Noise-resistant hemispherical basis for image-based relighting

The spherical harmonic (SH) basis has been widely used for representing relighting data. However, under some situations, the magnitudes of the estimated SH coefficients could be very large. Hence, relit images are very sensitive to quantisation (or compression) noise of these estimated SH coefficients. To tackle this issue, this study proposes a new spherical basis, namely eigen hemispherical harmonic (EHSH) basis. Its approximation ability is the same as that of the SH basis. With this new basis, the magnitudes of the estimated coefficients are controllable. Hence, the artefacts in the relit images can be suppressed. Besides, the transform from the classical hemispherical SH coefficients to the EHSH coefficients is discussed. Finally, the authors present the way to relight images based on the EHSH basis.