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Computer Graphics SS 2014 Sampling

Computer Graphics SS 2014 Sampling. Rüdiger Westermann Lehrstuhl für Computer Graphik und Visualisierung. Overview . So far : Image synthesis Ray tracing ; models , transformations , shading & lighting , textures , acceleration Today Aliasing and antialiasing techniques

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Computer Graphics SS 2014 Sampling

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  1. Computer Graphics SS 2014 Sampling Rüdiger Westermann Lehrstuhl für Computer Graphik und Visualisierung

  2. Overview • So far: • Image synthesis • Ray tracing; models, transformations, shading & lighting, textures, acceleration • Today • Aliasing andantialiasingtechniques • Prefiltering • Supersampling • Postfiltering • Stochasticand adaptive sampling

  3. Sampling • Mathematically, point sampling using regularly spaced sample points is the multiplicationof the function with a comb function x 0 T 2T

  4. Sampling • Recall: imagesynthesismeanspointsamplingof a continuoussignal • Image containssamplesof a continuoussignal at a discretesetofpositions • Pixel spacingdeterminesthefrequencies (thesizeofdetails) thatcanbereconstructed • Undersamplingtheimage(takingtoolesssamplestoallow for thereconstructionofthesignalfromthesamples) causesaliasingartifacts (alias = ghost)

  5. Aliasing • Original sceneandluminosity (brightness) distributionalong a scanline

  6. Aliasing • Point sampling the scene at pixel centers

  7. Aliasing • The rendered image

  8. Aliasing • Jaggedprofiles

  9. Aliasing • Loss of details

  10. Aliasing • Note: thesamplingfrequencydecreaseswithincreasingdistancetotheviewpoint d0 d1 d2 d3 viewpoint

  11. Aliasing • Withincreasingdistancetotheviewerandslopeofthesurface, an ever larger surfaceareafalls in-betweenadjacentrays

  12. Aliasing • Causeofaliasing • Sampling frequencyis not highenoughto cover all details • ItisbelowtheNiquistlimit Shannons Sampling Theorem: The signalhastobesampled at a frequencythatisequaltoorhigherthantwotimesthehighestfrequency in thesignal

  13. Aliasing • Aliasing artefacts • Spatialaliasing • Temporal aliasing

  14. Antialiasing • Howtoavoidaliasingcausedby an undersamplingofthesignal, i.e. thesamplingfrequencyis not highenoughto cover all details • Supersampling - increasesamplingfrequency • Prefiltering - decreasethehighestfrequency in thesignal, i.e. filterthesignalbeforesampling • Postfiltering– filtering after sampling, but just blurrestheimage

  15. Antialiasing • Supersampling- increasesamplingfrequency • Usemorerays per pixel, i.e. virtuallyincreasetheresolutionofthepixel raster • e.g. use 4x4 rays per pixel and computeaverageof all 16 colorsas final pixelcolor • Sharp edgesarewashed out • OK, but doesn´teliminatealiasingbecause sharp edgescontaininfinitelyhighfrequencies

  16. Antialiasing • Supersampling • Regular supersampling

  17. Antialiasing • Filtering: average weighted samples

  18. Antialiasing • Filtering example

  19. Antialiasing • Filtering - jitteredinsteadofregularsampling

  20. Antialiasing • Regular sampling • Visibilityofaliasesalso causedbytheregularsamplinggrid • Human visualsystemis sensitive againstregularstructures, but ratherinsensitiveagainsthigh frequencynoise • Stochasticsupersampling • Place samplesrandomlywithinpixel • Alias frequenciesareconvertedtonoise • But canresult in clustersof sample

  21. Antialiasing • Poisson-disksampling • Random generationofsampleswithlimitfortheminimumdistancebetweensamples • Jitteredsampling • Random jitteringfromregulargridpoints • Stratifiedrandomsampling • Regular partitioningofpixelregion • Onerandom sample per partition

  22. Antialiasing • Comparison • Regular, 1x1Regular 3x3Regular, 7x7Jittered, 3x3Jittered, 7x7

  23. Antialiasing • Example:

  24. Antialiasing • Example:

  25. Antialiasing • Example:

  26. Antialiasing • Example:

  27. Antialiasing • Prefiltering • Antialiasing beforesampling (mainlyused in texturemapping) • Filtering (smoothing) a signaltoremovedetailsbelowthefrequencywhichisusedto sample thesignal

  28. Antialiasing • Prefiltering combines color contributions into a pixel

  29. Antialiasing in texturemapping • Manytexels fall ontoonepixels

  30. Antialiasing in texturemapping • Mip-Mapping:prefilteredlevels of detail (LOD) in a pyramid • At every level:average 2x2texels from thefiner levelinto one texel

  31. Antialiasing in texturemapping

  32. Antialiasing in texturemapping

  33. Antialiasing in texturemapping • Mip-Mapping: howdoesitwork? • When a fragmentistexturemapped, themip-maplevelatwhichthetexelsizeisequaltothepixelsizeiscomputed • Fromthislevelthetextureisthensampled • Itremainstobeansweredhowtheleveliscomputed

  34. Antialiasing in texturemapping • Wewanttoknowwhatthesizeofonetexelwrtthesizeofonepixelis – thisallowsestimatinghowmanytexels fall intoonepixel

  35. Antialiasing in texturemapping • Computing themip-maplevel:Check screen pixel “size” in texture coordinates less than one texel per pixelwe call this magnification more than one texel per pixelwe call this minification u,v: fragmentstexturecoordinates x,y: pixelcoordinates

  36. Antialiasing in texturemapping

  37. Antialiasing in texturemapping without MipMapping with MipMapping

  38. Antialiasing in texturemapping Isotropicfiltering (mipmapping) Anisotropicfiltering

  39. Sample 0 assign Select resolution interpolate Sample 1 Antialiasing in texturemapping • Mip-Mapping • The mip-maponlystores a discretesetoflevels • Ifpixelsizematchestexelsizeat a level in between, itisinterpolatedbetweenthetwoadjacentlevels Bilinear in texture + linear betweenlevels = trilinear

  40. Summary • Quality ofrenderingstronglydepends on antialiasingalgorithmsused • Typically, supersampling in combinationwithprefilteringisused • Supersamplingandmipmapping • Wearenowreadytoimplement a highquality and efficientraytracingalgorithm • Whatcomesnextis an alternative imagesynthesisapproachbased on theprojectionofgeometryontotheimage plane

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