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Noise-Resistant Fitting for Spherical Harmonics
March/April 2006 (vol. 12 no. 2)
pp. 254-265

Abstract—Spherical harmonic (SH) basis functions have been widely used for representing spherical functions in modeling various illumination properties. They can compactly represent low-frequency spherical functions. However, when the unconstrained least square method is used for estimating the SH coefficients of a hemispherical function, the magnitude of these SH coefficients could be very large. Hence, the rendering result is very sensitive to quantization noise (introduced by modern texture compression like S3TC, IEEE half float data type on GPU, or other lossy compression methods) in these SH coefficients. Our experiments show that, as the precision of SH coefficients is reduced, the rendered images may exhibit annoying visual artifacts. To reduce the noise sensitivity of the SH coefficients, this paper first discusses how the magnitude of SH coefficients affects the rendering result when there is quantization noise. Then, two fast fitting methods for estimating the noise-resistant SH coefficients are proposed. They can effectively control the magnitude of the estimated SH coefficients and, hence, suppress the rendering artifacts. Both statistical and visual results confirm our theory.

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Index Terms:
Spherical harmonics, BRDF, image-based relighting, precomputed radiance transfer, constrained least square, texture compression, noise-resistant fitting.
Ping-Man Lam, Chi-Sing Leung, Tien-Tsin Wong, "Noise-Resistant Fitting for Spherical Harmonics," IEEE Transactions on Visualization and Computer Graphics, vol. 12, no. 2, pp. 254-265, March-April 2006, doi:10.1109/TVCG.2006.34
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