Patchwise PDE-based Mesh Progressive Compression And Denoising

Among the existing partial differential equation(PDE)methods,due to its computational efficiency the Bloor-Wilson PDE(BWPDE)method has been widely used in interactive geometry design,solid modeling,computer-aided manufacturing,mesh reconstruction and medical visualization etc.Nevertheless,the BWPDE method cannot be used to represent geometric models with irregular details and branching shapes due to its smoothness.The patchwise PDE(PPDE)method solves this problem by building a local coordinate system for each patch,making it possible to represent complex geometric models.Since the current PPDE method is unsuitable for 3D mesh signal processing,the main purpose of this paper is to improve the existing PPDE method and extend it to the mesh compression and denoising.The detailed contributions of this paper are as follows:(1)Upgrading the existing PPDE method in mesh partitioning,boundary condition extraction and patch merging.The upgradings in mesh partitioning and boundary condition extration make geometric details of the original model in the reconstructed mesh better preserved;the upgrading in patch merging avoids increasement of storage and human intervention caused by the position fixers used in the existing PPDE method.(2)Extending the spectral characteristic of the PPDE method to mesh compression by proposing a mesh progressive compression method.A coarse shape of the original mesh can be reconstructed by only transmitting the PDE low-frequency coefficients,with more PDE high-frequency coefficients received,the coarse mesh is gradually refined by restoring more geometric details of the original mesh.(3)Extending the spectral characteristic of the PPDE method to mesh denoising by proposing a mesh denoising method in the spectral domain.During reconstructing the model with the PPDE method,mesh denoising can be achieved by retaining a certain number of PDE low-frequency coefficients while discarding the high-frequency ones.In this paper,a large number of experiments are carried out to verify the effectiveness of the proposed mesh compression and denoising methods,and we compare and analyze our methods with other competing methods from both the qualitative and quantitative aspects.The experimental results show that in comparison with other methods,with the same compression rate,the model obtained with our compression algorithm is closer to the original model;with the same mesh quality,a high compression ratio can be obtained with our compression algorithm.Compared to other denoising algorithms,our denoising method can generate desired denoising results with fewer iterations and is less affected by the noise intensity.During denoising our method can avoid mesh shrinkage too.