Shape from Shading Without Regularization

从明暗恢复形状是机器视觉的核心和难点问题。尽管它的表述是精确的，但它的解通常被认为是不适定的，只有在附加假设的情况下才可能实现。然而，在最近的论文中，PI给出了第一个证明，当照明来自相机的方向时，对于一般对象，形状形状阴影不仅是适定的，而且是唯一可解的。对于一般的照明方向，证明了在有限的模糊度范围内都能有效地确定解。因此，通过施加诸如光滑度等附加要求来选择单一的“物理上合理的”表面解决方案的标准技术正则化通常是不必要的。这项研究的目的是开发和实现不需要正则化的曲面重建算法，与以往的算法不同，该算法将显式地利用曲面解的强约束，使明暗处理中的形状成为良好的适定性。通过利用这些约束，算法可能是快速和健壮的。所提出的四种算法中有两种不同于以往的算法是非变分的，并且基于粘性解和动力系统理论的新的数学技术。长期目标是将从阴影恢复形状的算法与使用其他信息的技术相结合，例如稀疏深度数据，以从阴影图像进行稳健的表面重建。

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.//