Anisotropic Spherical Gaussians

Kun Xu1, Wei-Lun Sun1, Zhao Dong2, Dan-Yong Zhao1, Run-Dong Wu1, Shi-Min Hu1
1Tsinghua University
2Cornell University

Abstract: We present a novel anisotropic Spherical Gaussian (ASG) function, built upon the Bingham distribution [Bingham 1974], which is much more effective and efficient in representing anisotropic spherical functions than Spherical Gaussians (SGs). In addition to retaining many desired properties of SGs, ASGs are also rotationally invariant and capable of representing all-frequency signals. To further strengthen the properties of ASGs, we have derived approximate closed-form solutions for their integral, product and convolution operators, whose errors are nearly negligible, as validated by quantitative analysis. Supported by all these operators, ASGs can be adapted in existing SG-based applications to enhance their scalability in handling anisotropic effects. To demonstrate the accuracy and efficiency of ASGs in practice, we have applied ASGs in two important SG-based rendering applications and the experimental results clearly reveal the merits of ASGs.

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Supplemental Video: [AVI 45.8M]

Bibtex: @article{Xu13sigasia,
author = {Kun Xu and Wei-Lun Sun and Zhao Dong and Dan-Yong Zhao and Run-Dong Wu and Shi-Min Hu},
title = {Anisotropic Spherical Gaussians},
journal = {ACM Transactions on Graphics},
volume = {32},
number = {6},
year = {2013},
pages = {209:1--209:11},