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

a signal processing framework for inverse rendering
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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


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SLIDE 1

A Signal-Processing Framework for Inverse Rendering

Albert Liu Alessandro Farsi

CS 6630 Realistic Image Synthesis Ravi Ramamoorthi Pat Hanrahar Computer Graphics Laboratory , Stanford University

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SLIDE 2

Inverse Rendering

Photographs Geometric model

Inverse Rendering Algorithm

Lighting BRDF

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SLIDE 3

Why inverse rendering

Precision measurement Data extraction

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SLIDE 4

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

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SLIDE 5

L=0 L=1 L=2 L=3

m=1 m=0 m=2 m=3 m=-3 m=-2 m=-1

Spherical Harmonics

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SLIDE 6

Spherical Harmonics

Analog to Fourier base for angles Coefficients obtained via projection Orthonormality

Yl

m ,

2 l 1 4 l m l m Pl

m cos

eim

Cl

m

f ,

Yl

m

,

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SLIDE 7

Inverse rendering

  • Known geometry
  • Fixed ‘far’ light
  • Reflection

Looks like convolution (and convolution simple in Fourier’s space)

(a,b)

w w’

B , , L R , ' ', '

B L ' ',

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SLIDE 8

Inverse Rendering

Ym

l R ,

Dm,m'

l m

Ym'

l

B , , Ll

m q,s p,r

Yl

m R ,

' Yq

p

' Ys

r

q,s p,r q,s p

  • Plugging in SH
  • Rotation in SH
  • Symmetry in BRDF
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SLIDE 9

Inverse Rendering

  • Reflection expanded in SH base

l Lm l p,q l

Bp,q

l,m

B , ,

l Lm l p,q l

Cp,q

l,m

, , Bp,q

l,m Cp,q l,m

, ,

Normalization Lightings BRDF Reflection (measured)

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SLIDE 10

Mirror BRDF

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SLIDE 11

Single directional source

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SLIDE 12

Lambertian BRDF

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SLIDE 13

Lambertian BRDF

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SLIDE 14

Phong BRDF

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SLIDE 15

Phong BRDF

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SLIDE 16

Microfacet BRDF

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SLIDE 17

Decomposition of Lights for Microfacets

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SLIDE 18

BRDF Recovery

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SLIDE 19

From Complex Geometry

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SLIDE 20

Questions?