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Measurement Equation

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

- 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

- 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 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

- 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)

- Refraction (with improper formulation)

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