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Interactive Hair Rendering and Appearance Editing under Environment Lighting

This research explores the challenges of hair appearance editing under natural illumination and proposes a solution using circular Gaussians to approximate the scattering function. The results show accurate and efficient representation of hair scattering parameters under environment lighting.

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Interactive Hair Rendering and Appearance Editing under Environment Lighting

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  1. Interactive Hair Rendering and Appearance Editing under Environment Lighting Kun Xu1, Li-QianMa1, Bo Ren1, Rui Wang2, Shi-Min Hu1 1Tsinghua University 2University of Massachusetts

  2. Hair Appearance Editing under Environment Lighting • Motivation • hair appearance editing • Natural illumination • Challenges • Light integration complexity

  3. Related Works • Hair scattering function/models • Self Shadowing • deep shadow maps [Lokovic & Veach 2000] • opacity shadow maps [Kim & Neumann 2001] • density clustering [Mertens et al. 2004] • deep opacity maps [Yuksel & Keyser 2008] • occupancy maps [Sintorn & Assarson 2009] [Kajiya & Kay 89] [Zinke & Webber 07] [Marschner 03] [Sadeghi 10] [d’Eon 11]

  4. Related Works • Multiple scattering • Photon Mapping [Moon & Marschner 2006] • Spherical Harmonics [Moon et al. 2008] • Dual Scattering [Zinke et al. 2008] • Environment lighting [Ren 2010] • Model lighting using SRBFs • Precomputed light transport into4D tables • Fix hair scattering properties hair appearance editing under environment lighting remains unsolved

  5. Light Integration Single scattering • : environment lighting • : self shadowing • : hair scattering function

  6. Light Integration Single scattering • Approximate by a set of SRBFs [Tsai and Shih 2006]

  7. Light Integration Single scattering • Approximate by a set of SRBFs [Tsai and Shih 2006] • Move T out from the integral [Ren 2010] Problem: evaluate scattering Integral

  8. Single ScatteringIntegral • Previous Approach [Ren 2010] • Precompute the integral into 4D table • Our key insight • Is there an approximated analytic solution? • YES • Decompose SRBF into products of circular Gaussians • Approximate scattering function by circular Gaussians

  9. Circular Gaussian • SRBF (Spherical Radial Basis Function) • Typically spherical Gaussian • Widely used in rendering • Environment lighting [Tsai and Shih 2006] • Light Transport [Green 2007] • BRDF [Wang 2009] • Circular Gaussian • 1D case of SRBF • Share all benefits of SRBFs

  10. Circular Gaussian • Useful Properties • Local approximation by Gaussian , error < 1.3%, • Closed on product center bandwidth

  11. Circular Gaussian • SRBF Decomposition = * 1D Longitudinal circular Gaussian 1D Azimuthal circular Gaussian 2D SRBF

  12. Scattering Function • Sum of three modes: R, TT, TRT [Marschner03] R mode: Reflection (p=0) TRT Mode: Transmission-Reflection-Transmission (p=2) hair fiber longitudinal angle TT Mode: Transmission-Transmission (p=1) tilted angle

  13. Scattering Function • Sum of three modes: R, TT, TRT [Marschner03] R mode: Reflection (p=0) hair fiber cross section azimuthal angle TT Mode: Transmission-Transmission (p=1) TRT Mode: Transmission-Reflection-Transmission (p=2)

  14. Scattering Function • Definition [Marschner03]

  15. Scattering Function • Definition [Marschner03] • Longitudinal function : normalized Gaussian simulates specular reflection along longitudinal direction

  16. Scattering Function • Definition [Marschner03] • Azimuthal function • Complex analytic functions • Different for each mode • Fresnel reflection term • exponential attenuation term

  17. Azimuthal Functions • R mode • Fresnel term (Schlick’s approximation) • Approximated by polynomial of

  18. Azimuthal Functions • TT mode • Simple shape: look like Gaussian • approximated by 1 circular Gaussian centered at • Parameters fitted by preserving energy

  19. TT mode approximation • : coefficient • set as the peak value, • : bandwidth • Preserving energy • : fresnel reflection • : attenuation function

  20. TT mode approximation • : coefficient • set as the peak value, • : bandwidth • Preserving energy • : fresnel reflection • : attenuation function Precompute into 2D tables 4-th order Taylor expansion

  21. Azimuthal Functions • TRT mode: • Shape: sum of Circular Gaussians • : approximated by 3 circular Gaussians • approximated by 1 circular Gaussian • Fitted by preserving energy similar as TT mode

  22. Single ScatteringIntegral Analytic Integral Circular Gaussian Circular Gaussian Gaussian Cosine / Circular Gaussian • =: SRBF decomposition • : scattering func. def.

  23. Light Integration Multiple scattering [Ren 2010] • Spread function: • BCSDF: [Zinke2010] • Approximate scattering function similarly Analytic Integral

  24. Results

  25. Results

  26. Results

  27. Performance • Testing Machine • Intel Core 2 Duo 3.00 GHz CPU, 6 GB RAM NVIDIA GTX 580 • 720 * 480 with 8x antialias

  28. Conclusion • 1D circular Gaussian • Accurate and compact for representing hair scattering functions • Closed form integral with SRBF lights • New effects • interactive hair appearance editing under environment lighting • Rendering of spatially varying hair scattering parameters under environment lighting

  29. Future works • View transparency effects [Sintorn and Assarsson 2009] • Other hair scattering models • Artist friendly model [Sadeghi2010] • Energy conserving model [d’Eon2011] • Near-field light sources • Accelerate off-line hair rendering

  30. Acknowledgement • Anonymous Siggraph and Siggraph Asia reviewers • Ronald Fedkiw, CemYuksel, Arno Zinke, Steve Marschner • Sharing their hair data • ZhongRen • Useful discussion Thank you for your attention.

  31. Circular Gaussian vs Gaussian • 1D Circular Gaussian • Defined on unit circle : • 1D Gaussian • Defined on x-axis

  32. Single ScatteringIntegral Outer integral inner integral: • =: SRBF seperation • : scattering func. def. • Two dimensional integral over and

  33. Inner Integral R Mode • Hair scattering function approx. • polynomial of : • Inner integral Precompute into 2D tables

  34. Inner IntegralTT & TRT modes • Hair scattering function approx. • sum of circular Gaussians : • Inner integral Analytic Integral

  35. Outer Integral Gaussian Smooth Function Piecewise Linear approximation Analytic Integral

  36. Summary ofSingle Scattering • Hair scattering function approximation • R mode: polynomial of cosine • TT/TRT mode: circular Gaussian • Inner integral • R mode: 2D tables • TT/TRT mode: 2D tables, analytic integral • Outer integral • Piecewise linear approximation for smooth func. • Analytic integral.

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