Estimating the illumination and the reflectance properties
of an object surface from a sparse set of images is an
important but inherently ill-posed problem. The problem
becomes even harder if we wish to account for the spatial
variation of material properties on the surface. In this
paper, we derive a novel method for estimating the spatially
varying specular reflectance properties, of a surface
of known geometry, as well as the illumination distribution
from a specular-only image, for instance, captured using
polarization to separate reflection components. Unlike previous
work, we do not assume the illumination to be a single
point light source. We model specular reflection with
a spherical statistical distribution and encode the spatial
variation with radial basis functions of its parameters. This
allows us to formulate the simultaneous estimation of spatially
varying specular reflectance and illumination as a
sound probabilistic inference problem, in particular, usi...