Surface approximation via sparse representation and parameterization optimization. (September 2016) - Xu, Linlin; Wang, Ruimin; Yang, Zhouwang; Deng, Jiansong; Chen, Falai; Liu, Ligang
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: