A Convexity Measurement Based On Connectivity

Shape analysis has been playing a fundamental role in computer graphics and other fields.In shape analysis,research on how to quantify a shape with global descriptors such as convexity,concavity,linearity,rectangularity and ellipticity has been booming.Among these descriptors convexity has been most commonly used in shape decomposition,classification and retrieval.This paper will introduce existing convexity measurements and propose a new convexity measurement.The main contributions of this paper are summarized as:(1)This paper introduces convexity measurements for 2D shapes and 3D meshes.We divide current mainstream 2D measurements into three categories.The area-based measurements are robust against noise but insensitive to slight boundary changes.The boundary-based measurements are simple to calculate but sensitive to noise.The probability-based measurements are perfect in theory deduction but suffer from range shrinkage of the convexity value.The pros and cons of 3D convexity measurements are also analysed through experiments.(2)This paper proposes a new convexity measurement based on connectivity for 2D shapes.The basic idea is that convex hull of any 2D shape consists of the shape itself and its dents;firstly,every pixel inside the convex hull is given a distance-weight;and then use the connectivity of every pixel to modify the distance-weight;finally,the convexity of the shape is the ratio of the weights of shape to the weights of its convex hull.In addition,annother connectivity correction definition is provided,performing better on shapes with a high degree of internal dispersion.(3)This paper proposes a new convexity measurement based on distance dictionary for 3D meshes.The basic idea is that any 3D mesh can be normalized to several voxels,and be regarded as collapsed from its convex hull towards the geometric center of the convex hull;every voxel inside the convex hull is first given a distance-weight;and then the convexity is the ratio of the distance-weights of mesh to the distance-weights of convex hull(4)This paper proposes a new convexity measurement based on connectivity for 3D meshes.This convexity measurement is based on the distance dictionary convexity measurement and uses the connectivity of voxels to modify the distance-weights.Moreover,annother connectivity correction definition(noise voxels,internal voxels,and surface voxels)has a better correction effect on meshes with a high degree of internal dispersionThis paper verifies the feasibility of the convexity measurements through theory deduction,and proves the validity of the convexity measurements with numerous experiments.