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A constructive theory of sampling for image synthesis using reproducing kernel bases

Lessig, Christian and Desbrun, Mathieu and Fiume, Eugene (2014) A constructive theory of sampling for image synthesis using reproducing kernel bases. ACM Transactions on Graphics, 33 (4). Art. No. 55. ISSN 0730-0301. http://resolver.caltech.edu/CaltechAUTHORS:20140819-131956034

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Abstract

Sampling a scene by tracing rays and reconstructing an image from such pointwise samples is fundamental to computer graphics. To improve the efficacy of these computations, we propose an alternative theory of sampling. In contrast to traditional formulations for image synthesis, which appeal to nonconstructive Dirac deltas, our theory employs constructive reproducing kernels for the correspondence between continuous functions and pointwise samples. Conceptually, this allows us to obtain a common mathematical formulation of almost all existing numerical techniques for image synthesis. Practically, it enables novel sampling based numerical techniques designed for light transport that provide considerably improved performance per sample. We exemplify the practical benefits of our formulation with three applications: pointwise transport of color spectra, projection of the light energy density into spherical harmonics, and approximation of the shading equation from a photon map. Experimental results verify the utility of our sampling formulation, with lower numerical error rates and enhanced visual quality compared to existing techniques.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1145/2601097.2601149DOIArticle
http://dl.acm.org/citation.cfm?doid=2601097.2601149PublisherArticle
Additional Information:© 2014 ACM, Inc. Publication Date: July 2014 We thank Tyler de Witt and George Drettakis for helpful discussions and the anonymous reviewers for their constructive criticism. Shuoran Yang (now ETH Zürich) helped with implementing the application in Sec. 4.1 and Eric Yao (now UC Berkeley) explored the use of reproducing kernel bases for wavelet space discussed in Sec. 4 in the supplementary material. Support by NSERC, GRAND National Centres of Excellence, and by NSF grant CCF-1011944 is gratefully acknowledged. CL would also like to thank the computer graphics group at TU Berlin for their hospitality.
Funders:
Funding AgencyGrant Number
NSERC (Canada)UNSPECIFIED
GRAND National Centres of ExcellenceUNSPECIFIED
NSFCCF-1011944
Subject Keywords:sampling; light transport simulation; reproducing kernel Hilbert space
Record Number:CaltechAUTHORS:20140819-131956034
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20140819-131956034
Official Citation:Lessig, C., Desbrun, M., Fiume, E. 2014. A Constructive Theory of Sampling for Image Synthesis using Reproducing Kernel Bases. ACM Trans. Graph. 33, 4, Article 55 (July 2014), 14 pages. DOI = 10.1145/2601097.2601149 http://doi.acm.org/10.1145/2601097.2601149.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:48690
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:19 Aug 2014 20:59
Last Modified:19 Aug 2014 21:00

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