A comparison theorem for a piecewise Lipschitz continuous Hamiltonian and application to Shape-from-Shading problems
A comparison theorem for a piecewise Lipschitz continuous Hamiltonian and application to Shape-from-Shading problems
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分段 Lipschitz 连续哈密顿量的比较定理及其在阴影形状问题中的应用
DOI：
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发表时间：
1992
期刊：
影响因子：
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通讯作者：
A. Tourin
中科院分区：
文献类型：
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作者：
A. Tourin
摘要：从由单个远距离点光源照明的朗伯非自阴影表面的阴影图像进行重建可以写成一阶哈密尔顿-雅可比方程。在本文中，我们继续从 E. Rouy 和 A. Tourin 开始对该方程解的唯一性进行研究；该方法基于粘度解理论和动态规划原理。更准确地说，我们在此关注该方程粘度解的唯一性，以防表面反射的测量发光强度沿平滑曲线不连续。我们证明了分段 Lipschitz 连续哈密顿量的一般比较结果，并通过数值实验对其进行了说明。
SummaryThe reconstruction from a shaded image of a Lambertian and not self-shadowing surface illuminated by a single distant pointwise light source may be written as a first-order Hamilton-Jacobi equation.In this paper, we continue the investigation begun in E. Rouy and A. Tourin into the uniqueness of the solution of this equation; the approach is based on the viscosity solutions theory and the dynamic programming principle.More precisely, we concentrate here on the uniqueness of the viscosity solution of this equation in case the measured luminous intensity reflected by the surface is discontinuous along a smooth curve. We prove a general comparison result for a piecewise Lipschitz continuous Hamiltonian and illustrate it by numerical experiments.