SFS的变分方法研究与实现

Study and realization of variational approach to shape from shading

摘要: 变分法是解SFS问题的经典方法,其关键是在合适的约束模型下构造相应的泛函,然后通过变分法寻求泛函极小化问题的解.本文提出了一种新的综合约束模型,并基于此约束模型构建了泛函,然后泰勒展开变分处理后的等效欧拉方程,再应用有限差分方法将偏微分方程离散化,最后进行迭代计算得到了曲面各点的高度值.Matlab的编程实现表明该算法有效可行.

Abstract: The variational approach is a classical way to shape from shading.This approach depends on minimizing a functional based on suitable constraints.A new combined constraint is presented for variational solution that is achieved by Taylor series expansion and difference scheme in this paper.Obtaining surface height by iterative proves availability and feasibility of our solution.