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

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Measurement equation

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


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‚Äôd 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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