Despite the longtime research aimed at retrieving geometrical information of an object from polarimetric imaging, physical limitations in the polarisation phenomena constrain current approaches to provide ambiguous depth estimation.

As an additional constraint, polarimetric imaging formulation differs when light is reflected off the object specularly or diffusively. This introduces another source of ambiguity that current formulations cannot overcome. With the aim of deriving a formulation capable of dealing with as many heterogeneous effects as possible, we propose a differential formulation of the Shape from Polarisation problem that depends only on polarimetric images. This allows the direct geometrical characterisation of the level-set of the object keeping consistent mathematical formulation for diffuse and specular reflection. We show via synthetic and real-world experiments that diffuse and specular reflection can be easily distinguished in order to extract meaningful geometrical features from just polarimetric imaging.

The inherent ambiguity of the Shape from Polarization problem becomes evident through the impossibility of reconstructing the whole surface with this differential approach. To overcome this limitation, we consider shading information elegantly embedding this new formulation into a two-light calibrated photometric stereo approach.