Real-time Shading with Filtered Importance Sampling (sap 0073)

Real-time Shading with Filtered Importance Sampling(sap0073)Mark Colbert∗University of Central FloridaJaroslav Kˇr iv´a nek†Czech Technical University inPrague(a)(b)(c)(d)ofl iimage plane1/p(x1)1/p(x2)1/p(x6)1/p(x3)1/p(x4)1/p(x5)(e)Figure1:(a)Rendering using deterministic importance sampling withoutfiltering produces aliasing in the estimate of the illumination integral,which translates into image artifacts.(b)Randomizing the directions for each image pixel trades alias for visible noise.(c)Our filtered importance sampling suppresses the alias at the cost of slightly blurred highlights.(d)Reference solution.Images(a),(b),and(c) are rendered with40importance samples per pixel.(e)Illustration of the size of thefilter used on the environment map i.1IntroductionCorrect perception of materials requires complex,natural illumina-tion[Fleming et al.2003].Thus for material or lighting design ap-plications,realistic,interactive rendering of objects with arbitrarymaterials under natural illumination is essential.We present a sim-ple and efficient technique for real-time,image-based lighting ofobjects with spatially-varying,glossy materials.The key to ouralgorithm is combining BRDF-proportional importance samplingwith environment mapfiltering to attain computationally efficientrendering amenable to the GPU.Environment map pre-filtering[Kautz et al.2000]and some fre-quency space solutions provide real-time visualizations,but theiruse may be too cumbersome since it requires a hefty amount of pre-computation and/or a sizable code base.Ourfiltered importancesampling requires minimal pre-computation and operates within aGPU shader,therebyfitting into almost any production pipelineneeding real-time dynamically changing materials or lighting.2Filtered Importance SamplingThe color of one pixel is given by the illumination integral,i.e.theintegral of the lighting and BRDF product.Our approach to evalu-ating this integral on the GPU is motivated by BRDF-proportionalMonte Carlo importance sampling.For each pixel,we take uni-formly distributed numbers,transform them in the GPU shader intoimportant sample directions,and evaluate the sample.Here,theuniformly distributed numbers are a precomputed deterministic setused for all pixels.This results in aliasing in our estimate of the illu-mination integral causing image artifacts(Figure1a).Monte Carlowould use random numbers to trade aliasing for more visually ac-ceptable noise(Figure1b).Since generating random numbers onthe GPU is expensive,we reduce the artifacts via afiltering opera-tion(Figure1c).Our main contribution is determining the appropriatefilter size foreach importance sample.Intuitively,thefilter size should be smallfor densely sampled directions around the BRDF lobe and largerelsewhere(Figure1e).This suggests thatfilter size is inversely pro-portional to the probability density function(PDF)associated withthe sample direction.Performing a formal analysis of numerical∗colbert@†xkrivanj@fel.cvut.czintegration in the frequency domain supports this intuition.We usehardware accelerated MIP-maps for fast environment mapfilteringwith the PDF-proportionally sizedfilter.A formal analysis offiltered importance sampling exposes theapproximations used in the described implementation.Notably,isotropicfilter with its size inversely proportional to the PDF is acrude approximation of the ideal,spatially variant,anisotropicfil-ter.However,anisotropicfiltering with MIP-mapping is not possi-ble due to current hardware limitations.By performing the MIP-map look ups via the aforementioned technique,we achieve a goodperformance at the cost of slight blurring.3ConclusionOur novel shading technique,filtered importance sampling,pro-vides real-time rendering for dynamically changing illuminationand spatially-varying BRDFs.The algorithm runs at about90frames per second on an nVidia7800GTX SLI,when render-ing a sphere at a resolution of512x512with40samples perpixel.However,the true strength of the algorithm is its simplic-ity andflexibility–itfits in a single GPU shader,it handles anyBRDF model that can be importance sampled,and has modest pre-computation and memory requirements(a MIP-map of the environ-ment).To support diffuse surfaces,we use low-order spherical harmon-ics[Ramamoorthi and Hanrahan2001].Our work currently ignoresself-occlusion,and we leave this for future work.However,we pro-vide the necessary adaptability for interactive material and lightingdesign within any production pipeline.ReferencesF LEMING,R.W.,D ROR,R.O.,AND A DELSON,E.H.2003.Real-worldillumination and the perception of surface reflectance properties.Journalof Vision3(July),347–368.K AUTZ,J.,V´AZQUEZ,P.-P.,H EIDRICH,W.,AND S EIDEL,H.-P.2000.Aunified approach to prefiltered environment maps.In11th EurographicsWorkshop on Rendering,Eurographics Association,185–196.R AMAMOORTHI,R.,AND H ANRAHAN,P.2001.An efficient represen-tation for irradiance environment maps.In Proc.of SIGGRAPH2001,ACM Press.。