Minimum Entropy Light and Shading Approximation

An estimation method for approximating the lighting of a multi-view scene is developed. It is assumed that a set of scene patches can be obtained with estimates of their normals and depths from a given camera. The effect of lighting on the scene is modelled as multiplicative and additive bias-fields, represented by spherical harmonic (SH) basis functions. Parameters of a weighted sum of SHs to a given order are sought by minimising the entropy of the patch colours as the bias is taken out. The method performs a gradient descent using the entropy as a loss function. The entropy is estimated by sampling using a Parzen window estimator which allows its change with respect to the SH weights to be calculated analytically. We illustrate our estimator on 2D retrospective shading correction and then define Phong illumination as a bias field estimation problem and its continuous generalisation. Results on simple modelled scenes lit by one or more Phong point light sources without scattering are presented. We discuss how the lighting estimation could be extended to handle shadows and propose a model for estimation of parametric BRDFs in arbitrary lighting using the same framework.