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Motivation

The Natural-Constraint Representation of the Path Space for Efficient Light Transport Simulation Anton S. Kaplanyan 1,2 and Johannes Hanika 1 and Carsten Dachsbacher 1 1 Karlsruhe Institute of Technology, 2 Lightrig. Motivation. [Wikipedia Commons]. [Wikipedia Commons].

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Motivation

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  1. The Natural-Constraint Representation of the Path Space for Efficient Light Transport Simulation Anton S. Kaplanyan1,2 and Johannes Hanika1and Carsten Dachsbacher1 1Karlsruhe Institute of Technology, 2Lightrig

  2. Motivation [Wikipedia Commons] [Wikipedia Commons] Rendered with manifold exploration [JakobMarschner12] Jewelry Rendered with out method

  3. Intuition: Constraints in a Lens System • Two endpoints with specular constraints

  4. Idea: Deviate from Specular Path • Rough scattering: use soft constraints

  5. Outline • Introduction • Prior work • New generalized coordinates • Properties of the domain • Overview: Metropolis light transport • New half-vector mutation • Results • Conclusion Theory Practice

  6. Rendering with Light Transport • Generate image by computing • Flux incident on the sensor • Sample all possible paths • Stochastic integration Path space

  7. Path Integral Framework • Path integral • Measurement contribution is in area measure • Becomes singular with specular BSDFs Emission BSDFs Absorption Geometric terms

  8. Prior Work: Specular Paths • Specular paths are hard constraints • Obey Fermat principle [Alhazen1021] • Ray transfer matrices used in optics [Gauss1840] • Pencil tracing in graphics [Shinya87] End point Start point Optical system

  9. Prior Work: Specular Paths • Rendering specular paths with geometric knowledge • Solving for constraints [MitchellHanrahan92] • First and second order analysis [ChenArvo00] • Predictor-corrector perturbations [JakobMarschner12] • Our work is inspired by manifold exploration [Mitchell and Hanrahan 1992] [Chen and Arvo 2000] [Jakob and Marschner 2012]

  10. The Domain of Halfway Vectors for Light Paths Theory

  11. Generalized Coordinates • Generalized coordinates: two endpoints + halfway vectors • Specular surfaces: halfway vectors coincide with surface normal • If halfway vector surface normal Path deviates from the specular path

  12. Deviating the Half Vectors • A path in generalized coordinates

  13. Path Contribution with New Formulation • Path measurement in new domain • Only one geometric term left (avoid singularities) • Transfer matrices are extended to scattering Area measure Emission Scattering distributions Camera responsivity Transfer matrix + Geometric term = Generalized G Half vector domain

  14. Simplified Measurement Projected solid angle Surface area measure [Jakob13] [Walter et al.07] Half vector domain

  15. Decomposition of Path Integral • Decorrelated islands • Set of 2D integrals • Easy-to-predict spectrum • Mostly changes local BSDF • Well-studied sampling

  16. Mutation Strategy for Metropolis Light Transport Practical Rendering

  17. Metropolis Light Transport • Take a path and perturb it [VeachGuibas97] • Specialized mutation strategies • Manifold exploration (ME) [JakobMarschner12]

  18. Metropolis Light Transport

  19. Half-vector Space Mutation • Mutation 1. Perturb half-vectors 2. Find a new path • Similar machinery to ME (see ME paper) • Specular chains: fall back to ME • Jump over geometric parts • Take prediction as a proposal

  20. Importance-Sample All BSDFs • Query avg. BSDF roughness • Approximate with Beckmann lobe • Sample as ~2D Gaussian • Known optimal step sizes from MCMC

  21. Results: Kitchen HSLT VMLT MEMLT PSSMLT HSLT

  22. Results: Necklace VMLT HSLT MEPT MEMLT HSLT

  23. Conclusion • Convenient domain for paths on surfaces • Generalized coordinates • Beneficial properties of path integral • Sampling in generalized coordinates • Robust light transport (especially glossy and specular) • Importance sampling of all BSDFs along a path • Practical stratification for MLT

  24. Limitations and Future Work • Geometric smoothness • Level of detail for displaced geometry • Rare events: needle in a haystack • Probability-1 search • Participating media • More dimensions, new soft constraints

  25. Thank You Questions?

  26. Backup: Stratification for MCMC • Expected change on the image from changes in half vectors Without stratification With stratification

  27. Backup: Spectral Sampling • How to distribute step sizes among half vectors? • Spectral sampling for MC [SubrKautz2013] • Convex combination based on bandwidth (see paper) Without redistribution With redistribution

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