Towards efficient image irradiance modelling of convex Lambertian surfaces under single viewpoint and frontal illumination
Under local illumination assumption, phenomenological appearance models capture surface appearance through the mathematical modelling of the reflection process. Theoretically, due to the arbitrariness of the lighting function, the space of all possible images of a fixed-pose object under all possible illumination conditions is infinite dimensional. Nonetheless, due to their low- frequency nature, irradiance signals can be represented using low-order basis functions, where spherical harmonics (SH) has been extensively adopted. When capturing image irradiance from a single viewpoint, the visible part of the object's surface constructs the upper hemisphere of the surface normals where the SH is no longer orthonormal. In this paper, we propose the use of hemispherical harmonics (HSH) to model image irradiance of convex Lambertian objects perceived from single viewpoint under unknown distant as well as near illumination. We prove analytically, and validate experimentally, that the Lambertian reflectance kernel has a more compact harmonic expansion in the hemispherical domain when compared to its spherical counterpart. Our experiments illustrate that, despite of having poor approximation accuracy under very close lights, such behavior improves exponentially with little increase in the distance to the light source relative to the object size.