Despite the longtime research aimed at retrieving geometrical information of an object from polarimetric imaging, physical limitations in the polarisation phenomena constrain current approaches to provide ambiguous depth estimation. As an additional constraint, polarimetric imaging formulation differs when light is reflected off the object specularly or diffusively. This introduces another source of ambiguity that current formulations cannot overcome. With the aim of deriving a formulation capable of dealing with as many heterogeneous effects as possible, we propose a differential formulation of the Shape from Polarisation problem that depends only on polarimetric images. This allows the direct geometrical characterisation of the level-set of the object keeping consistent mathematical formulation for diffuse and specular reflection. We show via synthetic and real-world experiments that diffuse and specular reflection can be easily distinguished in order to extract meaningful geometrical features from just polarimetric imaging. The inherent ambiguity of the Shape from Polarization problem becomes evident through the impossibility of reconstructing the whole surface with this differential approach. To overcome this limitation, we consider shading information elegantly embedding this new formulation into a two-light calibrated photometric stereo approach..

中文翻译：

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极化形状的差分方法：水平集表征

尽管长期研究旨在从偏振成像中检索对象的几何信息，但偏振现象的物理限制限制了当前提供模糊深度估计的方法。作为额外的限制，当光以镜面反射或漫射方式从物体反射时，偏振成像公式会有所不同。这引入了当前公式无法克服的另一个含糊不清的来源。为了推导出能够处理尽可能多的异质效应的公式，我们提出了一种仅依赖于偏振图像的偏振问题形状的差分公式。这允许对象的水平集的直接几何特征保持一致的漫反射和镜面反射数学公式。我们通过合成和真实世界的实验表明，可以轻松区分漫反射和镜面反射，以便仅从偏振成像中提取有意义的几何特征。通过使用这种微分方法重建整个表面的可能性，来自极化问题的形状的固有模糊性变得明显。为了克服这一限制，我们考虑将这种新公式优雅地嵌入到两光校准光度立体方法中的着色信息。通过使用这种微分方法重建整个表面的可能性，来自极化问题的形状的固有模糊性变得明显。为了克服这一限制，我们考虑将这种新公式优雅地嵌入到两光校准光度立体方法中的着色信息。通过使用这种微分方法重建整个表面的可能性，来自极化问题的形状的固有模糊性变得明显。为了克服这一限制，我们考虑将这种新公式优雅地嵌入到两光校准光度立体方法中的着色信息。