Research On Mesh Simplification Via Sparse Optimization

Simplification of complex 3D mesh model and reduce the amount of data in the model is of great importance for the digital geometry processing technology,especially for the real-time rendering and transmission.Because of the development of the science and technology,the demand for visualization technology is gradually enhanced,The requirement of the mesh simplification technology becomes more and more urgent.In this paper,we introduce a mesh approximation method,so that the input model can be approximately represented by a small number of polygonal plane meshes.not only maintains the model contour and features,but also reduces the model data.In this paper,we start from the simplification of 3D mesh,introduce a novel sparse optimization based simplification method to represent a 3D model using planar pieces,obtain a designer specified reasonable and fixed number of planes.The method pro-posed in this paper mainly includes two aspects:On the one hand we first give a mini-mization algorithm to optimize the face normal of input model,and then update vertex position based on optimized normal information.i.e.we first give a L0 norm sparse optimization algorithm to optimize the face normal,so that we can force the optimized face normal will be piece-wise constant.And then we adopt the idea of the Poisson Mesh Deformation to solve this normal driven vertex updating problem.On the other hand,we give a segmentation and clustering algorithm to the existing model,we be-gin with a random face and regard it as a seed,set the cutoff value of the difference between adjacent face normal,iteratively segmentation and clustering.To this end,we have developed a boundary vertex gradient L0 norm minimization algorithm for solv-ing a global energy function based on the clustering result,and get a planar polygonal approximated model.There is a wide range of applications for our proposed system.Our method can be used for geometry processing,3D rendering,data storage and other industries.A large number of experiments show the validity of proposed model and algorithm and the stability of the algorithm when solving mesh simplification problems in dynamic environments.The development and growth of multi-resolution mesh technology and real-time rendering technology,which are all due to the continuous improvement and innovation of technology of mesh simplification.With the increasing demand of graph-ics technology,exploring better mesh simplification methods is also a very important research topics for researchers.