Curvature estimation is a basic step in many point relative applications such as feature recognition, segmentation,shape analysis and simplification.This paper proposes a moving-least square(MLS) surface based method to evaluate curvatures for unorganized point cloud data.First a variation of the projection based MLS surface is adopted as the underlying representation of the input points.A set of equations for geometric analysis are derived from the implicit definition of the MLS surface.These equations are then used to compute curvatures of the surface.Moreover,an empirical formula for determining the appropriate Gaussian factor is presented to improve the accuracy of curvature estimation.The proposed method is tested on several sets of synthetic and real data.The results demonstrate that the MLS surface based method can faithfully and efficiently estimate curvatures and reflect subtle curvature variations.The comparisons with other curvature computation algorithms also show that the presented method performs well when handling noisy data and dense points with complex shapes.
In the field of 3D model matching and retrieval,an effective method for feature extraction is spherical harmonic or its mutations,and is acted on the spherical images.But the obtainment of spherical images from 3D models is very time-consuming,which greatly restrains the responding speed of such systems.In this paper, we propose a quantitative evaluation of the whole process and give a detailed two-sided analysis based on the comparative size between pixels and voxels.The experiments show that the resultant optimized parameters are fit for the practical application and exhibit a satisfactory performance.
A novel algorithm to voxelize 3D mesh models with gray levels is presented in this paper.The key innovation of our method is to decide the gray level of a voxel according to the total area of all surfaces contained by it.During the preprocessing stage,a set of voxels in the extended bounding box of each triangle is established.Then we travel each triangle and compute the areas between it and its set of voxels one by one.Finally,each voxel is arranged a discrete gray level from 0 to 255.Experiments show that our algorithm gets a comparatively perfect result compared with the prevenient ones and approaches the original models in a more accurate way.
