Lighting Estimation of a Convex Lambertian Object Using Redundant 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 redundant spherical harmonic frame with geometric symmetry on the sphere S². 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 spherical harmonic basis functions. Compared with the orthogonal spherical harmonic basis, the redundant 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 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 spherical harmonic frames can better characterize the complex lighting environments finely and robustly.