中文摘要：

针对基于单幅图像的3D重构因其约束条件的严重匮乏,致使重构结果不确定的原因与机理进行了深入研究。以SFS重构方案为研究对象,提出将SFS问题规划为仅含二次约束的多项式系统,进而递次使用同伦分析法和精确线搜索技术,最后基于变量集构造一个SDP凸松弛。实验结果表明,这种重构方案不仅可以寻找所有全局解,优化迭代过程,加快收敛速度,而且可以避免产生不理想的局部解,彻底摆脱对初始假定的依赖,确保迭代过程收敛于一个全局极小值。借助多项式系统的完备解空间特性,大大提高了3D重构的精确度和唯一性,非常适用于非刚体表面重构。

英文摘要：

In allusion to causation and principium of serious under-constrained and uncertainty of reconstruction result about3 D reconstruction based on a single image,it had an in-depth and far-ranging study. SFS was used for general research,this paper suggested that maybe to formulate SFS into a polynomial system which composed only of quadratic item at first,and following that the homotopy analysis methed and exact line search were used. Finally,it constructed a SDP convex relaxations in an extended set of variables. Experimentation demonstrates that this scheme not only can obtain all global solutions,optimize the iterative procedures and speed the convergence,but also can avoid suboptimal local minima,ensure the iterativer of SFS independent of initial guess and constringing to a global minimum. By the self-contained solution space of polynomial system the programme will advance the efficiency and accuracy of 3D reconstruction,and will be fit for nonrigid surface.