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PingMan Lam, ChiSing Leung, TienTsin Wong, "NoiseResistant Fitting for Spherical Harmonics," IEEE Transactions on Visualization and Computer Graphics, vol. 12, no. 2, pp. 254265, March/April, 2006.  
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@article{ 10.1109/TVCG.2006.34, author = {PingMan Lam and ChiSing Leung and TienTsin Wong}, title = {NoiseResistant Fitting for Spherical Harmonics}, journal ={IEEE Transactions on Visualization and Computer Graphics}, volume = {12}, number = {2}, issn = {10772626}, year = {2006}, pages = {254265}, doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2006.34}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Visualization and Computer Graphics TI  NoiseResistant Fitting for Spherical Harmonics IS  2 SN  10772626 SP254 EP265 EPD  254265 A1  PingMan Lam, A1  ChiSing Leung, A1  TienTsin Wong, PY  2006 KW  Spherical harmonics KW  BRDF KW  imagebased relighting KW  precomputed radiance transfer KW  constrained least square KW  texture compression KW  noiseresistant fitting. VL  12 JA  IEEE Transactions on Visualization and Computer Graphics ER   
Abstract—Spherical harmonic (SH) basis functions have been widely used for representing spherical functions in modeling various illumination properties. They can compactly represent lowfrequency 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 noiseresistant 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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