Shape from Shading Without Regularization

阴影形状是机器视觉的一个核心难题。虽然它的公式是精确的，但它的解通常被认为是不适定的，只有在附加的假设下才有可能。然而，在最近的论文中，pi首次证明，当照明来自相机方向时，对于一般物体，形状阴影不仅是适定的，而且是唯一可解的。对于一般照明方向，在模糊度有限的情况下，求解是有效的。因此，通过施加诸如平滑等额外要求来选择单个“物理上合理”的表面解决方案的标准技术的规范化通常是不必要的。所提出的研究的目的是开发和实现无正则化的表面重建算法，与以前的算法不同，它将明确地利用表面解的强约束，使形状从阴影中得到良好的定位。利用这些约束条件，可以提高算法的速度和鲁棒性。提出的四种算法中的两种是非变分的，不像以前的大多数算法，并且基于粘度解的新数学技术和动力系统理论。长期目标是将阴影算法的形状与使用其他信息（如稀疏深度数据）的技术相结合，以便从阴影图像中进行鲁棒的表面重建

Shape from shading is a central, difficult problem of machine vision. Although its formulation is precise, its solution has usually been considered ill-posed, possible only with additional assumptions. In recent papers, however, the PIs gave the first proof that shape form shading is not only well-posed but solvable uniquely, for general objects, when the illumination is from the direction of the camera. For general illumination direction, it was shown that the solution is determined effectively up to a finite ambiguity. Thus, regularization the standard technique for selecting a single `physically reasonable' surface solution by imposing additional requirements such as smoothness is generally unnecessary. The aim of the proposed research is to develop and implement algorithms for surface reconstruction without regularization, which, unlike previous algorithms, will explicitly utilize the strong constraints on the surface solutions that make shape from shading well posed. Through exploiting these constraints, the algorithms may be fast and robust. Two of the four algorithms proposed are non-variational unlike most previous ones, and are based on the novel mathematical techniques of the viscosity solution, and dynamical systems theory. The long term aim is to combine shape from shading algorithms with techniques using other information, such as sparse depth data, for robust surface reconstruction from shaded images.//