## Abstract

The reconstruction of a complete watertight model from scan data is still a difficult process. In particular, since scanned data is often incomplete, the reconstruction of the expected shape is an ill-posed problem. Techniques that reconstruct poorly-sampled areas without any user intervention fail in many cases to faithfully reconstruct the topology of the model. The method that we introduce in this paper is topology-aware: it uses minimal user input to make correct decisions at regions where the topology of the model cannot be automatically induced with a reasonable degree of confidence. We first construct a continuous function over a three-dimensional domain. This function is constructed by minimizing a penalty function combining the data points, user constraints, and a regularization term. The optimization problem is formulated in a mesh-independent manner, and mapped onto a specific mesh using the finite-element method. The zero level-set of this function is a first approximation of the reconstructed surface. At complex under-sampled regions, the constraints might be insufficient. Hence, we analyze the local topological stability of the zero level-set to detect weak regions of the surface. These regions are suggested to the user for adding local inside/outside constraints by merely scribbling over a 2D tablet. Each new user constraint modifies the minimization problem, which is solved incrementally. The process is repeated, converging to a topology-stable reconstruction. Reconstructions of models acquired by a structured-light scanner with a small number of scribbles demonstrate the effectiveness of the method.

Original language | English |
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DOIs | |

State | Published - 2007 |

Event | 34th Annual Meeting of the Association for Computing Machinery's Special Interest Group on Graphics - San Diego, CA, United States Duration: 5 Aug 2007 → 9 Aug 2007 |

### Conference

Conference | 34th Annual Meeting of the Association for Computing Machinery's Special Interest Group on Graphics |
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Country/Territory | United States |

City | San Diego, CA |

Period | 5/08/07 → 9/08/07 |

## Keywords

- Interactive tools
- Surface reconstruction