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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未经校准的两源光测色立体。

在本文中，我们介绍了在变化但未知的光照下（即在未校准的情况下）从偏振和阴影信息估计形状的方法，即光偏振形状估计。我们提出了一些依赖于表面的偏导数的可选光偏振约束，并展示了如何在偏微分方程的统一系统中表达它们，以前的工作是特例。通过对约束的仔细组合和操作，我们展示了如何消除非线性，从而可以使用线性最小二乘法来解决问题的离散版本。我们为两个光源照度推导了最小的组合方法，我们将其与RANSAC一起用于鲁棒的光方向和强度估算。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。我们根据合成数据和实际数据评估照明，形状，反照率和折射率估计方法，以显示对现有技术的改进。