Measurement Equation

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Measurement Equation

• Ray space (throughput) measure
• for bundle of rays r
• Define F space of functions over ray space
• F is a Hilbert space
• A linear operator is a linear mapping

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Measurement Equation

• Imagine a sensor anywhere in the scene
• It has a response to its input
• So a measurement is
• Light paths start with an emitter and end at a
  measurement
• Can also do paths in reverse, measurement to
  light
• Call the quantity transported in reverse
  importance

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Importance transport

• Importance transport requires adjoint operators
  for each light transport operator
• The adjoint of an operator is its
  conjugate-transpose, defined wrt some inner
  product
• Wed like our transport operators to be
  self-adjoint
• Light transport and importance transport would be
  the same
• Photon tracing, reverse path tracing, etc all
  kinds of importance tracing

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Non-symmetric BSDFs

• When are transport operators not self adjoint?
• When the BSDF they use is not symmetric
• When are BSDFs not symmetric?
• Refraction (with improper formulation)
• Refracted rays need to be scaled by
• Phong shading (with regular angle measure)
• Shading normals (fake normals for shading, bump
  mapping, etc)