In this paper we present methods for estimating shape from polarisation and shading information, i.e. photo-polarimetric shape estimation, under varying, but unknown, illumination, i.e. in an uncalibrated scenario. We propose several alternative photo-polarimetric constraints that depend upon the partial derivatives of the surface and show how to express them in a unified system of partial differential equations of which previous work is a special case. By careful combination and manipulation of the constraints, we show how to eliminate non-linearities such that a discrete version of the problem can be solved using linear least squares. We derive a minimal, combinatorial approach for two source illumination estimation which we use with RANSAC for robust light direction and intensity estimation. We also introduce a new method for estimating a polarisation image from multichannel data and provide methods for estimating albedo and refractive index. We evaluate lighting, shape, albedo and refractive index estimation methods on both synthetic and real-world data showing improvements over existing state-of-the-art.

中文翻译：

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未校准的两源光偏振立体

在本文中，我们提出了根据偏振和阴影信息估计形状的方法，即光偏振形状估计，在变化但未知的光照下，即在未校准的情况下。我们提出了几种替代的光偏振约束，它们取决于表面的偏导数，并展示了如何在偏微分方程的统一系统中表达它们，以前的工作是一个特例。通过仔细组合和操纵约束，我们展示了如何消除非线性，以便可以使用线性最小二乘法解决问题的离散版本。我们推导出了一种用于两个源照明估计的最小组合方法，我们将其与 RANSAC 一起用于稳健的光方向和强度估计。我们还介绍了一种从多通道数据估计偏振图像的新方法，并提供了估计反照率和折射率的方法。我们在合成数据和真实世界数据上评估照明、形状、反照率和折射率估计方法，显示对现有最先进技术的改进。