This paper addresses the problem of estimating the shape of objects that exhibit spatially-varying reflectance. We assume that multiple images of the object are obtained under a fixed view-point and varying illumination, i.e., the setting of photometric stereo. At the core of our techniques is the assumption that the BRDF at each pixel lies in the non-negative span of a known BRDF dictionary.This assumption enables a per-pixel surface normal and BRDF estimation framework that is computationally tractable and requires no initialization in spite of the underlying problem being non-convex. Our estimation framework first solves for the surface normal at each pixel using a variant of example-based photometric stereo. We design an efficient multi-scale search strategy for estimating the surface normal and subsequently, refine this estimate using a gradient descent procedure. Given the surface normal estimate, we solve for the spatially-varying BRDF by constraining the BRDF at each pixel to be in the span of the BRDF dictionary, here, we use additional priors to further regularize the solution. A hallmark of our approach is that it does not require iterative optimization techniques nor the need for careful initialization, both of which are endemic to most state-of-the-art techniques. We showcase the performance of our technique on a wide range of simulated and real scenes where we outperform competing methods.

解决采用光度立体法获取不同光照下物体表面法向和反射率的问题，应用已知BRDF字典的非负线性组合的假设，设计了一个基于实例的光度立体法的多尺度搜索策略以及梯度下降方法来求解每个像素点的表面法向和反射率，并且使用其他的约束优化方法以得到更好结果，该方法不需要迭代优化技巧和精心设计的初值，并在仿真和实际场景中表现出比竞争方法更好的性能。

从虚拟实例推断形状和空间变化反射率