Measurement Equation

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# Measurement Equation - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about 'Measurement Equation' - kanoa

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Presentation Transcript
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 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 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
• 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)