Appearance Models for Graphics

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Appearance Models for Graphics

• COMS 6998-3
• Brief Overview of Reflection Models

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Assignments

• E-mail me name, status, Grade/PF. If you dont
  do this, you wont be on class list. and give me
  e-mails now
• Let me know if you dont receive e-mail by
  tomorrow
• E-mail me list of papers to present (rank 4 in
  descending order). Must receive by Fri or you
  might be randomly assigned.
• Next week, e-mail brief descriptions of proposed
  projects. Think about this when picking papers

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Today

• Appearance models
• Physical/Structural (Microfacet
  Torrance-Sparrow, Oren-Nayar)
• Phenomenological (Koenderink van Doorn)

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n
a
?a
da
Masking
Interreflection
Shadowing
dA
Symmetric Microfacets
Brdf of grooves simple specular/Lambertian
Torrance-Sparrow Specular Grooves. Specular
direction bisects (half-angle) incident, outgoing
directions
Oren-Nayar Lambertian Grooves. Analysis more
complicated. Lambertian plus a correction
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Phenomenological BRDF model Koenderink and van
Doorn

• General compact representation
• Domain is product of hemispheres
• Same topology as unit disk, adapt basis
• Zernike Polynomials

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Paper presentations

• Torrance-Sparrow (Kshitiz)
• Oren-Nayar (Aner)
• Koenderink van Doorn (me, briefly)

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Phenomenological BRDF model Koenderink and van
Doorn

• General compact representation
• Preserve reciprocity/isotropy if desired
• Domain is product of hemispheres
• Same topology as unit disk, adapt basis
• Outline
• Zernike Polynomials
• Brdf Representation
• Applications

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Zernike Polynomials

• Optics, complete orthogonal basis on unit disk
  using polynomials of radius
• R has terms of degree at least m. Even or odd
  depending on m even or odd
• Orthonormal, using measure ?d?d?

n-m even m?n
Cool Demo http//wyant.opt-sci.arizona.edu/zernik
es/zernikes.htm
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m
0 1
2
n
m ? n
m ? n
0
n-m must be even
m ? n
n-m must be even
1
n-m must be even
n-m must be even
2
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Hemispherical Zernike Basis

• Measure Disk Hemisphere sin(?)d?d?
• Set

?d?d?
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BRDF representation

• Reciprocity aklmnamnkl

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BRDF representation

• Reciprocity aklmnamnkl
• Isotropy Dep. only on ? ?i-?r Expand as a
  function series of form cos(m?i-?r)
• Can define new isotropic functions
• Symmetry (Reciprocity) alnm anlm

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BRDF Representation Properties

• First two terms in series
• 5 terms to order 2,14 to order 4, 55 order 8
• Lambertian First term only
• Retroreflection ?ln
• Mirror Reflection (-1)m ?ln
• Very similar to Fourier Series

alnm ?l0 ?n0 ?m0 alnm ?ln alnm (-1)m ?ln
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Applications

• Interpolating, Smoothing BRDFs
• Fitting coarse BRDFs (e.g. CURET). Authors
  Order 2 often sufficient
• Extrapolation
• Some BRDF models can be exactly represented
  (Lambertian, Opik)
• Others to low order after filtering/truncation
• High-order terms are typically noisy

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Discussion/Analysis

• Strong unified foundation
• Spectral analysis interesting in own right
• Ringing!! Must filter
• Dont handle BRDF features well
• Specularity requires many terms
• Theoretically superior to spherical harmonics but
  in practice?