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Mip-NeRF 360: Unbounded Anti-Aliased Neural Rad...
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peisuke
April 30, 2023
Technology
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Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields
第58回 コンピュータビジョン勉強会@関東
深層学習+3D論文読み会
Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields
peisuke
April 30, 2023
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Transcript
Mip-NeRF 360: Unbounded Anti- Aliased Neural Radiance Fields Authors: Jonathan
T. Barron, Ben Mildenhall, Dor Verbin Presenter: @peisuke
ࣗݾհ ໊લɿ౻ຊ ܟհ ॴଐɿ"#&+"ʢ-BCTϥϘʣ ෭ۀɿ.-Λத৺ʹ૬ஊ͔Β։ൃ·Ͱͬͯ·͢ ੋඇ͓͕͚Լ͍͞ ׆ಈɿ5XJUUFS!QFJTVLF (JUIVC IUUQTHJUIVCDPNQFJTVLF 2JJUB
IUUQTRJJUBDPNQFJTVLF 4MJEF4IBSF IUUQTXXXTMJEFTIBSFOFU'VKJNPUP,FJTVLF 4QFBLFS%FDL IUUQTTQFBLFSEFDLDPNQFJTVLF গ͚ͩ͠ॻ͍ͯ·͢
֓ཁ • ͲΜͳจʁ • /F3'ͰϘϦϡʔϜϨϯμϦϯάʹ͓͍֤ͯͷ৭ɾີΛ//Ͱ ग़ྗ͢Δ͜ͱͰը૾Λੜ • /F3'ʹ͓͍ͯɺத৺͔Βԕ͍େͳۭؒΛ//Ͱ࠶ݱ͢Δ͜ͱ͕͠ ͘ɺத৺Ҏ֎ͷ෮ݩ͕͔ͬͨ͠Λղܾ •
ʁ • ۭؒΛมͯ͠ԕ͍ྖҬΛখ͍͞ྖҬʹຒΊࠐΉ͜ͱͰԕ͞ͷΛ ղܾ • ͦͷଞʹɺৠཹʹΑΔߴԽɾਖ਼نԽʹΑΔϊΠζݮͳͲΛ͍ͯ͠ Δ
ख๏ͷσϞ
/F3'ͷ֓ཁʢʣ • ۭؒͷʢҐஔ͖ͷ࣍ݩʣʹؔ͢Δ৭ɾີΛ༧ଌ͢Δ ωοτϫʔΫ • ΧϝϥͷҐஔΛܾΊΔͱɺωοτϫʔΫͷग़ྗ͢ΔΛݩʹϘ ϦϡʔϜϨϯμϦϯά͢Δ͜ͱͰը૾Λੜ 1PTJUJPOBM&ODPEJOH͞Εͨͷ ใ ࣍ϖʔδͰઆ໌
ີ͔Β XΛܭࢉ
/F3'ͷ֓ཁʢʣ • ۭؒͷΛߴ࣍ݩͷಛྔʹมʢQPTJUJPOBMFODPEJOHɺ 1&ʣ͢Δ͜ͱͰߴਫ਼Խ 𝛾 𝒙 = sin 2!𝒙𝜋 ,
cos 2!𝒙𝜋 , … , sin 2"𝒙𝜋 , cos 2"𝒙𝜋
NJQ/F3'ͷ֓ཁʢʣ • 𝛾 𝒙 Λͱͯ͠ѻ͍ɺͦͷҐஔͷ৭ΛϨϯμϦϯά͢Δͱɺ पғͷใΛಘΒΕͣδϟΪʔ͕ൃੜ͢Δ • ࢹઢΛίʔϯͰଊ͑ɺίʔϯͷੵΛ༻͍ΔࣄͰߴਫ਼Խ • ίʔϯΛΨεͰۙࣅɺ1&ͷظΛ͏͜ͱͰɺੵΛ
؆қతʹܭࢉ Ͱͳ͘ɺ֤ྖҬͷ 1&ͷظΛ͏
NJQ/F3'ͷ֓ཁʢʣ • 1&ͨ͠ಛྔͷظΛऔΔͱɺࢹ͔Βԕ͍ྖҬͰߴपྖ Ҭ͕খ͘͞ͳΔ • ڑʹԠͨ͡ૈ͞ΛՃຯͯ͠ωοτϫʔΫ͕৭Λग़ྗͯ͘͠ΕΔ ࢹۙ͘Ͱɺ͕ ڱ͍ͨΊߴपྖҬͷ ใ͕Δ ࢹ͔ΒΕΔͱɺ
͕͘ͳΔͨΊप ͷΈʹͳΔ
NJQ/F3'ͷ՝ • Χϝϥ͔Βԕ͍ྖҬίʔϯ ͕େ͖͘ͳΔ • த৺ʹ͋ΔମҎ֎ͷपғ ڥͷ෮ݩ͕ࠔ த৺ྖҬ΄Ͳࡉ͔ ͍ใ͕ඞཁ पғͷใૈͯ͘ྑ͍
֎ଆͷྖҬͷσʔλ͕ૄʹͳΔͨΊɺ ্ख͘෮ݩͰ͖ͳ͍
4DFOFBOE3BZ1BSBNFUFSJ[BUJPO • த৺͔ΒܘͷྖҬ·ͰมΘΒͣ • ܘҎ্ͷྖҬɺԕ͘ͳΔ΄ͲڑΛॖΊɺܘͷྖҬʹ ແݶԕํ͕ऩ·ΔΑ͏ʹม • ࣍ۙࣅͯ͠ϠίϏߦྻΛ͍ΨεΛม ਤͷପԁҎԼͰม
ৠཹΛ༻͍ͨߴԽʢʣ • NJQ/F3'Ͱɺ·ͣશҬΛૈཻ͍ͰϨΠτϨʔγϯά͠ɺମ͕Կ ॲʹ͋Δͷ͔Λେ·͔ʹѲ • ࣍ʹɺମ͕ଘࡏ͢ΔҐஔʹ੍ݶ͠ɺ࠶ϨΠτϨʔγϯά • ͜ΕΛ܁Γฦ͢͜ͱͰৄࡉͳܗঢ়Λ෮ݩՄೳɺܭࢉ͕͍ͱ͍͏՝͕͋ Δ
ৠཹΛ༻͍ͨߴԽʢ̎ʣ • ૈ͍ྖҬ୳ࡧϑΣʔζͰɺ৭ͷใΛ࣋ͨͳ͍ɺΑΓখ͞ͳϞσϧ ʢ1SPQ.-1ʣͰମͷҐஔΛ୳ࡧ • ࠷ޙͷϨϯμϦϯάͷΈɺ৭ͷใΛ࣋ͭϞσϧʢ/F3'.-1ʣͰ୳ࡧ • ֤ϞσϧʹҰ؏ੑΛ࣋ͨͤΔͨΊɺωοτϫʔΫͷৠཹΛ༻͍Δ
ωοτϫʔΫͷৠཹʹ͍ͭͯ • /F3'.-1͔ΒಘΒΕΔମͷҐஔͷใΛ༻͍ͯɺ1SPQ.-1Λֶश ͢Δ͜ͱͰҰ؏ੑΛอͭ • ྆ํͷωοτϫʔΫؒͰඞཁͱͳΔCJOͷີҟͳΔͷͰ Λൺֱͨ͠ৠཹ͕ग़དྷͳ͍ • /F3'.-1͔ΒಘΒΕΔॏΈͷώετάϥϜΑΓɺ1SPQ.-1ͷώε τάϥϜ͕େ͖͘ͱ͍͏੍Λ͏
• ͜ΕͪΐͬͱෳࡶͳͷͰ࣍ͷϖʔδͰઆ໌ ࠷ऴతʹɺମྖҬʹ͓ ͍ͯX͕େ͖͘ͳΔɻ· ͨɺૈ͍CJOͷ1SPQ.-1 ͕ಘΒΕΔ
• ϨΠ্ʹ͋ΔମͷॏΈXͷώετάϥϜΛߟ͑Δ ώετάϥϜͷൺֱ ϨΠ্ͷମͷॏΈ w ମͷॏΈͷώετάϥϜ
ώετάϥϜͷൺֱ /F3'.-1ͷ ώετάϥϜ 1SPQ.-1ͷ ώετάϥϜ /F3'.-1ͷͱ͋ΔྖҬ5JͷॏΈXJ ΑΓɺ5JΛؚΉྖҬ5Kͷώετά ϥϜXKͷ໘ੵͷํ͕େ͖͘ͳΔ
ਖ਼ଇԽ • /F3'Λֶश͢Δͱɺಛʹԕ͍ΤϦΞʹ͓͍ͯܗঢ়෮ݩͷͨ Ίͷใ͕Γͣෆྑઃఆ͕ൃੜ͠ɺϊΠζ͕ൃੜ • ਖ਼ଇԽʹΑͬͯϊΠζͷݮΛߦ͏
ਖ਼ଇԽ • ॏΈ͆ͷ͕ͳΔ͘σϧλؔʹۙ͘ͳΔΑ͏ͳ੍Λͭ ͚Δ σϧλؔʹͳΔͱɺ X V ɺX W ͕ڞʹͷ࣌
ʹɺVW͕ʹ͖ۙͮɺͦ ΕҎ֎ɺΑ্ͬͯࣜ θϩʹۙͮ͘ 𝑢 ≠ 𝑣ͷ࣌ʹɺw 𝑢 , 𝑤 𝑣 > 0 Ͱ͋ΔͱϖφϧςΟͱͳΔ
ਖ਼ଇԽ • ઌఔͷੵܭࢉͰ͖ͳ͍͕ɺX֤ΠϯλʔόϧͰҰఆ ʹͳΔͷͰɺҎԼͷΑ͏ʹॻ͖දͤΔ • ޯΛܭࢉ͢ΔͱɺਤͷΑ͏ͳํʹॏΈ͕มԽ͢Δྗ͕ಇ͘
࠷దԽ • ը૾ͷ෮ݩϩεɺਖ਼ଇԽʹΑͬͯ/F3'.-1Λɺ࠷ޙͷ߲Ͱ 1SPQ.-1Λֶश • Ϟσϧ • 1SPQ.-1ύϥϝʔλͷӅΕΛ࣋ͭɺϨΠϠʔͷ.-1 • /F3'.-1ύϥϝʔλͷӅΕΛ࣋ͭɺϨΠϠʔͷ.-1
ը૾ͷ෮ݩϩε ਖ਼ଇԽ߲ 1SPQ.-1ͷֶश
࣮ݧ݁Ռ • σʔλ • ৽͍͠σʔληοτɺͭͷ֎ɺͭͷ • ݅ • /F3' NJQ/F3'
/F3' ͱൺֱ • $0-."1ͰࣗݾҐஔਪఆ • ܭࢉڥ • 516WXJUIDPSFT • ࢦඪ • 14/3 44*. -1*14
ఆྔධՁ
ఆੑධՁ
·ͱΊ • NJQ/F3'ͷ՝Ͱ͋ͬͨԕํͷྖҬΛਫ਼ྑ͘෮ݩ͢Δख๏ ΛఏҊ • 4DFOFBOE3BZ1BSBNFUFSJ[BUJPOʹΑΔԕํ෮ݩߴਫ਼Խɺ ৠཹʹΑΔߴԽɺਖ਼ଇԽʹΑΔϊΠζআڈΛఏҊ