max planck institut informatik

Progressive Spectral Ray Differentials
@ Vision, Modelling and Visualization Workshop (VMV) 2014

Oskar Elek^1,2      Pablo Bauszat^3,1      Tobias Ritschel^1,2      Marcus Magnor^3,1      Hans-Peter Seidel^{1     
1}MPI Informatik      ²MMCI / Saarland University      ³Technical University Braunschweig     

The main limitation of Spectral Ray Differentials (SRD) is that the solution they produce contains bias, which is inherent to the first-order approximation we employ. This work resolves this issue by progressively decreasing the size of each sample's footprint, so that the solution converges to the correct, unbiased one. At the same time the variance reduction properties of SRD still remain, so that producing a smooth solution is still about an order of magnitude faster than with basic Monte Carlo solvers.

Abstract

Light travelling though refractive objects can lead to beautiful colourful illumination patterns resulting from dispersion on the object interfaces. While this can be accurately simulated by stochastic Monte-Carlo methods, their application is costly and leads to significant chromatic noise. This is greatly improved by applying spectral ray differentials, however, at the cost of introducing bias into the solution. We propose progressive spectral ray differentials, adapting concepts from other progressive Monte-Carlo methods. Our approach takes full advantage of the variance-reduction properties of spectral ray differentials but progressively converges to the correct, unbiased solution in the limit.

Downloads

VMV Paper (15 MB)

Slides (static) (2.5 MB)

Slides (animated) (120 MB)

Caustic – Spectral Differentials (160 MB uncompressed)

Basic MC convergence (pass) (69 MB uncompressed)

Basic MC convergence (acc.) (69 MB uncompressed)

SRD convergence (pass) (69 MB uncompressed)

SRD convergence (acc.) (69 MB uncompressed)

PSRD convergence (pass) (69 MB uncompressed)

PSRD convergence (acc.) (69 MB uncompressed)

Citation

Spectral Ray Differentials
Best Student Paper @ Eurographics Symposium on Rendering (EGSR) 2014 and Computer Graphics Forum 2014

Oskar Elek^1,2      Pablo Bauszat^3,1      Tobias Ritschel^1,2      Marcus Magnor^3,1      Hans-Peter Seidel^{1     
1}MPI Informatik      ²MMCI / Saarland University      ³Technical University Braunschweig     

We extend the classic (spatial) ray differentials proposed by Igehy in 1999. These can be applied to tracing camera or light samples (left half of the figure); the represented information can then be used as a reconstruction prior, most notably for texture and caustic filtering. Our work extends these to the spectral domain on light transport (right half of the figure). In analogy with the spatial ray differentials the information carried by the spectral differentials can be used to reconstruct spectrally-variant phenomena, primarily arising from dispersive refraction.

Abstract

Light refracted by a dispersive interface leads to beautifully colored patterns that can be rendered faithfully with spectral Monte-Carlo methods. Regrettably, results often suffer from chromatic noise or banding, requiring high sampling rates and large amounts of memory compared to renderers operating in some trichromatic color space. Addressing this issue, we introduce spectral ray differentials, which describe the change of light direction with respect to changes in the spectrum. In analogy with the classic ray and photon differentials, this information can be used for filtering in the spectral domain. Effectiveness of our approach is demonstrated by filtering for offline spectral light and path tracing as well as for an interactive GPU photon mapper based on splatting. Our results show considerably less chromatic noise and spatial aliasing while retaining good visual similarity to reference solutions with negligible overhead in the order of milliseconds.

Downloads

EGSR Paper (21 MB)

Supplemental Material – Derivation (0.1 MB)

Supplemental Material – Figures (22 MB)

Slides (static) (3 MB)

Slides (animated) (65 MB)

Submission Video (10 MB MPEG4)

Caustic – Spectral Decomposition (40 MB uncompressed)

Caustic – Naive Sampling (160 MB uncompressed)

Caustic – Spectral Differentials (160 MB uncompressed)

Submission Video

Citation