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

2. 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 Don Fussell

3. 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 Don Fussell

4. 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 Don Fussell

5. 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 Don Fussell