# Variational Surface Approximation and Model Selection

## Abstract

We consider the problem of approximating an arbitrary generic surface with a given set of simple surface primitives. In contrast to previous approaches based on variational surface approximation, which are primarily concerned with finding an optimal partitioning of the input geometry, we propose to integrate a model selection step into the algorithm in order to also optimize the type of primitive for each proxy. Our method is a joint global optimization of both the partitioning of the input surface as well as the types and number of used shape proxies. Thus, our method performs an automatic trade-off between representation complexity and approximation error without relying on a user supplied predetermined number of shape proxies. This way concise surface representations are found that better exploit the full approximative power of the employed primitive types.

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## Bibtex

@ARTICLE{vsams, author = {Li, Bao and Schnabel, Ruwen and Shiyao, Jin and Klein, Reinhard}, title = {Variational Surface Approximation and Model Selection}, journal = {to appear in Computer Graphics Forum (Proc. of Pacific Graphics)}, volume = {28}, number = {7}, year = {2009}, month = oct, abstract = {We consider the problem of approximating an arbitrary generic surface with a given set of simple surface primitives. In contrast to previous approaches based on variational surface approximation, which are primarily concerned with finding an optimal partitioning of the input geometry, we propose to integrate a model selection step into the algorithm in order to also optimize the type of primitive for each proxy. Our method is a joint global optimization of both the partitioning of the input surface as well as the types and number of used shape proxies. Thus, our method performs an automatic trade-off between representation complexity and approximation error without relying on a user supplied predetermined number of shape proxies. This way concise surface representations are found that better exploit the full approximative power of the employed primitive types.} }