Linear Differential Constraints for Photo-polarimetric Height Estimation
This addresses shape estimation in computer vision by introducing a novel method that bypasses normal vector computation, though it is incremental in combining existing techniques.
The paper tackled photo-polarimetric shape estimation by proposing a unified differential approach that directly reconstructs surface height using shading and polarisation information, reducing the problem to a linear system and showing effectiveness on synthetic and real-world data.
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.