Existence and Uniqueness of Solutions of Surface Reconstruction Problem

• Published in: Acta Mathematicae Applicatae Sinica Vol. 27; no. 2; pp. 263 - 276
• Main Authors: Jing, Zhu-cui, Xu, Guo-liang
• Format: Journal Article
• Language: English
• Published: Heildeberg Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.04.2011
• Subjects: Applications of Mathematics; Math Applications in Computer Science; Mathematical and Computational Physics; Mathematics; Mathematics and Statistics; Theoretical; 偏微分方程; 散乱数据; 曲面重建; 水平集方法; 结构调查; 计算机辅助设计; 逆向工程; 35D05; 35K20; viscosity solution; surface reconstruction; 35K15; existence and uniqueness; 35B50; 35K55
• ISSN: 0168-9673; 1618-3932
• DOI: 10.1007/s10255-011-0054-1

Surface reconstruction from scattered data is an important problem in such areas as reverse engineering and computer aided design. In solving partial differential equations derived from surface reconstruction problems, level-set method has been successfully used. We present in this paper a theoretical analysis on the existence and uniqueness of the solution of a partial differential equation derived from a model of surface recon- struction using the level-set approach. We give the uniqueness analysis of the classical solution. Results on the existence and uniqueness of the viscosity solution are also established.