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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 . Measurement Equation. Imagine a sensor anywhere in the scene It has a response to its input

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Presentation Transcript
measurement equation
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

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell

measurement equation1
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

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell

importance transport
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
    • We’d 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

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell

non symmetric bsdfs
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)

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell

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