Sparsity Optimization Based Triangular Mesh Filtering

Triangular meshes are often used for representing 3D shapes of objects or real scenes in many fields,for examples,survey and mapping,computer graphics,virtual reality,heritage preservation and so on.In recent years,with the popular of consuminggrade scanning devices(e.g.,Laser scanner,Microsoft Kinect,etc.),lots of triangular meshes have obtained by the two steps,scanning and reconstruction.However,due to the physical limitations of scanning devices and the errors of reconstruction algorithms,those scanned meshes are inevitably polluted by noise.For suppressing noise,we study the high-fidelity triangular mesh filtering algorithm in this paper.Specifically,by adopting sparsity methods,we propose several solutions for overcoming two problems.The first one is to preserve sharp features(e.g.,corners and edges)simultaneously recovering smoothly curved regions well when the noise level is relatively high,and the second one is to handle different kinds of noise.For keeping both sharp features and smoothly curved regions well,this paper proposes a variational mesh denoising method based on total variation and anisotropic Laplace operator.By combining total variation model and anisotropic Laplacian regularization terms,this method constructs a variational normal filtering model which can efficiently remove noise while preserving sharp features as well as not introducing undesired staircase effects in smoothly curved regions.Besides,with taking the orientations of triangles into account,this method also presents a novel vertex position updating method which can robustly reconstruct denoising results without foldover triangles.Extensive experiment results demonstrate that the proposed method can produce high fidelity filtering results,especially for those meshes containing both sharp features and smoothly curved regions.For overcoming the problems of adjusting parameters and high computation complexity of the previous combining method,this paper also proposes a novel mesh denoising method based on an anisotropic second order regularization model.This method first designs an anisotropic second order operator,which can measure the second order variations over the triangulated surfaces.Then,with the second order operator,this method proposes a filtering model based on anisotropic second order regularizations.This filtering model,applied to face normal field,can efficiently remove noise while recovering the sharp features and smoothly curved regions well.Extensive experiment results show that the proposed method can rapidly and efficiently produce high-fidelity filtering results.For handling different kinds of noise,this paper proposes a robust mesh denoising method based on triple sparsity.Firstly,the method introduces a fidelity model based on the sparsity prior on the residual of face normal field.This fidelity model can deal different kinds of noise including Gaussian noise,impulsive noise and Gaussianimpulsive mixed noise.Then,the method presents two regularization models based on a double sparsity prior on the first order and second order variations of face normal field.These two models can recover sharp features and smoothly curved regions well.Extensive experiment results show that the proposed method can robustly produce high-fidelity filtering results,especially for handling real scanned meshes.Since the quality of the triangle mesh directly affects user experience,the above presented high-fidelity triangular mesh filtering methods are not only the precondition for ensuring conduct the subsequent geometry processings(e.g.,segmentation and simplification)accurately,but also the basis for improving the qualities of the upper applications,such as 3D digital city,virtual reality,and so on.