08 Gradent Doman Metropols Lght Transport..:..:.... dspavlov_@edu.hse.ru vfrolov@graphcs.cs.msu.ru - -. - -.. - -.. : ( ϕr θr = L( ϕ θ R( ϕ θ ϕr θr cos( n lϕ θ ϕ θ dϕ dθ L R -. - - - - -. [Kaa 986]. (Path Tracng PT - - - ( -. [Kaa 986] -. - - - - [Pharr 06; Mtchell 99]. - / / -. -. - - -. [Pharr 06] -. - ( : ( PT -. [Mtchell 99] - - - -. - - ( -. - -
Gradent Doman Metropols Lght Transport - [Veach 997; Kelemen 00].. -. - - ---. - g(. N N g( C g( g( d = ( N = p ( N = f ( g( ; f ( ~ p ( = ; C f (- C - -; f( ( - g(. - [Veach 997 Kelemen 00] g( f( MLT (. [Veach 997 Kelemen 00] f(. [MacKa 003]. [Hoberock 00] - - -. [Lehtnen 03] Gradent-doman Metropols Lght Transport (GDMLT. GDMLT.... [Lehtnen 03].. - - ( -. -. (.. - -. [Kettunen 05] Gradent-doman Path Tracng (GDPT. -. PT : = h ( f ( d ( ( µ h - - ; - ; f( - ; dµ ( - k da( 0... k - = 0 A( - - [Pharr 06 ch. 5.4; Veach 997 ch. 4.]. - -. -. - (... - -
08 = h( h( f ( dµ ( ( f ( dµ ( ( 3 : ( - ( X (3 - Y. : d d H g arg mn + ( d α d H d d - ; g - ; α - - ( α = 0 ; d d ; H H - - ( - (+ ( ; - L L. -. -. GDMLT [Lehtnen 03]. GDPT -. GDMLT. 3 [Lehtnen 03] - GDMLT - Veach-stle Path space Metropols Lght Transport. GDMLT Prmar Sample Space MLT [Kelemen 00] ( PSSMLT - -. - -. Gradent Doman Prmar Sample Space Lght Transport GDPSSMLT. 3. - : ( * = h ( f ( dµ ( ( h - - ; - ; f * ( - - ; dµ ( - da( k = 0 Metropols Lght Transport - ( (: C N N = * h ( f ( f ( f - - ( f * ( ; C - -. 3. Naïve PT [Kelemen 00 Veach 997] [Veach 997 ch. 0]. PSSMLT (... MLT GDMLT... - 3 -
Gradent Doman Metropols Lght Transport. MLT ( PT MLT. GDMLT.. GDMLT MLT [Lehtnen 03]. ( - MLT.. ( PT PT [Veach 997] MLT. 3.3. - c. : d = + d : = +. T( s ( s ( s + Offset + Offset : d = (3 = + d{ µ οt } * 0 * h ( f ( T0 ( ( f ( dµ ( dµ d { µ οt 0} - dµ.. (... [Lehtnen 03]. - -. - -... 4 - : (- 0; ( 0; (0 -; (0. GDPT - 4 4 GDMLT. -. - -. = {( 0( + 0(0 (0 + } - PSSMLT. Large Step -. - 4 -
08 -. d = + -. d : = --. 3.4.. - (.. 3 : (.. 3.. [Lehtnen03] - - -. half-vector - - -. [Kettunen 05] (GDPT - GDMLT. [Lehtnen 03] Manfold Eploraton [Jacob 0]. Manfold Eploraton MLT (Path Space MLT[Veach 997] [Kettunen 05].. w w h h half-vector n n - n n - θ. : : = h : = h h h n ω + n = n ω + n ω h = ω h o o ω o o ω h ω ω h ( : cos θ = = cosθ. (3. 3.5. - 5 -
Gradent Doman Metropols Lght Transport * * f ( z = f ( z + α f ( 4 f * ( z - f * ( - - (lumnance ; α [0; ]-. - - -. - PSSMLT. f * ( z. (lumnance (. 3.6. - d d H g arg mn + ( d α d H d d g - ; - - ; α - - ; d d ; H H - - - L L.. [Lehtnen03]. L [Shewchuk 994] L teratvel Reweghted Least Squares [Burrus 0] L. gradent-doman [Bhat 008]. 4 (GDPSSMLT : (PT (GDPT (PSSMLT. Sponza. (... 800800 ~3. ( 3 4 5 6 7. ntel Embree [Wald et. All 04]. 3. 3. 4 (GDPT.. 5 (PSSMLT... -.. 3-6 GDMLT GDPSSMLT. - 6 -
08 5 : - (PT GDPT... : PSSMLT. 3: GDMLT... ( 3.5 -. 4: GDPSSMLT PSSMLT. (. : GDMLT MLT ( Non Loal Means.. James T. Kaa. 986. The renderng equaton. n Proceedngs of the 3th annual conference on Computer graphcs and nteractve technques (SGGRAPH '86 Davd C. Evans and Russell J. Atha (Eds.. ACM NY USA 43-50. Matt Pharr Wenzel Jakob and Greg Humphres. 06. Phscall Based Renderng: From Theor to mplementaton (3rd ed.. Morgan Kaufmann Publshers nc. San Francsco CA USA. Don P. Mtchell. 99. Spectrall optmal samplng for dstrbuton ra tracng. n Proceedngs of the 8th annual conference on Computer graphcs and nteractve technques (SGGRAPH '9. ACM New York NY USA 57-64. Erc Veach. 997. Robust Monte Carlo Methods for Lght Transport Smulaton. Ph.D. Dssertaton. Stanford Unverst Stanford CA USA. Advsor (s Leondas J. Gubas. AA98376. Csaba Kelemen László Szrma-Kalos Görg Antal and Ferenc Csonka. 00. Smple and Robust Mutaton Strateg for the Metropols Lght Transport Algorthm. EUROGRAPHCS 00 / G. Drettaks and H.-P. Sedel. 00 v. 3. Davd J. C. MacKa. 00. nformaton Theor nference & Learnng Algorthms. Cambrdge Unverst Press New York NY USA. Jared Hoberock and John C. Hart. 00. "Arbtrar mportance functons for metropols lght transport." Computer Graphcs Forum. Blackwell Publshng Ltd. v.9 6. Jaakko Lehtnen Tero Karras Samul Lane Mka Attala Frédo Durand and Tmo Ala. 03. Gradent-doman metropols lght transport. ACM Trans. Graph. 3 4 Artcle 95 (Jul 03 pages. Markus Kettunen Marco Manz Mka Attala Jaakko Lehtnen Frédo Durand and Matthas Zwcker. 05. Gradent-doman path tracng. ACM Trans. Graph. 34 4 Artcle 3 (Jul 05 3 pages. DO: https://do.org/0.45/766997 Wenzel Jakob and Steve Marschner. 0. Manfold eploraton: a Markov Chan Monte Carlo technque for renderng scenes wth dffcult specular transport. ACM Trans. Graph. 3 4 Artcle 58 (Jul 0 3 pages. Jonathan R Shewchuk. 994. An ntroducton to the Conugate Gradent Method Wthout the Agonzng Pan. Techncal Report. Carnege Mellon Unv. Pttsburgh PA USA. C.S. Burrus. 0. teratve reweghted least squares. OpenSta-CNX Web Publcaton. http://cn.org/content/m4585/. Pravn Bhat et al. 008. Fourer analss of the D screened Posson equaton for gradent doman problems. n European Conference on Computer Vson. Sprnger Berln Hedelberg. 4-8. ngo Wald Sven Woop Carsten Benthn Gregor S. Johnson and Manfred Ernst. 04. Embree: a kernel framework for effcent CPU ra tracng. ACM Trans. Graph. 33 4 Artcle 43 (Jul 04 8 pages. 6-3-60048. - 7 -
4 Gradent Doman Metropols Lght Transport GDPT PT PSSMLT &. 3. GDPSSMLT $ (GDPSSMLT &. 4. " #. 3. : PT GDPT PSSMLT GDPSSMLT - 8 -
PT GDPT PSSMLT GDPSSMLT &. 5. $ (GDPSSMLT &. 6. " #. 3. : PT GDPT PSSMLT GDPSSMLT - 9-08