Mip-NeRF 360: Unbounded Anti- Aliased Neural Radiance Fields Authors: Jonathan T. Barron, Ben Mildenhall, Dor Verbin Presenter: @peisuke 

ࣗݾ঺հ ໊લɿ౻ຊ ܟհ ॴଐɿ"#&+"
ʢ-BCT
ϥϘ௕ʣ ෭ۀɿ.-Λத৺ʹ૬ஊ͔Β։ൃ·Ͱ΍ͬͯ·͢ ੋඇ͓੠͕͚Լ͍͞ ׆ಈɿ5XJUUFS
!QFJTVLF (JUIVC IUUQTHJUIVCDPNQFJTVLF 2JJUB IUUQTRJJUBDPNQFJTVLF 4MJEF4IBSF IUUQTXXXTMJEFTIBSFOFU'VKJNPUP,FJTVLF 4QFBLFS%FDL IUUQTTQFBLFSEFDLDPNQFJTVLF গ͚ͩ͠ॻ͍ͯ·͢ 

֓ཁ • ͲΜͳ࿦จʁ • /F3'Ͱ͸ϘϦϡʔϜϨϯμϦϯάʹ͓͍֤ͯ஍఺ͷ৭ɾີ౓Λ//Ͱ ग़ྗ͢Δ͜ͱͰը૾Λੜ੒ • /F3'ʹ͓͍ͯɺத৺͔Βԕ͍޿େͳۭؒΛ//Ͱ࠶ݱ͢Δ͜ͱ͕೉͠ ͘ɺத৺Ҏ֎ͷ෮ݩ͕೉͔ͬͨ͠໰୊Λղܾ • ޻෉఺͸ʁ • ۭؒΛม׵ͯ͠ԕ͍ྖҬΛখ͍͞ྖҬʹຒΊࠐΉ͜ͱͰԕ͞ͷ໰୊Λ ղܾ • ͦͷଞʹɺৠཹʹΑΔߴ଎Խɾਖ਼نԽʹΑΔϊΠζ࡟ݮͳͲΛ͍ͯ͠ Δ 

ख๏ͷσϞ 

/F3'ͷ֓ཁʢʣ • ۭؒ಺ͷ఺ʢҐஔ޲͖ͷ࣍ݩʣʹؔ͢Δ৭ɾີ౓Λ༧ଌ͢Δ ωοτϫʔΫ • ΧϝϥͷҐஔΛܾΊΔͱɺωοτϫʔΫͷग़ྗ͢Δ஋ΛݩʹϘ ϦϡʔϜϨϯμϦϯά͢Δ͜ͱͰը૾Λੜ੒ 1PTJUJPOBM
&ODPEJOH͞Εͨ఺ͷ ৘ใ ࣍ϖʔδͰઆ໌ ີ౓͔Β XΛܭࢉ 

/F3'ͷ֓ཁʢʣ • ۭؒ಺ͷ఺Λߴ࣍ݩͷಛ௃ྔʹม׵ʢQPTJUJPOBM
FODPEJOHɺ 1&ʣ͢Δ͜ͱͰߴਫ਼౓Խ 𝛾 𝒙 = sin 2!𝒙𝜋 , cos 2!𝒙𝜋 , … , sin 2"𝒙𝜋 , cos 2"𝒙𝜋 

NJQ/F3'ͷ֓ཁʢʣ • 𝛾 𝒙 Λ఺ͱͯ͠ѻ͍ɺͦͷҐஔͷ৭ΛϨϯμϦϯά͢Δͱɺ पғͷ৘ใΛಘΒΕͣδϟΪʔ͕ൃੜ͢Δ • ࢹઢΛίʔϯͰଊ͑ɺίʔϯ಺ͷੵ෼Λ༻͍ΔࣄͰߴਫ਼౓Խ • ίʔϯΛΨ΢ε෼෍Ͱۙࣅɺ1&ͷظ଴஋Λ࢖͏͜ͱͰɺੵ෼Λ ؆қతʹܭࢉ ఺Ͱ͸ͳ͘ɺ֤ྖҬͷ 1&ͷظ଴஋Λ࢖͏ 

NJQ/F3'ͷ֓ཁʢʣ • 1&ͨ͠ಛ௃ྔͷظ଴஋ΛऔΔͱɺࢹ఺͔Βԕ͍ྖҬͰ͸ߴप೾ྖ Ҭ͕খ͘͞ͳΔ • ڑ཭ʹԠͨ͡ૈ͞ΛՃຯͯ͠ωοτϫʔΫ͕৭Λग़ྗͯ͘͠ΕΔ ࢹ఺ۙ͘Ͱ͸ɺ෼෍͕ ڱ͍ͨΊߴप೾ྖҬͷ ৘ใ͕࢒Δ ࢹ఺͔Β཭ΕΔͱɺ෼ ෍͕޿͘ͳΔͨΊ௿प ೾੒෼ͷΈʹͳΔ 

NJQ/F3'ͷ՝୊ • Χϝϥ͔Βԕ͍ྖҬ͸ίʔϯ ͕େ͖͘ͳΔ • த৺ʹ͋Δ෺ମҎ֎ͷपғ؀ ڥͷ෮ݩ͕ࠔ೉ த৺ྖҬ΄Ͳࡉ͔ ͍৘ใ͕ඞཁ पғͷ৘ใ͸ૈͯ͘ྑ͍ ֎ଆͷྖҬͷσʔλ͕ૄʹͳΔͨΊɺ ্ख͘෮ݩͰ͖ͳ͍ 

4DFOF
BOE
3BZ
1BSBNFUFSJ[BUJPO • த৺͔Β൒ܘͷྖҬ·Ͱ͸มΘΒͣ • ൒ܘҎ্ͷྖҬ͸ɺԕ͘ͳΔ΄Ͳڑ཭ΛॖΊɺ൒ܘͷྖҬʹ ແݶԕํ͕ऩ·ΔΑ͏ʹม׵ • ࣍ۙࣅͯ͠ϠίϏߦྻΛ࢖͍Ψ΢ε෼෍Λม׵ ਤͷପԁ͸ҎԼͰม׵ 

ৠཹΛ༻͍ͨߴ଎Խʢʣ • NJQ/F3'Ͱ͸ɺ·ͣ͸શҬΛૈཻ͍౓ͰϨΠτϨʔγϯά͠ɺ෺ମ͕Կ ॲʹ͋Δͷ͔Λେ·͔ʹ೺Ѳ • ࣍ʹɺ෺ମ͕ଘࡏ͢ΔҐஔʹ੍ݶ͠ɺ࠶౓ϨΠτϨʔγϯά • ͜ΕΛ܁Γฦ͢͜ͱͰৄࡉͳܗঢ়Λ෮ݩՄೳɺܭࢉ͕஗͍ͱ͍͏՝୊͕͋ Δ 

ৠཹΛ༻͍ͨߴ଎Խʢ̎ʣ • ૈ͍ྖҬ୳ࡧϑΣʔζͰ͸ɺ৭ͷ৘ใΛ࣋ͨͳ͍ɺΑΓখ͞ͳϞσϧ ʢ1SPQ
.-1ʣͰ෺ମͷҐஔΛ୳ࡧ • ࠷ޙͷϨϯμϦϯάͷΈɺ৭ͷ৘ใΛ࣋ͭϞσϧʢ/F3'
.-1ʣͰ୳ࡧ • ֤ϞσϧʹҰ؏ੑΛ࣋ͨͤΔͨΊɺωοτϫʔΫͷৠཹΛ༻͍Δ 

ωοτϫʔΫͷৠཹʹ͍ͭͯ • /F3'
.-1͔ΒಘΒΕΔ෺ମͷҐஔͷ৘ใΛ༻͍ͯɺ1SPQ
.-1Λֶश ͢Δ͜ͱͰҰ؏ੑΛอͭ • ௚઀྆ํͷωοτϫʔΫؒͰඞཁͱͳΔCJOͷີ౓͸ҟͳΔͷͰ௚઀਺஋ Λൺֱͨ͠ৠཹ͕ग़དྷͳ͍ • /F3'
.-1͔ΒಘΒΕΔॏΈͷώετάϥϜΑΓ΋ɺ1SPQ
.-1ͷώε τάϥϜ͕େ͖͘ͱ͍͏੍໿Λ࢖͏ • ͜Ε͸ͪΐͬͱෳࡶͳͷͰ࣍ͷϖʔδͰઆ໌ ࠷ऴతʹɺ෺ମྖҬʹ͓ ͍ͯX͕େ͖͘ͳΔɻ· ͨɺૈ͍CJOͷ1SPQ.-1 ͕ಘΒΕΔ 

• ϨΠ্ʹ͋Δ෺ମͷॏΈXͷώετάϥϜΛߟ͑Δ ώετάϥϜͷൺֱ ϨΠ্ͷ෺ମͷॏΈ w ෺ମͷॏΈͷώετάϥϜ 

ώετάϥϜͷൺֱ /F3'
.-1ͷ ώετάϥϜ 1SPQ
.-1ͷ ώετάϥϜ /F3'
.-1ͷͱ͋ΔྖҬ5JͷॏΈXJ ΑΓ΋ɺ5JΛؚΉྖҬ5Kͷώετά ϥϜXKͷ໘ੵͷํ͕େ͖͘ͳΔ 

ਖ਼ଇԽ • /F3'Λֶश͢Δͱɺಛʹԕ͍ΤϦΞʹ͓͍ͯ͸ܗঢ়෮ݩͷͨ Ίͷ৘ใ͕଍Γͣෆྑઃఆ໰୊͕ൃੜ͠ɺϊΠζ͕ൃੜ • ਖ਼ଇԽʹΑͬͯϊΠζͷ࡟ݮΛߦ͏ 

ਖ਼ଇԽ • ॏΈ͆ͷ෼෍͕ͳΔ΂͘σϧλؔ਺ʹۙ͘ͳΔΑ͏ͳ੍໿Λͭ ͚Δ σϧλؔ਺ʹͳΔͱɺ X V ɺX W ͕ڞʹͷ࣌ ʹɺVW͕ʹ͖ۙͮɺͦ ΕҎ֎͸ɺΑ্ͬͯࣜ͸ θϩʹۙͮ͘ 𝑢 ≠ 𝑣ͷ࣌ʹɺw 𝑢 , 𝑤 𝑣 > 0 Ͱ͋ΔͱϖφϧςΟͱͳΔ 

ਖ਼ଇԽ • ઌఔͷੵ෼͸௚઀ܭࢉͰ͖ͳ͍͕ɺX͸֤ΠϯλʔόϧͰҰఆ ஋ʹͳΔͷͰɺҎԼͷΑ͏ʹॻ͖දͤΔ • ޯ഑Λܭࢉ͢ΔͱɺਤͷΑ͏ͳํ޲ʹॏΈ͕มԽ͢Δྗ͕ಇ͘ 

࠷దԽ • ը૾ͷ෮ݩϩεɺਖ਼ଇԽʹΑͬͯ/F3'
.-1Λɺ࠷ޙͷ߲Ͱ 1SPQ
.-1Λֶश • Ϟσϧ • 1SPQ
.-1͸ύϥϝʔλͷӅΕ૚Λ࣋ͭɺϨΠϠʔͷ.-1 • /F3'
.-1͸ύϥϝʔλͷӅΕ૚Λ࣋ͭɺϨΠϠʔͷ.-1 ը૾ͷ෮ݩϩε ਖ਼ଇԽ߲ 1SPQ
.-1ͷֶश 

࣮ݧ݁Ռ • σʔλ • ৽͍͠σʔληοτɺͭͷ԰֎ɺͭͷ԰಺ • ৚݅ • /F3'
NJQ/F3'
/F3'ͱൺֱ • $0-."1ͰࣗݾҐஔਪఆ • ܭࢉ؀ڥ • 516
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XJUI

DPSFT • ࢦඪ • 14/3
44*.
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·ͱΊ • NJQ/F3'ͷ՝୊Ͱ͋ͬͨԕํͷྖҬΛਫ਼౓ྑ͘෮ݩ͢Δख๏ ΛఏҊ • 4DFOF
BOE
3BZ
1BSBNFUFSJ[BUJPOʹΑΔԕํ෮ݩߴਫ਼౓Խɺ ৠཹʹΑΔߴ଎Խɺਖ਼ଇԽʹΑΔϊΠζআڈΛఏҊ