Quick survey about PRT Valentin JANIAUT KAIST (Korea Advanced Institute of Science and Technology)

2 Some Math before. ● Wavelet ● Spherical Harmonic ● Spherical Radial Basis Function

3 Wavelet: How to compress signal Fourier Transform Wavelet Discrete Cosinus transform Goal: Express a function as a set of coefficients. Sum of sinus and cosinus. NO TIME (OR SPACE) RESOLUTION Fourier transform restricted to cosinus. Cut the signal into different window for better analysis.

4 Wavelet: Intuitive approach FEATURES Orthonormal basis Catch the high-frequency Quite complicate Used in JPEG-2000 A lot of possible kernels

5 Spherical Harmonic FEATURES Spherical basis Catch large features Quite complicate Used in geology Use Legendre polynomial as kernel.

6 Spherical Radial Basis Function Gaussian Distribution FEATURES Spherical basis Catch high and low frequency. Fairly simple Use Gaussian or Poison kernel

7 What is PRT? ● A set of technique to pre-compute various function related to the Radiance Transfer. How to integrate the rendering equation over large- scale lighting environment? ● Monte-Carlo Ray Tracing ● Radiosity ● Multi-pass rendering No real-time

8 Some key paper in this field 2002 Precomputed Radiance Transfer for Real-Time Rendering in dynamic, low-frequency lighting environment. [Sloan] Clustered principal components for precomputed radiance transfer. [Sloan] All frequency shadows using non-linear wavelet lighting approximation. [Ng] Precomputed Radiance Transfer: Theory and Practice SIGGRAPH05 Course All frequency interactive relighting of translucent objects with Single and Multiple Scattering. [Wang] Importance sampling of products from illumination and BRDF using spherical radial basis functions. [Tsai] Real-time editing and relighting of homogeneous translucent materials. [Wang] All-frequency Rendering of Dynamic, Spatially-Varying Reflectance. [Wang]

9 An example of Transfer Matrix Rendering Equation Geometry relightingImage Relighting B = TL

10 Precomputed Radiance Transfer for Real-Time Rendering in dynamic, low-frequency lighting environment. ● Use Spherical Harmonic to represent how an object scatter light. LIMITS ● No High-Frequency (too many SH coeff.) ● Only diffuse and glossy surface.

11 Clustered principal components for precomputed radiance transfer ● Similar than the previous approach. ● Add support for diffuse multiple scattering

12 All frequency shadows using non- linear wavelet lighting approximation ● Same framework than [SLOAN02] ● Approximate the environment map in a wavelet basis keeping only the largest terms (=non-linear approximation) LIMITS ● Rigid scene (but relighting is OK) ● Only diffuse and glossy surface.

13 All frequency interactive relighting of translucent objects with Single and Multiple Scattering. ● Add support for Diffuse Multiple Scattering in [Ng] framework. with T is precomputed into Wavelet like in [Ng].

14 Importance sampling of products from illumination and BRDF using spherical radial basis functions. ● No transfer function, use directly precomputation of BRDF and the environment map into SRBF. LIMITS ● Support only BRDF. ● Needs more data, but only one product at the Running time.

15 Real-time editing and relighting of homogeneous translucent materials. ● Improved version of the previous article. ● Reading not done yet.

16 All-frequency Rendering of Dynamic, Spatially-Varying Reflectance ● Proposed an unified technique to represent SVBRDF using SRBF. ● Using the micro-facet model.

17 Back to our problem Hair Geometry dependent. Fiber property dependent.

18 Current solution Implemented using marschner model. Extract the SRBF coefficient using L- BFGS-B solver like [Tsai08] DOES NOT SOLVE THE HAIR GEOMETRY DEPENDANT TERMS

19 Better approach ● Find a way to pre-compute the different terms of the equation using SRBF. ● Look to the visibility map ● Look to PRT techniques with support to geometry modification

20 Papers to read ● Local, deformable precomputed radiance transfer [Sloan05] ● Generalized wavelet product integral for rendering dynamic glossy objects [Sun06] ● Real-time soft shadows in dynamic scenes using spherical harmonic exponentiation [Ren06] ● Real-time, all-frequency shadows in dynamic scenes [Annen08]