Object shape reconstruction from images has been an active topic in computer vision. Shape-from-shading (SFS) is an important approach for inferring 3D surface from a single shading image. In this paper, we present a unified SFS approach for surfaces of various reflectance properties using fast eikonal solvers. The whole approach consists of three main components: a unified SFS model, a unified eikonal-type partial differential image irradiance (PDII) equation, and fast eikonal solvers for the PDII equation. The first component is designed to address different reflectance properties including diffuse, specular, and hybrid reflections in the imaging process of the camera. The second component is meant to derive the PDII equation under an orthographic camera projection and a single distant point light source whose direction is the same as the camera. Finally, the last component is targeted at solving the resultant PDII equation by using fast eikonal solvers. It comprises two Godunov-based schemes with fast sweeping method that can handle the eikonal-type PDII equation. Experiments on several synthetic and real images demonstrate that each type of the surfaces can be effectively reconstructed with more accurate results and less CPU running time.

中文翻译：

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使用快速Ekonnal解算器的3D表面重建的统一的从阴影到形状的方法

从图像重建对象形状一直是计算机视觉中的活跃话题。阴影形状（SFS）是从单个阴影图像推断3D表面的重要方法。在本文中，我们使用快速的电子求解器为各种反射率特性的表面提供了统一的SFS方法。整个方法包括三个主要部分：一个统一的SFS模型，一个统一的Eikonal型偏微分图像辐照度（PDII）方程，以及用于PDII方程的快速本征求解器。第一个组件旨在解决相机成像过程中的不同反射特性，包括漫反射，镜面反射和混合反射。第二部分是在正交摄影机投影和方向与摄影机相同的单个遥远点光源下导出PDII方程。最后，最后一个组件的目标是通过使用快速电子求解器来求解所得的PDII方程。它包括两个基于Godunov的方案，具有快速扫描方法，可以处理Eikonal型PDII方程。在多个合成图像和真实图像上进行的实验表明，可以有效地重建每种类型的表面，从而获得更准确的结果和更少的CPU运行时间。