Noise-proofing the doubly SH-projected coefficients for synthesizing images under environment lighting

The brute-force way to synthesize images of an object under various lighting environments is very time consuming. To speed up the synthesizing process, we can model the bidirectional reflectance distribution function (BRDF) of each surface element as a spherical harmonic (SH) coefficient matrix based on the double SH projection. With the SH coefficient matrices of all surface elements, we can relight an object under the global illumination. However, applying the classical least square method for the double SH projection, the returned SH coefficients are prohibitively large in magnitude because samples are available on the upper hemisphere only. Hence, the synthesizing process is very sensitive to small quantization noise introduced by the compression process. Existing methods to this noise-sensitivity problem mainly focus on the single SH projection. It should be noticed that the double SH projection further amplifies the artifacts. Straightforwardly extending existing methods to the double SH projection may not be theoretically nor practically feasible. In this paper, we present a robust estimation method for the double SH projection. With the proposed method, severe artifacts in synthesized images can be significantly reduced. Comparison with the existing Sloan's method is performed to support the effectiveness of the proposed method.