘࡏ͢. ΔͨΊɼޫً‫ײ‬͸͋·Γ‫͡ײ‬ΒΕͳ͘ͳΔɽ͜ͷΑ͏ʹɼ. ΔͱԾఆͰ͖ΔɽͦͷͨΊɼද໘๏ઢͱಉ͡ํ޲Λ޲͍ͯ. ϝλϦοΫృ૷ΛධՁ͢Δࡍʹ͸ɼϝλϦοΫͷޫً‫͕ײ‬. ͍Δද໘Լ๏ઢ͸Ұͭͷ๏ઢͱͯ͠ѻ͏ɽΑͬͯɼຊ࿦จ. ‫͡ײ‬ΒΕΔద੾ͳ‫؍‬ଌεέʔϧΛઃఆ͢Δඞཁ͕͋Δɽ. ͰऔΓѻ͏ද໘Լ๏ઢ෼෍ͷϞσϧΛࣜ (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. ࠞ߹Ψ΢ε෼෍Ͱѻ͏࠲ඪ‫ܥ‬. Rotary tables. ϧΰϦζϜΛ༻͍ͯɼද໘Լ๏ઢͷ໬౓ʹࠞ߹Ψ΢ε෼෍. ਤ 8. Λ౰ͯ͸ΊΔɽ. N=. K . ‫ܭ‬ଌ૷ஔ. ࠞ߹Ψ΢ε෼෍Λ౰ͯ͸ΊΔࡍʹ͸ɼߏ੒͢ΔΨ΢ε෼. Ci N (μi , Σi ). (2). ෍ͷ਺Λઃఆ͢Δඞཁ͕͋Δɽͦͷߏ੒਺͕ଟ͚Ε͹શͯ ͷσʔλΛΧόʔ͢Δ͜ͱ͸؆୯ʹͳΔ͕ɼաద߹ʹͳͬ. i=1. 4. ද໘Լ๏ઢͷ෼෍ղੳ. ͯ͠·͍ɼ৑௕ͳද‫͏·ͯͬ͠ͳʹݱ‬ɽͦͷͨΊɼϞσϧ. 4.1 ๏ઢํ޲ͷਪఆ. Ϋ൓ࣹͷ৔߹ɼҰͭͷϑϨʔΫʹΑΔ൓ࣹ͸ɼҰͭͷ൓ࣹ. ʹର͢Δద੾ͳߏ੒਺Λܾఆ͢Δඞཁ͕͋ΔɽϝλϦο. ද໘Լ๏ઢ෼෍Λਪఆ͢ΔͨΊʹɼද໘Լ๏ઢͷ໬౓Λ. ϐʔΫΛ࣋ͭɽ͜ͷ‫؍‬ଌʹ‫͖ͮج‬ɼ‫؍‬ଌ͞Εͨ൓ࣹσʔλ. ‫ٻ‬ΊΔඞཁ͕͋Δɽ؆୯ԽͷͨΊʹ‫ڸ‬໘൓ࣹͷΦϑεϖ. ͷதͷ൓ࣹϐʔΫͷ਺Λɼද໘Լ๏ઢͷ෼෍ͷߏ੒਺Ͱ͋. ΩϡϥʔΛແࢹ͢Δͱɼ‫ڸ‬໘൓ࣹΛੜ͡Δ෺ମͷ๏ઢํ޲. ΔͱԾఆ͢Δɽ. ͸ޫ‫ͱ޲ํݯ‬൓ࣹํ޲ͷೋ౳෼ํ޲ͱҰக͢Δɽ͢ͳΘ ͪɼ๏ઢํ޲͸ɼࢹઢϕΫτϧ v ͱޫ‫ݯ‬ϕΫτϧ l ͷ 2 ౳ ෼ํ޲Λࣔ͢ϋʔϑϕΫτϧ h ͱͳΔɽϋʔϑϕΫτϧ h ͸࣍ࣜͰ‫ٻ‬ΊΔ͜ͱ͕Ͱ͖Δɽ. 4.3 ද໘Լ๏ઢͷ౷‫ྔܭ‬ͷࢉग़ ͜͜Ͱ͸ɼਪఆͨ͠ද໘Լ๏ઢ෼෍ͱ࣮ࡍͷϑϨʔΫͷ ঢ়ଶͱͷؔ܎ੑʹ͍ͭͯड़΂ΔɽఏҊϞσϧͰ͸ɼҰͭͷ. v+l h= |v + l|. (3). ͭ·Γɼ෺ମʹର༷ͯ͠ʑͳํ޲͔ΒޫΛরࣹ͠ɼ‫؍‬ଌ͞. ද໘Լ๏ઢ෼෍ΛҰͭͷΨ΢ε෼෍ʹ౰ͯ͸Ί͍ͯΔɽͦ ͷͨΊɼࠞ߹Ψ΢ε෼෍ͷߏ੒਺͸‫؍‬ଌըૉ಺ͷϑϨʔΫ ͷ‫ʹ਺ݸ‬ରԠ͍ͯ͠Δɽ. Εͨ൓ࣹޫͷ‫͚ڧ͕౓ڧ‬Ε͹‫Ͳ΄͍ڧ‬ɼͦͷϋʔϑϕΫτ. ·ͨɼ֤๏ઢ෼෍ͷ෼ࢄͷ஋͸ɼۚଐϑϨʔΫͷද໘ૈ. ϧํ޲ʹ๏ઢ͕͋ΔՄೳੑ͕ߴ͍ͱ͍͑ΔɽͦͷͨΊɼ‫؍‬. ͞Λද͢ɽۚଐϑϨʔΫͷද໘͕ૈ͚Ε͹ɼରԠ͢Δ֤๏. ଌͨ͠൓ࣹͷ‫౓ڧ‬Λɼޫ‫ݯ‬ϕΫτϧͱࢹઢϕΫτϧΛ༻͍. ઢ෼෍ͷ෼ࢄ͸େ͖͘ͳΓɼද໘͕‫׈‬Β͔Ͱ͋Ε͹๏ઢ෼. ͯϋʔϑϕΫτϧํ޲ʹ౰ͯ͸ΊΕ͹ɼද໘Լ๏ઢͷ໬౓. ෍ͷ෼ࢄ͸খ͘͞ͳΔɽ͞Βʹɼ֤෼෍͕౳ํͰ͋Δ͔Λ. Λࢉग़͢Δ͜ͱ͕Ͱ͖Δɽ. ௐ΂Δ͜ͱͰɼҟํੑΛఆྔԽͰ͖Δɽ͜ͷࡍɼ֤ਖ਼‫ن‬෼. ͦͷͨΊͷ‫ܭ‬ଌํ๏ͱͯ͠ɼΧϝϥͱ‫؍‬ଌ෺ମ͸‫ݻ‬ఆ͠ɼ. ෍ͷҟํੑ͸ɼਖ਼‫ن‬෼෍ͷ௕࣠ͱ୹࣠ͷൺ཰Ͱද‫͢ݱ‬Δ͜. ޫ‫ݯ‬ͷΈΛճసͤ͞Δɽ͢ͳΘͪɼਤ 8 ʹࣔ͢Α͏ͳηο. ͱ͕ग़དྷΔɽ௕࣠ͱ୹࣠ͷൺ཰͸ɼਖ਼‫ن‬෼෍ͷ‫ڞ‬෼ࢄߦྻ. ςΟϯάͰޫ‫( ޲ํݯ‬θ, φ) ͝ͱʹ൓ࣹޫΛ‫ܭ‬ଌ͢Δɽ͜ͷ. ͷ 2 ͭͷ‫ݻ‬༗஋ͷൺ཰Λ‫ٻ‬ΊΕ͹Α͍ɽ. ࡍɼ֦ࢄ൓ࣹޫ͸‫ڸ‬໘൓ࣹޫʹൺ΂ͯे෼ʹখ͍ͨ͞Ίɼ. ϑϨʔΫͷํ޲ͳͲɼํ޲ʹؔ͢Δσʔλ͸୯७ʹ֯౓ ͷࢉज़ฏ‫ۉ‬Λ‫ٻ‬Ίͯ΋ਖ਼͍͠ฏ‫ۉ‬తͳํ޲͸‫ٻ‬ΊΔ͜ͱ͸. ແࢹͰ͖ΔͱԾఆ͢Δɽ. Ͱ͖ͳ͍ [10]ɽͦͷͨΊɼํ޲౷‫ֶܭ‬ͷ֓೦ʹ͕ͨͬͯ͠. 4.2 EM ΞϧΰϦζϜΛ༻͍ͨද໘Լ๏ઢͷ෼෍ਪఆ ਪఆͨ͠ද໘Լ๏ઢͷ໬౓Λࠞ߹Ψ΢ε෼෍ʹ౰ͯ͸Ί. ํ޲ͷฏ‫ͱۉ‬෼ࢄΛ‫ٻ‬ΊΔඞཁ͕͋Δɽํ޲ͷฏ‫ۉ‬Λ‫ٻ‬Ί ΔͨΊʹ͸ɼ֯౓ΛͦΕͧΕͷ֯౓ํ޲ͷ୯ҐϕΫτϧʹ. Δ͜ͱͰද໘Լ๏ઢ෼෍Λਪఆ͢Δɽͨͩ͠ɼϋʔϑϕΫ. ม‫ͯ͠׵‬ɼ୯ҐϕΫτϧͷฏ‫޲ํۉ‬Λ‫ٻ‬ΊΕ͹Α͍ɽ·ͣɼ. τϧͷํ޲Λ‫ํͱ֯ڼ‬Ґ֯ (θh , φh ) ͱ͢Δͱɼφh = 0◦ ͱ. N ‫ݸ‬ͷ֯౓ํ޲ͷฏ‫޲ํۉ‬Λ‫ٻ‬ΊΔͳΒ͹ɼ֯౓ํ޲ʹର. φh = 360 ͕ಉ֯͡౓ʹͳΓɼ·ͨɼθh = 0 Ͱ͸ θh Λม. ͯ͠ͷ୯ҐϕΫτϧ n Λ༻͍ͯɼฏ‫߹ۉ‬੒ϕΫτϧ͸࣍ࣜ. Խͤͯ͞΋ಉ֯͡౓ʹͳΔͳͲɼѻ͍͕൥ࡶʹͳΔɽͦ͜. Ͱද͞ΕΔɽ. ◦. ◦. N 1  n ¯= ni N. Ͱɼਤ 9 ʹࣔ͢Α͏ʹɼ‫ٿ‬Λఱ௖ํ޲͔Β‫͖ͱͨݟ‬ͷ 2 ࣍ ‫ݩ‬ฏ໘Ͱߟ͑ͨͱ͖ͷ࠲ඪ‫ʹܥ‬ม‫ͯ͠׵‬ѻ͏ɽ ࠷໬ਪఆͷख๏ͱͯ͠ɼෆ‫׬‬શσʔλ͔Β࠷໬ਪఆ஋Λ. (4). i=1. ͜ͷϕΫτϧͷํ޲͕ N ‫ݸ‬ͷ֯౓ํ޲ͷฏ‫͋Ͱ޲ํۉ‬Δɽ. ‫ٻ‬ΊΔख๏Ͱ͋Δ EM ΞϧΰϦζϜ (‫ظ‬଴஋࠷େԽ๏)[9]. ·ͨɼํ޲ͷ෼ࢄ͸ circular variance[11] Λ༻͍Δ͜ͱͱ. ͕ར༻͞ΕΔ͜ͱ͕ଟ͍ɽͦͷͨΊɼຊ‫Ͱڀݚ‬΋ɼEM 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. ϝλϦοΫృ૷ͷ‫ܭ‬ଌ෺ମɽ্ஈࠨ͔Βॱʹ 5ɼ20ɼ40ɼ55ɼ. 90μm ͷΞϧϛϑϨʔΫ͕‫ؚ‬༗ྔ 1%ɼԼஈࠨ͔Βॱʹ 30ɼ 40ɼ60ɼ90μm ͷΞϧϛϑϨʔΫ͕‫ؚ‬༗ྔ 2%ͰຒΊࠐ·Ε ͍ͯΔɽ. Var(n) = 1 − |¯ n|. (5) ϳ ŽŶƚĞŶƚ;йͿͲ&ůĂŬĞƐŝnjĞ;ƵŵͿ. ͜ͷ஋͕ 1 ʹ͚ۙΕ͹෼ࢄ͕େ͖͘ɼ0 ʹ͚ۙΕ͹෼ࢄ͕ λΛద੾ʹѻ͏͜ͱ͕Ͱ͖Δɽ ͜ΕΒͷ෺ཧతಛ௃ྔʹؔͯ͠ɼͦΕͧΕͷ౷‫ܭ‬తͳฏ ‫ۉ‬஋ͱ෼ࢄ͕෼͔Ε͹ɼ࣭‫ײ‬ΛఆྔԽ͢Δ͜ͱ͕Ͱ͖Δɽ ·ͨɼଟॏ๏ઢߏ଄ʹಛ༗ͳΩϥΩϥͨ͠൓ࣹʹ͸ɼද໘ Լ๏ઢͷ‫ͦͱ਺ݸ‬ͷ๏ઢํ޲ͷ෼ࢄ͕େ͖͘‫ى‬Ҽ͢Δͱ ༧૝Ͱ͖ΔɽͦͷͨΊɼ͜ΕΒೋͭͷύϥϝʔλʹண໨͢. EƵŵďĞƌŽĨŶŽƌŵĂůƐ. খ͍͞ͱ͍͑Δɽ͜ΕʹΑΓɼํ޲ʹؔ͢Δ౷‫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. WŝdžĞůƐŝnjĞ΀Ƶŵ΁. Δ͜ͱͰɼ෺ମ͕ͲΕ͚ͩΩϥΩϥ͍ͯ͠Δͷ͔ఆྔԽͰ ਤ 12. ըૉαΠζ͝ͱͷ๏ઢ਺ɽʮ‫ؚ‬༗ྔʢ%ʣ-ϑϨʔΫͷେ͖͞ ʢμmʣ ʯͷϓϨʔτΛ༻͍͍ͯΔɽ. 5. ࣮‫ݧ‬ 5.1 ࣮‫ڥ؀ݧ‬. 5.2 ద੾ͳࡱӨεέʔϧͷ֬ೝ. ϝλϦοΫృ૷ͷΑ͏ʹ༷ʑͳํ޲ʹ๏ઢ͕ଘࡏ͢Δ෺. ଟॏ๏ઢߏ଄Λ࣋ͭ෺ମ͸ɼࡱӨεέʔϧʹԠͯ͡ɼ1. ମͷ๏ઢ෼෍Λਪఆ͢ΔͨΊʹ͸ɼର৅෺ମʹରͯ͠൒‫ٿ‬. ըૉ಺Ͱͷ൓ࣹͷৼΔ෣͍͕େ͖͘ҟͳΔɽͦͷͨΊɼద. ঢ়ʹޫΛরࣹ͢Δඞཁ͕͋ΔɽͦͷͨΊɼ࣮‫૷ݧ‬ஔͱͯ͠. ੾ͳࡱӨεέʔϧͰղੳ͢Δࣄ͸ॏཁͱͳΔɽ. ਤ 10 Ͱࣔ͢Α͏ͳɼ൒‫ٿ‬ঢ়ʹޫ‫( ݯ‬೔ਐిࢠ޻‫ࣜגۀ‬ձ. ద੾ͳࡱӨεέʔϧΛௐ΂ΔͨΊɼ1 ըૉͷεέʔϧΛ. ࣾ W3VP-8) Λಈ͔ͯ͠ࡱӨͰ͖ΔγεςϜΛ࡞੡ͨ͠ɽ. ༷ʑʹมԽͤͯ͞‫ܭ‬ଌͨ͠ࡍͷ൓ࣹϐʔΫͷ਺Λ‫ٻ‬ΊΔɽ. ϑϨʔΫʹΑΔΩϥΩϥͨ͠൓ࣹΛऔಘ͍ͨͨ͠Ίɼޫ‫ݯ‬. ͨͩ͠ɼࡱӨεέʔϧͷมߋ͸࣮ࡍʹΧϝϥͷࡱӨഒ཰Λ. ʹ͸఺ޫ‫ ͍ۙʹݯ‬LED Λ࠾༻ͨ͠ɽͳ͓ɼ෺ମͱޫ‫·ݯ‬. มԽͤ͞ΔͷͰ͸ͳ͘ɼͰ͖Δ͚ͩߴഒ཰ͰࡱӨͨ͠ը. Ͱͷ‫཭ڑ‬͸ 50cm ཭ͨ͠ɽଟॏ๏ઢߏ଄Λ࣋ͭ෺ମͷৄࡉ. ૾ʹμ΢ϯαϯϓϦϯάॲཧΛద༻͢Δ͜ͱͰ̍ըૉͷ. ͳ൓ࣹͷมԽΛ‫؍‬ଌ͢ΔͨΊɼΧϝϥ͸ϞϊΫϩΧϝϥ. εέʔϧΛԾ૝తʹมԽͤ͞Δɽຊ࣮‫Ͱݧ‬͸য఺‫͕཭ڑ‬. (PointGrey GS3-U3-28S4M-C) Λ࢖༻͢ΔɽΧϝϥͷҐஔ. 75mm ͷϨϯζʹΤΫεςϯγϣϯɾνϡʔϒΛऔΓ෇͚. ͸෺ମͷ๏ઢํ޲Ͱ͸ɼද໘ͷ‫ڸ‬໘൓ࣹͷӨ‫ڹ‬Λେ͖͘ड. Δ͜ͱͰɼ‫ۃ‬Ίͯߴഒ཰ͰͷࡱӨΛߦͬͨɽͦͷ݁Ռɼ1. ͚ͯ͠·͍ඍࡉߏ଄ͷ๏ઢͷ൓ࣹ͕‫ܭ‬ଌ͠ʹ͍͘ͷͰɼ‫ڼ‬. ըૉͷαΠζ͕໿ 7μm ͰࡱӨ͢Δ͜ͱ͕Ͱ͖ͨɽର৅෺. ֯Λ 45◦ ͣΒͨ͠ (45, 0) ͷҐஔ͔ΒࡱӨ͢Δɽ͜ͷͱ͖ɼ. ମͱͯ͠ɼਤ 11 ʹࣔ͢ɼΞϧϛϑϨʔΫ͕ຒΊࠐ·Εͨ. ଟॏ๏ઢߏ଄Ͱ͸ྡΓ߹ͬͨըૉͰ΋๏ઢํ޲͕ҟͳΔ͜. ΞΫϦϧथࢷϓϨʔτ (JIDA ελϯμʔυαϯϓϧζɾ2). ͱʹΑͬͯ൓ࣹ͕ҟͳΔͷͰɼ10×10 ͷྡ઀ 100 ըૉ෼ͷ. Λ༻͍ͨɽ. ൓ࣹޫΛ‫ܭ‬ଌ͢ΔɽΧϝϥͷઃఆ͸ ISO ‫౓ײ‬͸ 100ɼF ஋. ͦͷ݁ՌɼըૉαΠζ͝ͱͷ๏ઢ਺͕ਤ 12 ͷΑ͏ʹͳͬ. ͸ 11ɼγϟολʔ଎౓͸‫؍‬ଌ݁Ռʹ߹Θͤͯద੾ʹઃఆ͢. ͨɽ͜ͷ݁Ռ͔Βɼ‫؍‬ଌεέʔϧʹԠͨ͡ 1 ըૉͷ൓ࣹͷ. ΔɽΧϝϥͷ༗ޮϏοτ਺͸ 14bit Ͱ͋ΔɽຊγεςϜʹ. ৼΔ෣͍ͷมԽΛ֬ೝͰ͖ΔɽըૉαΠζ͕খ͍͞ͱ͖ʹ. ◦. ΑΓɼ֯౓ θ ͱ φ ΛͦΕͧΕ 3 ͣͭճసͤͯ͞൓ࣹޫΛ. ๏ઢ਺͕ҰͭʹͳΒͳ͍ͷ͸ɼද໘๏ઢͱද໘Լ๏ઢ͕ࠞ. ‫ܭ‬ଌ͢Δɽ. ࡏ͍ͯ͠ΔͨΊͰ͋Δͱ༧૝Ͱ͖ɼ࣮ࡍͷද໘Լ๏ઢ͸ද. 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๏ઢͷ਺ҰͭΛҾ͍ͨ਺ʹͳΔͱ༧૝Ͱ͖ΔɽҎ‫ޙ‬ɼղ. Ϭ͘Ϭϯ. ੳͷࡍʹ͸ɼ࠷΋ϝλϦοΫͷޫً‫͡ײ͕ײ‬ΒΕΔ 1 ըૉ ͋ͨΓͷද໘Լ๏ઢ਺͕ଟ͍ըૉαΠζͰͦΕͧΕղੳΛ. ϮйͲϵϬƵŵ. Ϭ͘ϬϮϱ. ʹͳΔɽ ࣭‫ײ‬͸ਓؒͷ‫ͨݟ‬໨Ͱ൑அ͞ΕΔͨΊɼධՁ‫ج‬४ͱͯ͠ ඪ४తͳਓؒͷࢹྗΛߟྀ͢Δඞཁ͕͋Δɽࢹྗ‫ࠪݕ‬Λ‫ج‬ ४ʹͨ͠ͱ͖ɼࢹྗ 1.0 ͷਓؒ͸ 5m ͷ‫͔཭ڑ‬Βϥϯυϧτ ‫؀‬ͷ 1.45mm ͷ੾Ε໨Λೝࣝ͢Δ͜ͱ͕Ͱ͖Δɽͭ·Γɼ. 5m ͷ‫͚͓ʹ཭ڑ‬Δਓؒͷ໨ͷղ૾౓͸ 17.52ppi ͱ͍͏͜. ŝƌĐƵůĂƌǀĂƌŝĂŶĐĞ. ߦ͏ɽͦΕΒΛฏ‫͢ۉ‬Δͱɼ1 ըૉ͕໿ 170μm ͷεέʔϧ Ϭ͘ϬϮ Ϭ͘Ϭϭϱ. ϮйͲϰϬƵŵ ϮйͲϯϬƵŵ. Ϭ͘Ϭϭ. ϭйͲϮϬƵŵ Ϭ͘ϬϬϱ ϭйͲϱƵŵ. ͱʹͳΔɽ͜ͷߟ͑ʹ‫ͱͮ͘ج‬ɼ1 ըૉͷαΠζ͕ 170μm ͱ͍͏εέʔϧ͸ɼਓ͕ؒ໿ 58cm ͔Β෺ମΛ‫͖ͱͨݟ‬ͷ. ϭйͲϱϱƵŵ ϭйͲϵϬƵŵ ϭйͲϰϬƵŵ. Ϭ Ϭ. ‫؍‬ଌεέʔϧʹରԠ͢ΔͷͰɼ࣭‫ײ‬ධՁʹ΋ଥ౰ͳεέʔ ϧͰ͋Δͱ͍͑Δɽ. 5.3 ελϯμʔυαϯϓϧΛ༻͍ͨධՁ. ϮйͲϲϬƵŵ. ਤ 15. ϭ Ϯ ϯ ϰ ϱ EƵŵďĞƌŽĨƐƵďƐƵƌĨĂĐĞŶŽƌŵĂůƐŝŶϭƉdž. ϲ. 1 ըૉ಺ͷද໘Լ๏ઢ਺ͱ๏ઢํ޲ͷ෼ࢄͷؔ܎. ࣮‫ʹݧ‬͸ɼਤ 11 ʹࣔ͢ΞϧϛϑϨʔΫ͕ຒΊࠐ·Εͨ ΞΫϦϧथࢷϓϨʔτ༻͍ͯ൓ࣹͷ‫ܭ‬ଌΛߦͬͨɽೖࣹ֯. ࣍ʹɼۚଐϑϨʔΫͷද໘ૈ͞Λද͢ɼ‫ڞ‬෼ࢄߦྻͷ‫ݻ‬. ౓ͷํ޲ʹਖ਼‫ن‬Խͨ͠‫؍‬ଌً౓஋Λϓϩοτͨ͠൒‫ٿ‬ͷਤ. ༗஋ λ1 , λ2 (λ1 > λ2 ) ͷฏ‫ۉ‬஋ͱɼͦͷൺ཰ͷฏ‫͍ͯͭʹۉ‬. Λɼ୅දతͳ݁Ռͱͯ͠ 1%-40μmɼ1%-90μmɼ2%-90μm. ௐ΂ͨɽϑϨʔΫͷද໘ૈ͞ͷҟํੑʹؔͯ͠͸ɼϑϨʔ. ͷ݁ՌͷΈൈਮͯ͠ਤ 13 ʹࣔ͢ɽ͜ͷ݁Ռ͔Βɼଟॏ๏. ΫαΠζͱ‫ؚ‬༗ྔ͕ଟ͘ͳΔʹͭΕͯ౳ํʹۙͮ͘ɽ͜Ε. ઢ෺ମ͸ෳ਺ͷ൓ࣹͷϐʔΫΛ࣋ͭ͜ͱ͕֬ೝͰ͖Δɽͳ. ͸ɼϑϨʔΫ͕ີʹͳΔ΄Ͳ๏ઢ෼෍΋ີʹͳΔͨΊɼෳ. ͓ɼ͜ͷ‫؍‬ଌ݁Ռ͸ྡ઀ըૉͰ͸େ͖͘ҟͳΔɽ. ਺ͷ౳ํͳਖ਼‫ن‬෼෍Ͱ౰ͯ͸ΊΔͷ͕ྑ͍݁Ռʹͳ͍ͬͯ. ·ͨɼ͜ͷ‫؍‬ଌ஋Λ༻͍ͯද໘Լ๏ઢͷ෼෍Λਪఆͨ͠ ݁ՌΛਤ 14 ʹࣔ͢ɽશମతʹఱ௖ํ޲ʹ๏ઢ͕޲͍͍ͯ. Δͱ༧૝Ͱ͖Δɽ ࣍ʹɼ1 ըૉ಺ͷද໘Լ๏ઢ਺ͱ๏ઢํ޲ͷ෼ࢄ͔ΒɼͲ. Δ͕ɼͦͷํ޲ੑʹ͸όϥ͖͕ͭ‫ݟ‬ΒΕΔɽ·ͨɼ݁Ռ͸. ͷ͘Β͍ΩϥΩϥ͍ͯ͠Δͷ͔ͷؔ܎Λਤ 15 ʹࣔ͢ɽ࣮. ྡ઀ըૉͰ΋ද໘Լ๏ઢ෼෍͸େ͖͘ҟͳΔɽ. ෺ମͷ‫ͨݟ‬໨ͱ݁Ռͷൺֱ͔Βɼάϥϑதͷӈ্ʹϓϩο. ਪఆͨ͠ද໘Լ๏ઢ෼෍ͷ݁Ռ 100 ըૉ෼ͷσʔλΛ‫ݩ‬. τ͞ΕΔ΄ͲɼΩϥΩϥ‫ײ‬Λ‫͡ײ͘ڧ‬Δ͜ͱ͕֬ೝͰ͖Δɽ. ʹɼର৅෺ମͷ෺ཧతͳ౷‫ྔܭ‬Λ‫ٻ‬Ίͨ݁ՌΛද 1 ʹࣔ. ͜ͷ݁Ռ͔ΒɼϝλϦοΫృ૷ͳͲͷଟॏ๏ઢ෺ମͷΩϥ. ͢ɽ·ͣɼ1 ըૉ಺ͷ๏ઢ਺ͷฏ‫ۉ‬ɾඪ४ภࠩʹ͍ͭͯௐ. Ωϥͱً͘ಠಛͳ൓ࣹͷఆྔԽ͕࣮‫͕ͱ͖ͨ͜Ͱݱ‬Θ͔Δɽ. ΂ͨɽ1%-40μm ͱ 1%-90μm Λൺֱ͢Δͱɼಉ͡େ͖͞ͷ ըૉ಺ʹ‫·ؚ‬ΕΔ๏ઢ਺͸ɼϑϨʔΫαΠζ͕େ͖͍ํ͕. 6. ϔΞϥΠϯՃ޻΁ͷద༻. গͳ͍݁Ռͱͳͬͨɽ͔͠͠ɼਤ 12 ͷ݁ՌͷΑ͏ʹɼϑ. 6.1 ϔΞϥΠϯՃ޻ͷੑ࣭. ϨʔΫͷେ͖͞ͱ୯Ґ໘ੵ಺ʹ‫·ؚ‬ΕΔϑϨʔΫͷ๏ઢͷ. ύʔϧϚΠΧృ૷΍Ճ০ϑΟϧϜ͚ͩͰ͸ͳ͘ɼಠಛͳ. ‫ʹ਺ݸ‬͸ɼ໌നͳ૬ؔ͸֬ೝͰ͖ͳ͍ɽ·ͨɼ1%-40μm ͱ. ๏ઢ෼෍Λ࣋ͭ෺ମͱͯ͠ɼϔΞϥΠϯՃ޻͞Εͨۚଐ΋ɼ. 2%-40μm ΍ 1%-90μm ͱ 2%-90μm Λൺֱ͢Δͱɼ‫ؚ‬༗ྔ. զʑͷ਎ͷճΓʹଟ͘‫ݟ‬ΒΕΔɽۚଐ൘ͷද໘࢓্͛ํ๏. ͷগͳ͍ϓϨʔτͷํ͕๏ઢ਺͕খ͘͞ͳ͕ͬͨɼͦͷඪ. ͷ͏ͪɼۚଐද໘ʹ൅ͷໟͷΑ͏ʹࡉ͔͍ϥΠϯ͕௚ઢత. ४ภࠩ͸େ͖͍݁ՌͱͳΓɼ‫؍‬ଌ఺͝ͱͷ͕ࠩେ͖͍݁Ռ. ʹ‫ݚ‬ຏ͞Εͨ࢓্͛ͷ͜ͱΛϔΞϥΠϯՃ޻ͱ‫Ϳݺ‬ɽϔΞ. ͱͳͬͨɽ. ϥΠϯՃ޻͸ɼ෺ମΛ‫؍‬ଌ໘ͷ๏ઢΛ࣠ʹճసͤͨ͞ͱ͖. ࣍ʹɼද໘Լ๏ઢ͕Ͳͷํ޲Λ޲͍͍ͯΔͷ͔ʹ͍ͭͯ. ʹ໌Δ͕͞มԽ͢Δҟํੑ൓ࣹ͕‫؍‬ଌ͞ΕΔ෺ମͰ͋Δɽ. ͷฏ‫ͱ޲ํۉ‬ɼํ޲ͷ෼ࢄʹ͍ͭͯௐ΂ͨɽฏ‫ͭʹ޲ํۉ‬. ϔΞϥΠϯՃ޻͞ΕͨۚଐͰ͸ɼϒϥγํ޲ʹԠͯ͡൓ࣹ. ͍ͯ͸ɼ‫֯ڼ‬ɾํҐ֯Λ༻͍ͯ (θ, φ) [deg] Ͱද͢ɽͦͷ݁. ͕ઢରশʹͳΔɽ. ՌɼͲͷϓϨʔτ΋ද໘Լ๏ઢ͸ฏ‫ͯ͠ۉ‬ఱ௖ํ޲Λ޲͍. ϔΞϥΠϯՃ޻΋ϝλϦοΫృ૷ͱಉ༷ʹɼ‫؍‬ଌεέʔ. ͍ͯΔ͜ͱ͕֬ೝͰ͖Δɽ·ͨɼϑϨʔΫͷ‫ؚ‬༗ྔ͕ଟ͍. ϧʹԠͯ͡‫͕ํ͑ݟ‬େ͖͘ҟͳΔɽखͰ࣋ͬͯ‫ݟ‬ΔΑ͏ͳ. ΄Ͳ๏ઢํ޲ͷ෼ࢄ͕େ͖͍݁ՌͱͳͬͨɽϑϨʔΫαΠ. ௨ৗͷ‫؍‬ଌεέʔϧͰ͸ɼଟ਺ͷϔΞϥΠϯͷই͕‫͑ݟ‬ɼ. ζʹؔͯ͠͸໌֬ͳ૬ؔ͸֬ೝͰ͖ͳ͍͕ɼ1%ͷ‫ؚ‬༗ྔͷ. ‫ڸ‬໘࢓্͛ͱҟͳΓۚଐͷ࣭‫ײ‬Λ‫͡ײ͘ڧ‬ΒΕΔɽ‫؍‬ଌ‫ڑ‬. ΋ͷ͚ͩʹண໨͢ΔͱɼαΠζ͕େ͖͘ͳΔ΄Ͳ๏ઢ෼ࢄ. ཭Λۙͨ͘͠Γɼഒ཰Λߴͯ͘͠‫؍‬ଌͨ͠ͱ͖ʹ͸ɼ1 ͭ. ͕େ͖͘ͳΔ܏޲͕֬ೝͰ͖Δɽ. 1 ͭͷইʹண໨͍ͯ͠Δ͜ͱʹͳΓɼইͷஅ໘ํ޲ʹ๏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. ‫؍‬ଌً౓஋ɽ൒‫ٿ‬Λఱ௖ํ޲͔Β‫ͨݟ‬ਤͰ͋Γɼೖࣹํ޲࠲ඪʹ‫؍‬ଌ஋Λ౰ͯ͸Ίͯ ͍Δɽ. (a) 1%-40μm ਤ 14. (b) 1%-90μm. (c) 2%-90μm. ද໘Լ๏ઢ෼෍ɽਤ 9 ʹࣔ͢࠲ඪ‫Ͱܥ‬ද‫͓ͯ͠ݱ‬Γɼ൒‫ٿ‬Λఱ௖ํ޲͔Β‫ͨݟ‬ਤͰ͋Δɽ. ෼෍͕ଘࡏ͢Δɽ‫ʹٯ‬ɼ‫؍‬ଌ‫཭ڑ‬Λԕͨ͘͠Γɼഒ཰Λ௿ ͯ͘͠‫؍‬ଌͨ͠ͱ͖͸ɼແ਺ͷই͕ରԠͯ͠ɼই͕‫ͳ͑ݟ‬ ͍ҟํੑ൓ࣹ͕‫؍‬ଌ͞ΕΔɽ. 6.3 ϔΞϥΠϯՃ޻ͷ๏ઢ෼෍ͷ౷‫ྔܭ‬ͷࢉग़ ͜͜Ͱ͸ɼਪఆͨ͠๏ઢ෼෍ͱϔΞϥΠϯՃ޻ͷද໘ঢ় ଶͱͷؔ܎ੑʹ͍ͭͯड़΂ΔɽϔΞϥΠϯͷই͕‫͍ڧ‬৔ ߹ɼইͷࣼ໘ͷํ޲ʹରͯ͠ෳ਺ͷߏ੒਺ͷ෼෍͕ੜ͡Δɽ. 6.2 ϔΞϥΠϯՃ޻ͷ๏ઢ෼෍ਪఆ. ͦͷͨΊɼ෼෍ͷߏ੒਺͸ϔΞϥΠϯͷইͷ‫ͱ͞ڧ‬ରԠ͢. ϝλϦοΫృ૷Ͱ͸ɼۚଐϑϨʔΫ͕༷ʑͳํ޲Λ޲͍. Δɽ·ͨɼ๏ઢ෼෍ͷ෼ࢄ͕ϔΞϥΠϯՃ޻ͷද໘ૈ͞ʹ. ͍ͯΔӨ‫Ͱڹ‬ϑϨʔΫͷ๏ઢͷ਺͕ϑϨʔΫʹΑΔ൓ࣹ. ରԠ͢ΔɽಛʹɼϔΞϥΠϯՃ޻͸൓ࣹʹҟํੑΛੜ͡Δ. ϐʔΫͷ਺ͱରԠ͍ͯ͠ΔͷͰɼ൓ࣹϐʔΫͷ਺Ͱ๏ઢ෼. ͨΊɼ๏ઢ෼෍ͷҟํੑΛ‫ٻ‬ΊΔ͜ͱͰɼ൓ࣹͷҟํੑΛ. ෍ͷ਺Λܾఆͨ͠ɽ͔͠͠ɼϔΞϥΠϯՃ޻Ͱ͸ইͷେ͖. ‫ٻ‬ΊΔ͜ͱ͕ग़དྷΔɽ. ͕͞ҰఆͰ͸ͳ͘ɼେ͖ͳই͔Βখ͞ͳই·Ͱ‫·ؚ‬Ε͍ͯ ΔͨΊɼ๏ઢ෼෍ͷ਺ΛϝλϦοΫృ૷ͱಉ༷ʹܾఆ͢. ͜ΕΒͷ෺ཧతಛ௃ྔʹؔͯ͠ɼͦΕͧΕͷ౷‫ܭ‬తͳฏ ‫ۉ‬஋ͳͲ෼͔Ε͹ɼ࣭‫ײ‬ΛఆྔԽ͢Δ͜ͱ͕Ͱ͖Δɽ. Δ͜ͱ͸Ͱ͖ͳ͍ɽͦͷͨΊɼ๏ઢ෼෍ͷਪఆख๏͸ϝλ ϦοΫృ૷ͱಉ͡Ͱ͋Δ͕ɼࠞ߹Ψ΢ε෼෍ͷߏ੒਺ͷܾ. 6.4 ϔΞϥΠϯՃ޻ͷղੳ݁Ռ. ఆํ๏Λมߋ͢Δɽࠞ߹Ψ΢ε෼෍ͷߏ੒਺Λ૯౰ΓͰධ. ର৅෺ମʹ͸ਤ 16 ʹࣔ͢ϔΞϥΠϯՃ޻͞ΕͨۚଐΛ. Ձ͠ɼϞσϧʹର͢Δద੾ͳߏ੒਺Λܾఆ͢ΔͨΊͷࢦඪ. ࡾͭ༻͍ͨɽࠨ্ͷۚଐ͸ଞͷೋͭʹൺ΂ͯϔΞϥΠϯ͕. ͱͯ࣍ࣜ͠Ͱද͞ΕΔ BICʢϕΠζ৘ใྔʣΛ༻͍Δɽ. ऑ͘ɼԼͷۚଐ͸ଞͷೋͭʹൺ΂ͯϔΞϥΠϯ͕‫͍ڧ‬ɽӈ ্ͷۚଐ͸ࠨ্ͷۚଐͷཪ໘Λۚ΍͢ΓͰ‫ݚ‬ຏ͢Δ͜ͱ. BIC = −2 ln(L) + K ln(N ). ͰɼதؒతͳϔΞϥΠϯঢ়ଶΛ࡞੒ͨ͠ɽ͜ΕΒࡾͭͷϔ. (6). ΞϥϯՃ޻͞ΕͨۚଐΛ༻͍ͯղੳΛߦ͏ɽ ·ͣɼεέʔϧΛมԽͤͨ͞ࡍͷ 1 ըૉ಺ͷ๏ઢ෼෍਺. ͜͜ͰɼL ͸࠷େ໬౓ɼK ͸ύϥϝʔλ਺ɼN ͸ඪຊ਺Λ. Λਤ 17 ʹࣔ͢ɽϔΞϥΠϯͷই͕‫͚ڧ‬Ε͹‫Ͳ΄͍ڧ‬ɼ1 ը. ද͢ɽ͜ͷ BIC ͷ஋͕খ͍͞΋ͷ͕࠷దͳύϥϝʔλͰ. ૉ಺ͷ๏ઢ෼਺͕ଟ͍ɽεέʔϧΛมԽͤͨ͞ࡍͷ๏ઢ෼. ͋Γɼࠞ߹Ψ΢ε෼෍ͷߏ੒਺Λ‫ٻ‬ΊΔ͜ͱ͕Ͱ͖Δɽ. ෍਺ͷมԽ͕গͳ͍ͷ͸ɼ༷ʑͳεέʔϧͷই͕ࠞࡏͯ͠. 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. ϝλϦοΫృ૷ͷղੳ݁Ռ. 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. ๏ઢ਺ඪ४ภࠩ. 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). ๏ઢ෼ࢄ 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. Ө‫͕ͱ͍͜ͳ͠ڹ‬෼͔ͬͨɽͦΕ͸ɼۚଐϑϨʔΫͷΑ͏. Manual hairline. ͳେ͖ͳ෺ମ͕൓ࣹʹӨ‫ڹ‬Λ༩͑Δ৔߹Ͱ͸εέʔϧมԽ ʹରͯ͠΋େ͖͘Ө‫͢ڹ‬Δ͕ɼϔΞϥΠϯՃ޻Ͱ͸ɼইͷ தʹ΋͞Βʹඍখͳই͕ଘࡏ͢ΔͨΊεέʔϧมԽʹର͠ ͯ͸͋·Γଟ͘Ө‫ͱ͍ͳ͠ڹ‬༧૝Ͱ͖Δɽ·ͨɼϔΞϥΠ. Strong hairline. ϯͷইͷ‫͞ڧ‬΍ִؒͷҧ͍͸๏ઢ෼෍ʹ΋Ө‫ڹ‬Λ༩͑Δ͜ ͱ͕֬ೝͰ͖ͨɽͦͷͨΊɼ๏ઢ෼෍Λղੳ͢Δ͜ͱͰϔ ΞϥΠϯՃ޻ͷ࣭‫ײ‬ΛಡΈऔΕΔͱ༧૝Ͱ͖Δɽ. 7. Ή͢ͼ ਤ 16. ຊ‫Ͱڀݚ‬͸ɼද໘ԼͷϑϨʔΫͳͲʹΑͬͯ๏ઢͷ෼෍. ϔΞϥΠϯՃ޻ͷ‫ܭ‬ଌ෺ମ. ͕ಠಛʹมԽ͢Δද໘Λର৅ͱ͠ɼද໘Լͷ๏ઢ෼෍Λ౷ ‫ܭ‬తʹղੳ͢Δ͜ͱͰϝλϦοΫృ૷ͷ࣭‫ײ‬ఆྔԽΛߦͬ. EƵŵďĞƌŽĨŶŽƌŵĂůĚŝƐƚƌŝďƵƟŽŶ. ͨɽද໘Լ๏ઢ෼෍Λޫͷ൓ࣹ͔Βਪఆ͠ɼͦͷ౷‫͔ྔܭ‬. ϳ ϲ. Β 1 ըૉ಺ͷ๏ઢ਺ͱͦͷํ޲ͷฏ‫ͱۉ‬෼ࢄΛ‫ٻ‬ΊΔ͜ͱ. ϱ ϰ. tĞĂŬŚĂŝƌůŝŶĞ. ϯ. DĂŶƵĂůŚĂŝƌůŝŶĞ. Ϯ. ^ƚƌŽŶŐŚĂŝƌůŝŶĞ. ϭ. ͕Ͱ͖ͨɽ·ͨɼ1 ըૉͷαΠζ͝ͱͷ๏ઢ਺Λ‫ٻ‬ΊΔ͜ ͱͰɼద੾ͳ‫؍‬ଌεέʔϧͰͷධՁΛߦ͏͜ͱ͕Ͱ͖ͨɽ ͦͷ݁Ռɼ1 ըૉ಺ͷ๏ઢ਺ͱͦͷํ޲ͷ෼ࢄ͸ΩϥΩϥ. Ϭ Ϭ. ϮϬϬ. ϰϬϬ. ϲϬϬ. ϴϬϬ. ϭϬϬϬ. ϭϮϬϬ. ϭϰϬϬ. ϭϲϬϬ. ͱ࣭ͨ͠‫ײ‬Λද‫͢ݱ‬Δύϥϝʔλͱͯ͠༗ޮͰ͋Δ͜ͱΛ. WŝdžĞůƐŝnjĞ΀Ƶŵ΁. ֬ೝͨ͠ɽ ਤ 17. ըૉαΠζ͝ͱͷ๏ઢ෼෍਺. ·ͨɼಉ༷ʹϔΞϥΠϯՃ޻ͷ๏ઢ෼෍Λղੳ͢Δ͜ͱ ͰɼεέʔϧมԽʹର͢Δ๏ઢ෼෍ͷৼΔ෣͍ͷมԽΛ‫ٻ‬ Ίͨɽͦͷ݁ՌɼϔΞϥΠϯͷইͷ‫ִ͕ؒͱ͞ڧ‬๏ઢ෼෍. /ƐŽƚƌŽƉŝĐǀĂůƵĞ ϭ Ϭ͘ϵ Ϭ͘ϴ Ϭ͘ϳ Ϭ͘ϲ Ϭ͘ϱ Ϭ͘ϰ Ϭ͘ϯ Ϭ͘Ϯ. ʹӨ‫ڹ‬Λ༩͑Δ͜ͱΛ֬ೝͨ͠ɽ ຊ‫Ͱڀݚ‬͸࣭‫ײ‬Λද‫͢ݱ‬Δಛ௃ͷ‫ݕ‬ग़Λߦ͍ͬͯΔ͕ɼ tĞĂŬŚĂŝƌůŝŶĞ DĂŶƵĂůŚĂŝƌůŝŶĞ ^ƚƌŽŶŐŚĂŝƌůŝŶĞ. ࠓ‫ޙ‬͸ɼ͜Ε͕ϝλϦοΫృ૷ʹಛ༗ͳਂΈ΍ߴ‫Ͳͳײڃ‬ ͷਓؒͷ஌֮ͱͲͷΑ͏ʹରԠ͢Δͷ͔ௐ͍ࠪͨ͠ɽ· ͨɼϔΞϥΠϯՃ޻͞Εͨۚଐͷ࣭‫ײ‬ఆྔԽͷͨΊʹඞཁ. Ϭ. ϮϬϬ. ϰϬϬ. ϲϬϬ. ϴϬϬ. ϭϬϬϬ. ϭϮϬϬ. ϭϰϬϬ. ϭϲϬϬ. WŝdžĞůƐŝnjĞ΀Ƶŵ΁. ਤ 18. ըૉαΠζ͝ͱͷ๏ઢ෼෍ͷҟํੑ. ͍ΔͨΊͰ͋Δͱ༧૝Ͱ͖Δɽ. ͳಛ௃Λ͞Βʹ૿΍ͤΔΑ͏ʹղੳΛਐΊ͍͖͍ͯͨɽ ࢀߟจ‫ݙ‬ [1]. ·ͨɼεέʔϧΛมԽͤͨ͞ࡍͷ๏ઢ෼෍ͷҟํੑΛਤ. 18 ʹࣔ͢ɽਓҝతʹϔΞϥΠϯΛ͚ͭͨۚଐ͸ଞͷۚଐʹ. [2]. ൺ΂ͯϔΞϥΠϯͷই͕ଟ͘ɼϔΞϥΠϯͷִ͕ؒ‫͍ڱ‬ɽ ͜ͷ݁Ռ͔ΒɼϔΞϥΠϯͷִ͕ؒ‫Ͳ΄͍ڱ‬ҟํੑ͕‫͍ڧ‬. [3]. ͜ͱ͕෼͔ΔɽεέʔϧΛมԽͤͯ͞΋ɼ๏ઢ෼෍ͷҟํ ੑ͸େ͖͘มԽ͠ͳ͍ɽ Ҏ্ͷ͜ͱ͔ΒɼϝλϦοΫృ૷͸εέʔϧͷҧ͍͕ද ໘Լ෼෍ʹେ͖͘Ө‫͢ڹ‬Δ͕ɼϔΞϥΠϯՃ޻ʹ͸͋·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༸Ұɼߴ‫޷ًڮ‬ɼࢁ௕ɹ৳ɿϝλϦοΫΧϥʔʹ͓͚ Δ࣭‫ํݱ࠶ײ‬๏ɼృྉͷ‫ڀݚ‬ɼNo. 145, pp. 14–21 (2006). ෼ా௤உɼਗ਼ਫলࡾɼय़໦࿨༝ɼү୩೔ग़உɼ඼ాɹొɼ ࠤʑ໦ྑ෉ɼాลরඒɼߴ‫ڮ‬ɹ޺ɼ‫ٶ‬Լ޷߂ɼ‫܂‬໦ɹ੷ɼ ઒্‫ݩ‬࿠ɼฏҪහ෉ɿϝλϦοΫ‫ײ‬ͷ‫ܭ‬ଌํ๏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. ஛಺ɹపɼࣉ୔ल෉ɿϝλϦοΫృບͷఆྔతධՁ͓Α ͼଌఆ૷ஔʹ͍ͭͯɼୈ 10 ճృྉɾృ૷ٕज़૯߹‫ൃڀݚ‬ දձཁࢫूɼp. 42 (1992). ਗ਼Ҫ‫ܭ‬໻ɼࢁຊ৴࣍ɼ৿઒ɹऩɿϝλϦοΫ৭ͷཻࢠ‫ײ‬ͷ ଌఆɼ೔ຊ৭࠼ֶ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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