Mesh Remeshing And Morphing Based On Optimal Mass Transport

With the rapid development of 3D technology,3D models have been widely used in multiple fields,and 3D-related algorithms have been research hotspots in various fields.Easy to represent,store,process,and better supported by computer hardware,triangular meshes are main representation of 3D models.Currently,meshes are mainly obtained by 3D scanners or constructed by geometric modeling.However,original meshes are prone to have such problems as too large mesh complexity and multiple degenerated triangles,which not only seriously wastes computer resources,increases difficulty of rendering,processing and transferring,but also directly affects the reliability,stability and efficiency of related algorithms.Thus,as a key technique to optimize original mesh quality and to reduce mesh complexity,mesh remeshing has always been the basic content and research focus of mesh processing.Furthermore,mesh construction through 3D scanners or geometric modeling is time-consuming and money-consuming.Besides,it is impossible to stimulate how a mesh gradually deforms into another one.Thus,as a key technique to produce morphs between different meshes,mesh morphing has always been a research focus in the fields of computer vision,computer graphics,industrial design,films,and so on.Resampling is critical in mesh remeshing,and feature alignment is the most important in morphing.Mesh parameterization is a core technique used in both resampling and feature alignment.However,simply aiming to reduce angle or area distortion,current parameterization methods can not realize more specific and practical parameterizations that reflect how surface bends or enlarges ROIs(regions of interest),which results in great geometric loss of original meshes in remeshing.Currently,conformal parameterization methods are mainly adopted in morphing.Since conformal parameterization may induce large area distortion,feature regions of the meshes may be shrunk into small regions,causing serious loss of geometric details,and thus affecting morphing results.Therefore,a measure-controllable parameterization method,based on dynamic discrete Ricci flow and optimal mass transport,is proposed in this paper,and is applied to mesh remeshing and morphing,so as to improve related algorithms.Firstly,low-quality original meshes are conformally mapped onto the planar domain through dynamic discrete Ricci flow.Then,target measure is set by users in accordance with actual demand.At last,discrete optimal mass transport map is adopted to refine measure distortion and to get measure-preserving parameterization,like area preserving parameterization,curvature sensitive parameterization and ROI sensitive parameterization.Based on this parameterization method,we propose a new remeshing algorithm based on curvature sensitive parameterization.Uniformly sampling on the curvature-sensitive parameterization domain to distribute more samples in feature regions with larger area and curvature,this method can produce feature-preserving remeshing results.Experimental results demonstrate that our remeshing method can produce feature-preserving meshes with high quality and low complexity.Furthermore,a mesh morphing method based on area-preserving method is propo,sed.Firstly,the original input meshes are optimized using remeshing algorithm proposed above.Then,area-preserving parameterizations are computed using the measure-preserving parameterization method proposed in this paper.At last,Mobius transformation and radial basis functions are combined to get exact feature alignment.Experimental results demonstrate that the proposed morphing method advances in performance and mesh complexity,and generates high-quality,smoother and more elegant morphs.