In this paper we present a differential approach to photo-polarimetric shape
estimation. We propose several alternative differential constraints based on
polarisation and photometric shading information and show how to express them
in a unified partial differential system. Our method uses the image ratios
technique to combine shading and polarisation information in order to directly
reconstruct surface height, without first computing surface normal vectors.
Moreover, we are able to remove the non-linearities so that the problem reduces
to solving a linear differential problem. We also introduce a new method for
estimating a polarisation image from multichannel data and, finally, we show it
is possible to estimate the illumination directions in a two source setup,
extending the method into an uncalibrated scenario. From a numerical point of
view, we use a least-squares formulation of the discrete version of the
problem. To the best of our knowledge, this is the first work to consider a
unified differential approach to solve photo-polarimetric shape estimation
directly for height. Numerical results on synthetic and real-world data confirm
the effectiveness of our proposed method.Comment: To appear at International Conference on Computer Vision (ICCV),
Venice, Italy, October 22-29, 201