Image irradiance harmonics: a phenomenological model of image irradiance of arbitrary surface reflectance

Phenomenological appearance models capture surface appearance through mathematical modelling of the reflection process. Theoretically, the space of all possible images of a fixed-pose object under all possible illumination conditions is infinite dimensional. Nonetheless, because of their low-frequency nature, irradiance signals can be represented using low-order basis functions. Discounting subsurface scattering and surface emittance, this work seeks to address the question; how to compactly and accurately represent image irradiance under unknown general illumination, given that a surface point sees its surrounding world through the local upper hemisphere oriented by the surface normal at this point. In this study, we formulate the image formation process of isotropic surface reflectance under arbitrary distant illumination in the frequency space while addressing the physical compliance of hemispherical basis for representing surface reflectance, for example, Helmholtz reciprocity and isotropy. The term `irradiance harmonics´ is also defined which enables decoupling illumination and reflectance from the underlying geometry and pose. We provide a closed form of the energy content being maintained by different reflectance modes of the proposed irradiance harmonics. Since specular materials tend to require more basis functions when compared with diffuse ones, the presented harmonics captures same cumulative energy content, by providing larger number of orthogonal irradiance basis, at lower illumination orders when compared to similar basis in literature.