Modeling image irradiance under natural illumination and isotropic surface reflectance

Discounting subsurface scattering and surface emittance, this work seeks to address the question; how to accurately represent image irradiance under unknown general illumination and reflectance, given that a surface point sees its surrounding world through the local upper hemisphere oriented by the surface normal at this point. In this paper, we formulate the image formation process of isotropic surfaces under arbitrary distant illumination in the frequency space while addressing the physical compliance of hemispherical basis for representing surface reflectance, e.g. Helmholtz reciprocity and isotropy. This representation is further reduced in dimensionality through analytically deriving the principal components of the image irradiance. A database of natural illumination and real world surface materials are used to compute a general-purpose basis which captures the full behavior of illumination and reflectance in a lower-dimensional subspace for image irradiance representation. Compared to similar basis in literature, our proposed basis achieves higher accuracy levels at lower illumination orders.