Universität Des Saarlandes Fachrichtung 6.1 – Mathematik Perspective Shape from Shading: Ambiguity Analysis and Numerical Approximations Perspective Shape from Shading: Ambiguity Analysis and Numerical Approximations
Universität Des Saarlandes Fachrichtung 6.1 – Mathematik Perspective Shape from Shading: Ambiguity Analysis and Numerical Approximations Perspective Shape from Shading: Ambiguity Analysis and Numerical Approximations
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Universität Des Saarlandes Fachrichtung 6.1 – 阴影的数学透视形状：歧义分析和数值近似 阴影的透视形状：歧义分析和数值近似
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通讯作者：
Oliver Vogel
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作者：
M. Breuß;E. Cristiani;Jean;M. Falcone;Oliver Vogel
在本文中，我们研究了一个现代的，透视模型的形状从阴影和它的数值逼近。我们表明，一种新形式的经典凹/凸模糊性仍然存在，虽然该模型已被证明是在特定的假设下适定。这一分析结果得到了各种数值试验的证实。此外，我们目前的收敛性结果最近在文献中介绍的两个迭代逼近计划。第一个是基于有限差分离散，而第二个是基于半拉格朗日离散。收敛结果得到的基本偏微分方程的粘性解的一般框架。我们还表明，即使在复杂的场景中，也可以获得合理质量的结果。为此，我们解决了构成方程上的先前分割的输入图像，其中我们使用状态约束边界条件在段边界。
In this paper we study a modern, perspective model for shape from shading and its numerical approximation. We show that a new form of the classic concave/convex ambiguity is still present, although the model has been shown to be well-posed under particular assumptions. This analytical result is confirmed by various numerical tests. Moreover, we present convergence results for two iterative approximation schemes recently introduced in the literature. The first one is based on a finite difference discretization, whereas the second one is based on a semi-Lagrangian discretization. The convergence results are obtained in the general framework of viscosity solutions of the underlying partial differential equation. We also show that it is possible to obtain even in complex scenes results of reasonable quality. To this end we solve the constituting equation on a previously-segmented input image, where we use state constraints boundary conditions at the segment borders.