Similarity-based denoising of point-sampled surfaces

A non-local denoising (NLD) algorithm for point-sampled surfaces (PSSs) is presented based on similarities, including geometry intensity and features of sample points. By using the trilateral filtering operator, the differential signal of each sample point is determined and called "geometry intensity". Based on covariance analysis, a regular grid of geometry intensity of a sample point is constructed, and the geometry-intensity similarity of two points is measured according to their grids. Based on mean shift clustering, the PSSs are clustered in terms of the local geometry-features similarity. The smoothed geometry intensity, i.e., offset distance, of the sample point is estimated according to the two similarities. Using the resulting intensity, the noise component from PSSs is finally removed by adjusting the position of each sample point along its own normal direction. Ex- perimental results demonstrate that the algorithm is robust and can produce a more accurate denoising result while having better feature preservation.

A general framework for progressive point-sampled geometry

Recently unstructured dense point sets have become a new representation of geometric shapes. In this paper we introduce a novel framework within which several usable error metrics are analyzed and the most basic properties of the pro- gressive point-sampled geometry are characterized. Another distinct feature of the proposed framework is its compatibility with most previously proposed surface inference engines. Given the proposed framework, the performances of four representative well-reputed engines are studied and compared.

Differentials-Based Segmentation and Parameterization for Point-Sampled Surfaces

Efficient parameterization of point-sampled surfaces is a fundamental problem in the field of digital geometry processing. In order to parameterize a given point-sampled surface for minimal distance distortion, a differentialslbased segmentation and parameterization approach is proposed in this paper. Our approach partitions the point-sampled geometry based on two criteria： variation of Euclidean distance between sample points, and angular difference between surface differential directions. According to the analysis of normal curvatures for some specified directions, a new projection approach is adopted to estimate the local surface differentials. Then a k-means clustering （k-MC） algorithm is used for partitioning the model into a set of charts based on the estimated local surface attributes. Finally, each chart is parameterized with a statistical method -- multidimensional scaling （MDS） approach, and the parameterization results of all charts form an atlas for compact storage.

Curvature-aware simplification for point-sampled geometry

We propose a novel curvature-aware simplification technique for point-sampled geometry based on the locally optimal projection(LOP) operator.Our algorithm includes two new developments.First,a weight term related to surface variation at each point is introduced to the classic LOP operator.It produces output points with a spatially adaptive distribution.Second,for speeding up the convergence of our method,an initialization process is proposed based on geometry-aware stochastic sampling.Owing to the initialization,the relaxation process achieves a faster convergence rate than those initialized by uniform sampling.Our simplification method possesses a number of distinguishing features.In particular,it provides resilience to noise and outliers,and an intuitively controllable distribution of simplification.Finally,we show the results of our approach with publicly available point cloud data,and compare the results with those obtained using previous methods.Our method outperforms these methods on raw scanned data.