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Triple Product Wavelet Integrals for All-Frequency Relighting (2004)

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by Ren Ng , Ravi Ramamoorthi , Pat Hanrahan
Citations:85 - 9 self
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BibTeX

@MISC{Ng04tripleproduct,
    author = {Ren Ng and Ravi Ramamoorthi and Pat Hanrahan},
    title = {Triple Product Wavelet Integrals for All-Frequency Relighting},
    year = {2004}
}

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Abstract

This paper focuses on efficient rendering based on pre-computed light transport, with realistic materials and shadows under allfrequency direct lighting such as environment maps. The basic difficulty is representation and computation in the 6D space of light direction, view direction, and surface position. While image-based and synthetic methods for real-time rendering have been proposed, they do not scale to high sampling rates with variation of both lighting and viewpoint. Current approaches are therefore limited to lower dimensionality (only lighting or viewpoint variation, not both) or lower sampling rates (low frequency lighting and materials) . We propose a new mathematical and computational analysis of pre-computed light transport. We use factored forms, separately pre-computing and representing visibility and material properties. Rendering then requires computing triple product integrals at each vertex, involving the lighting, visibility and BRDF. Our main contribution is a general analysis of these triple product integrals, which are likely to have broad applicability in computer graphics and numerical analysis. We first determine the computational complexity in a number of bases like point samples, spherical harmonics and wavelets. We then give efficient linear and sublinear-time algorithms for Haar wavelets, incorporating non-linear wavelet approximation of lighting and BRDFs. Practically, we demonstrate rendering of images under new lighting and viewing conditions in a few seconds, significantly faster than previous techniques.

Citations

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135 All-frequency shadows using non-linear wavelet lighting approximation - Ng, Ramamoorthi, et al. - 2003
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87 Clustered principal components for precomputed radiance transfer - SLOAN, HALL, et al.
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57 B.: A framework for the analysis of error in global illumination algorithms - ARVO, TORRANCE, et al. - 1994
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39 Textures and radiosity: Controlling emission and reflection with texture maps - Gershbein, Schröder, et al. - 1994
38 Matrix radiance transfer - LEHTINEN, KAUTZ
32 Spherical harmonics: an elementary treatise on harmonic functions with applications - MACROBERT - 1967
29 Interactive design of complex time-dependent lighting - Dorsey, Arvo, et al. - 1995
20 Bi-scale radiance transfer - Sloan, Liu, et al.
13 Group theory and its application in physics - Inui, Tanabe, et al. - 1978
5 importance sampling of environment maps - Structured
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