Lighting estimation of a convex Lambertian object using weighted spherical harmonic frames
An explicit lighting estimation from a single image of Lambertian objects is influenced by two factors: data incompletion and noise contamination. Measurement of lighting consistency purely using the orthogonal spherical harmonic basis cannot achieve an accurate estimation. We present a novel signal-processing framework to represent the lighting field. We construct a weighted spherical harmonic frame with geometric symmetry on the sphere \({S^2}\). Weighted spherical harmonic frames are defined over the generating rotation matrices about symmetry axes of finite symmetry subgroups of \(SO(3)\), and the generating functions are weighted spherical harmonic basis functions. Compared with the orthogonal spherical harmonic basis, the redundant weighted spherical harmonic frames not only describe the multidirectional lighting distribution intuitively, but also resist the noise theoretically. Subsequently, we analyze the relationship of the irradiance to the incoming radiance in terms of weighted spherical harmonic frames and reconstruct the lighting function filtered by the Lambertian BRDF (bidirectional reflectance distribution function). The experiments show that the frame coefficients of weighted spherical harmonic frames can better characterize the complex lighting environments finely and robustly.
lighting estimation lambertian weighted spherical harmonic frame