Measurement Equation

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 2006 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 2006 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 2006 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 2006 Don Fussell