Linear Differential Constraints for Photo-polarimetric Height Estimation

TL;DR

This paper introduces a linear differential approach that combines polarisation and shading data to directly estimate surface height in photo-polarimetric imaging, simplifying the process and extending it to uncalibrated scenarios.

Contribution

It presents a unified linear differential framework for photo-polarimetric height estimation, including a new method for polarisation image estimation and uncalibrated illumination direction recovery.

Findings

Effective height reconstruction on synthetic data

Successful application to real-world images

Linear formulation simplifies computation

Abstract

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.