Adaptive Metrics for Adaptive Samples

We generalize the local-feature size definition of adaptive sampling used in surface reconstruction to relate it to an alternative metric on Euclidean space. In the new metric, adaptive samples become uniform samples, making it simpler both to give adaptive sampling versions of homological inference results and to prove topological guarantees using the critical points theory of distance functions. This ultimately leads to an algorithm for homology inference from samples whose spacing depends on their distance to a discrete representation of the complement space.

A Efficient Surface Reconstruction Method for Noisy Samples Based on Bilateral Filtering and down Sampling

Surface reconstruction is a hot topic in the field of computer graphics. Power Crust algorithm can reconstruct a triangle mesh that is topologically valid and convergent to the original surface. But it can not handle the points with noised and its running time is long. In this paper an efficient surface reconstruction algorithm for noisy samples is proposed. Firstly, we delete the noise by bilateral filter. Secondly, a non-uniformly sampling method is used to resample the input data in order decrease the number of the samples to the local feature size before reconstruction. Finally, Power crust algorithm is be used to reconstructed the surface. From the experiments, it can be seen the speed of reconstruction is increased and the features of the surface are preserved.

A New Surface Reconstruction Algorithm for Noisy 3D Unorganized Points

This paper puts forward a new method of surface reconstruction. Power crust algorithm can reconstruct a good surface that is topological valid and be proved theoretically. But when the point cloud is noisy, the surface reconstructed is not good and its running time is long. This paper proposes a improved method of fuzzy c-means clustering to delete the noisy points and a non-uniformly sampling method to resample the input data set according to the local feature size before reconstruction. Experimental results show that the efficiency of the algorithm has been improved much more.

DELAUNAY REFINEMENT ALGORITHMS FOR ESTIMATING LOCAL FEATURE SIZE IN 2D AND 3D

We present Delaunay refinement algorithms for estimating local feature size on the input vertices of a 2D piecewise linear complex and on the input vertices and segments of a 3D piecewise linear complex. These algorithms are designed to eliminate the need for a local feature size oracle during quality mesh generation of domains containing acute input angles. In keeping with Ruppert's algorithm, encroachment in these algorithms can be determined through only local information in the current Delaunay triangulation. The algorithms are practical to implement and several examples are given.