Surface approximation via sparse representation and parameterization optimization. (September 2016)

• Record Type: Journal Article
• Authors: Xu, Linlin; Wang, Ruimin; Yang, Zhouwang; Deng, Jiansong; Chen, Falai; Liu, Ligang
• Is Part Of: Computer aided design. Volume 78(2016)
• Page Start: 179
• Page End: 187
• Publication Date: 2016-09
• Subjects: Surface approximation -- Sparse representation -- Parameterization optimization; Computer-aided design -- Periodicals; Engineering design -- Data processing -- Periodicals; Computer graphics -- Periodicals; Conception technique -- Informatique -- Périodiques; Infographie -- Périodiques; Computer graphics; Engineering design -- Data processing; Periodicals; Electronic journals; 620.00420285
• DOI: 10.1016/j.cad.2016.05.013
• Languages: English
• ISSNs: 0010-4485

Abstract

Abstract: Surface approximation with smooth functions suffers the problems of choosing the basis functions and representing non-smooth features. In this work, we introduce a sparse representation for surfaces with a set of redundant basis functions, which efficiently overcomes the overfitting artifacts. Moreover, we propose an approach of parameterization transformation, which makes the possibility to represent non-smooth features by the composition of a smooth function and a non-smooth domain optimization. We couple the sparse representation and the parameterization transformation in a global optimization to respect sharp features with smooth polynomial basis functions. Our approach is capable for approximating a wide range of surfaces with different level of sharp features. Experimental results have shown the feasibility and applicability of our proposed method in various applications. Highlights: A new composite representation method is proposed for surface approximation. The results do not rely on basis functions with the parameterization optimization. Non-smooth features are fitted well even with smooth polynomial basis functions. An augmented Lagrange method based numerical algorithm is presented. Graphical abstract: