由影调恢复物体外形的唯一性

研究了当投射的平行光垂直于图像平面时图像以及成像物体区域内部的几何特性与边界特性,讨论了由一般物体所成的像唯一地求解SFS问题的条件,并由此提出了一个更为一般的整体区域上的唯一性定理和局部不唯一定理,推广了本领域现有的研究结果.定理的证明以微分几何和常微分方程几何理论为工具,其过程是构造性的,亦即在定理证明的同时指明了由单目图像恢复物体外形且不使用正则化技术的可能途径.

Uniqueness of Recoverig the Surface by Shading Patterns

Under the condition that the projecting light is perpendicular to the image plane, and from a study on the geometric and boundary properties of the imaged object, this paper discusses the uniqueness of the conditions for solving SFS problem form the image of a general object. Two theorems are established, the uniqueness of SFS for the global area and the non uniqueness in some local regions, both of them extend the research results in this field. The proofs are based on differential geometry and geometric theory of ordinary differential equations and are constructive. The proof itself provides a possible way to uniquely recover the surface of a monocular imaged object with the absence of regularization technique.