Geometric Model Reconstruction and Smoothing
In this project, we study the problem of automatic geometric model reconstruction from unorganized point cloud data. The focus is to automate the process of reconstruction of manifold surfaces. The goal is to contribute a significant advancement in reverse engineering of precision mechanical objects. In our project, we are developing a new technique of 3D surface reconstruction based on the radial basis functions (RBF). Traditionally, all of the dataset is taken as a whole domain to solve the problem of RBF interpolation, showed in Fig. 1. However, it is difficult to deal with the large scale problem in this way. In this situation, the large scale problem can be divided into several small local problems. Then the technique of partition of unity (POU) can be used to combine the local solutions to obtain the global solution. The main idea of the POU is to divide the global domain of interest into smaller overlapping subdomains where the problem can be solved locally. And the local solutions are combined together by using weighting functions to obtain the global solution, illustrated in Filg. 2, and 3. Conventionally, a lot of offsurface points are specified along the surface normal to the surface dataset to avoid the trivial solution of the RBF, showed in Fig. 4. It will double or triple the number of point dataset and make the problem more difficult to solve. In our project, only one nonsurface point is added in each subdomain, showed Filg. 5. So it will tremendously accelerate the reconstruction process. Fig.6 and 7 give some examples. Though with only one extra offsurface point can make the RBF reconstruction faster, there are some noise in the final result, seeing Fig. 7. A diffusion process is utilized to filter the coefficients of RBF in order to smooth the final model.

Fig. 1 RBF on whole domain	Fig.2 POU subdomains		Fig.3 Result of POU RBF

Fig.4 Traditional off-surface constraints		Fig. 5 Our off-surface constraints

Fig. 6 Point cloud data

Fig. 7 Reconstructed sufaces
Our research currently also focuses on the following
Efficient algorithms for point cloud data organization with binary tree structrue and quick sorting method. Algorithms for model smoothing based Isotropic and anisotropic diffusion process.
Supported by:
HKSAR Research Grants Council (RGC) Competitive Earmarked Research Grant (CERG).

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