A Signal-Processing Framework for Inverse Rendering Ravi - PowerPoint PPT Presentation

A Signal-Processing Framework for Inverse Rendering Ravi Ramamoorthi Pat Hanrahar Computer Graphics Laboratory , Stanford University Albert Liu Alessandro Farsi CS 6630 Realistic Image Synthesis

Inverse Rendering Inverse Photographs Rendering Algorithm BRDF Lighting Geometric model

Why inverse rendering Precision measurement Data extraction

Signal-Processing Framework • How much information can I extract? • The problem is well- or ill-posed? • What is the best way to express the model? Before only “ handwaving ” explanation

Spherical Harmonics L=0 L=1 L=2 L=3 m=2 m=3 m=0 m=1 m=-2 m=-1 m=-3

Spherical Harmonics Analog to Fourier base for angles 2 l 1 l m m , m cos e im Y l P l 4 l m Coefficients obtained via projection m C l f , , m Y l Orthonormality

Inverse rendering • Known geometry w • Fixed ‘far’ light w ’ • Reflection B L ' ', (a,b) B , , L R , ' ', ' Looks like convolution (and convolution simple in Fourier’s space)

Inverse Rendering • Plugging in SH m R , m p , r p r B , , L l Y l ' Y q ' Y s q , s • Rotation in SH l R , l m l Y m D m , m ' Y m ' • Symmetry in BRDF p , r p q , s q , s

Inverse Rendering • Reflection expanded in SH base l , m C p , q l , m l l l , m B p , q B , , , , l L m C p , q , , p , q BRDF l l l , m l L m B p , q p , q Normalization Reflection (measured) Lightings

Mirror BRDF

Single directional source

Lambertian BRDF

Lambertian BRDF

Phong BRDF

Phong BRDF

Microfacet BRDF

Decomposition of Lights for Microfacets

BRDF Recovery

From Complex Geometry

Questions?