Today, three-dimensional reconstruction of objects has many applications in various fields, and therefore, choosing a suitable method for high resolution three-dimensional reconstruction is an important issue and displaying high-level details in three-dimensional models is a serious challenge in this field. Until now, active methods have been used for high-resolution three-dimensional reconstruction. But the problem of active three-dimensional reconstruction methods is that they require a light source close to the object. Shape from polarization (SfP) is one of the best solutions for high-resolution three-dimensional reconstruction of objects, which is a passive method and does not have the drawbacks of active methods. The changes in polarization of the reflected light from an object can be analyzed by using a polarization camera or locating polarizing filter in front of the digital camera and rotating the filter. Using this information, the surface normal can be reconstructed with high accuracy, which will lead to local reconstruction of the surface details. In this paper, an end-to-end deep learning approach has been presented to produce the surface normal of objects. In this method a benchmark dataset has been used to train the neural network and evaluate the results. The results have been evaluated quantitatively and qualitatively by other methods and under different lighting conditions. The MAE value (Mean-Angular-Error) has been used for results evaluation. The evaluations showed that the proposed method could accurately reconstruct the surface normal of objects with the lowest MAE value which is equal to 18.06 degree on the whole dataset, in comparison to previous physics-based methods which are between 41.44 and 49.03 degree.

翻译：当前，物体的三维重建在众多领域具有广泛应用，因此选择合适的方法实现高分辨率三维重建至关重要，而在三维模型中呈现高精度细节是该领域面临的重要挑战。迄今为止，高分辨率三维重建主要采用主动式方法，但此类方法需要将光源置于物体近处。偏振三维重建（SfP）是实现物体高分辨率三维重建的最佳解决方案之一，作为一种被动式方法，它克服了主动式方法的固有缺陷。通过使用偏振相机或在数码相机前安装可旋转偏振滤光片，可分析物体反射光的偏振态变化。利用这些信息能够高精度重建表面法向量，从而实现表面细节的局部重建。本文提出一种端到端的深度学习方法用于生成物体表面法向量。该方法采用基准数据集训练神经网络并评估结果，通过定量与定性分析在不同光照条件下与其他方法进行对比。采用平均角度误差（MAE）作为评估指标，实验表明：相较于传统基于物理的方法（MAE介于41.44至49.03度之间），所提方法能够在完整数据集上以18.06度的最低MAE值精确重建物体表面法向量。