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A Spectral Segmentation Method for Large Meshes

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Communications in Mathematics and Statistics 2023年第3期11卷 583-607页

作者： Xiaohan Bao Weihua Tong falai chen School of Mathematical Sciences University of Science and Technology of ChinaHefei230026AnhuiPeople’s Republic of China

Mesh segmentation is a fundamental and critical task in mesh processing,and it has been studied extensively in computer graphics and geometric modeling communities.However,current methods are not well suited for segmenting large meshes which are now common in many applications.This paper proposes a new spectral segmentation method specifically designed for large meshes inspired by multi-resolution representations.Building on edge collapse operators and progressive mesh representations,we first devise a feature-aware simplification algorithm that can generate a coarse mesh which keeps the same topology as the input mesh and preserves as many features of the input mesh as possible.Then,using the spectral segmentation method proposed in Tong et al.(IEEE Trans Vis Comput Graph 26(4):1807–1820,2020),we perform partition on the coarse mesh to obtain a coarse segmentation which mimics closely the desired segmentation of the input mesh.By reversing the simplification process through vertex split operators,we present a fast algorithm which maps the coarse segmentation to the input mesh and therefore obtain an initial segmentation of the input mesh.Finally,to smooth some jaggy boundaries between adjacent parts of the initial segmentation or align with the desired boundaries,we propose an efficient method to evolve those boundaries driven by geodesic curvature flows.As demonstrated by experimental results on a variety of large meshes,our method outperforms the state-of-the-art segmentation method in terms of not only speed but also usability.

关键词： Mesh segmentation Spectral method Progressive mesh Feature-aware simplification Geodesic curvature flow

Boundary Correspondence for Iso-Geometric Analysis Based on Deep Learning

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Communications in Mathematics and Statistics 2023年第1期11卷 131-150页

作者： Zheng Zhan Ye Zheng Wenping Wang falai chen School of Mathematical Sciences University of Science and Technology of ChinaHefei 230026AnhuiPeople’s Republic of China College of Architecture Texas A&M UniversityCollege StationTX 77843-3112USA

One of the key problems in isogeometric analysis(IGA)is domain parameterization,i.e.,constructing a map between a parametric domain and a computational domain.As a preliminary step of domain parameterization,the mapping between the boundaries of the parametric domain and the computational domain should be established.The boundary correspondence strongly affects the quality of domain parameterization and thus subsequent numerical analysis.Currently,boundary correspondence is generally determined manually and only one approach based on optimal mass transport discusses automatic generation of boundary correspondence.In this article,we propose a deep neural network based approach to generate boundary correspondence for 2D simply connected computational domains.Given the boundary polygon of a planar computational domain,the main problem is to pick four corner vertices on the input boundary in order to subdivide the boundary into four segments which correspond to the four sides of the parametric domain.We synthesize a dataset with corner correspondence and train a fully convolutional network to predict the likelihood of each boundary vertex to be one of the corner vertices,and thus to locate four corner vertices with locally maximum likelihood.We evaluate our method on two types of datasets:MPEG-7 dataset and CAD model dataset.The experiment results demonstrate that our algorithm is faster by several orders of magnitude,and at the same time achieves smaller average angular distortion,more uniform area distortion and higher success rate,compared to the traditional optimization-based method.Furthermore,our neural network exhibits good generalization ability on new datasets.

关键词： Isogeometric analysis Domain parameterization Boundary correspondence Deep neural network

Modified Bases of PHT-Splines

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Communications in Mathematics and Statistics 2017年第4期5卷 381-397页

作者： Yuanpeng Zhu falai chen School of Mathematical Sciences University of Science and Technology of ChinaHefei 230026People’s Republic of China

Recently,it was found that during the process of certain refinement of hier-archical T-meshes,some basis functions of PHT-splines decay severely,which is not expected in solving numerical PDEs and in least square data fitting since the matrices assembled by these basis functions are likely to be ill-conditioned.In this paper,we present a method to modify the basis functions of PHT-splines in the case that the sup-ports of the original truncated basis functions are rectangular domains to overcome the decay problem.The modified basis functions preserve the same nice properties of the original PHT-spline basis functions such as partition of unity,local support,linear independency.Numerical examples show that the modified basis functions can greatly decrease the condition numbers of the stiffness matrices assembled in solving Poisson’s equation with Dirichlet boundary conditions.

关键词： PHT-spline B-spline Hierarchical T-mesh Poisson’s equation

A Review of Process Optimization for Additive Manufacturing Based on Machine Learning

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Annals of Applied Mathematics 2023年第4期39卷 493-543页

作者： Xiaoya Zhai falai chen School of Mathematical Sciences University of Science and Technology of ChinaHefeiAnhui 230026China

Additive manufacturing(AM),also known as 3D printing,has emerged as a groundbreaking technology that has transformed the manufacturing industry.Its ability to produce intricate and customized parts with remarkable speed and reduced material waste has revolutionized traditional manufacturing approaches.However,the AM process itself is a complex and multifaceted undertaking,with various parameters that can significantly influence the quality and efficiency of the printed parts.To address this challenge,researchers have explored the integration of machine learning(ML)techniques to optimize the AM process.This paper presents a comprehensive review of process optimization for additive manufacturing based on machine learning,highlighting the recent advancements,methodologies,and challenges in this field.

关键词： Additive manufacturing 3D printing machine learning process optimization

Joint head pose and facial landmark regression from depth images

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Computational Visual Media 2017年第3期3卷 229-241页

作者： Jie Wang Juyong Zhang Changwei Luo falai chen University of Science and Technology of China HefeiAnhui230026China.

This paper presents a joint head pose and facial landmark regression method with input from depth images for realtime application. Our main contributions are: firstly, a joint optimization method to estimate head pose and facial landmarks, i.e., the pose regression result provides supervised initialization for cascaded facial landmark regression, while the regression result for the facial landmarks can also help to further refine the head pose at each stage. Secondly,we classify the head pose space into 9 sub-spaces, and then use a cascaded random forest with a global shape constraint for training facial landmarks in each specific space. This classification-guided method can effectively handle the problem of large pose changes and occlusion.Lastly, we have built a 3D face database containing 73 subjects, each with 14 expressions in various head poses. Experiments on challenging databases show our method achieves state-of-the-art performance on both head pose estimation and facial landmark regression.

关键词： head pose facial landmarks depth images

Discontinuous Galerkin Methods for Isogeometric Analysis for Elliptic Equations on Surfaces

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Communications in Mathematics and Statistics 2014年第3期2卷 431-461页

作者： Futao Zhang Yan Xu falai chen School of Mathematical Sciences University of Science and Technology of ChinaHefei 230026AnhuiPeople’s Republic of China

We propose a method that combines isogeometric analysis(IGA)with the discontinuous Galerkin(DG)method for solving elliptic equations on 3-dimensional(3D)surfaces consisting of multiple patches.DG ideology is adopted across the patch interfaces to glue the multiple patches,while the traditional IGA,which is very suitable for solving partial differential equations(PDEs)on(3D)surfaces,is employed within each patch.Our method takes advantage of both IGA and the DG method.Firstly,the time-consuming steps in mesh generation process in traditional finite element analysis(FEA)are no longer necessary and refinements,including h-refinement and p-refinement which both maintain the original geometry,can be easily performed by knot insertion and order-elevation(Farin,in Curves and surfaces for CAGD,2002).Secondly,our method can easily handle the cases with non-conforming patches and different degrees across the patches.Moreover,due to the geometric flexibility of IGA basis functions,especially the use of multiple patches,we can get more accurate modeling of more complex surfaces.Thus,the geometrical error is significantly reduced and it is,in particular,eliminated for all conic sections.Finally,this method can be easily formulated and implemented.We generally describe the problem and then present our primal formulation.A new ideology,which directly makes use of the approximation property of the NURBS basis functions on the parametric domain rather than that of the IGA functions on the physical domain(the former is easier to get),is adopted when we perform the theoretical analysis including the boundedness and stability of the primal form,and the error analysis under both the DG norm and the L2 norm.The result of the error analysis shows that our scheme achieves the optimal convergence rate with respect to both the DG norm and the L2 norm.Numerical examples are presented to verify the theoretical result and gauge the good performance of our method.

关键词： Elliptic equation on(3D)surface Isogeometric analysis Discontinuous Galerkin method Multiple patches Non-conforming patches The optimal convergence rate

Diamond Inclusion Reconstruction

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Communications in Mathematics and Statistics 2020年第3期8卷 341-359页

作者： Zijian Yuan Yanzhi Song falai chen Zhouwang Yang School of Mathematical Sciences University of Science and Technology of ChinaHefei 230026People’s Republic of China

In this paper,we make an improvement on the conventional visual hull reconstruction method that runs on a single consumer graphics card.The target application is a high-precision diamond inclusion reconstruction system.One major contribution of this paper is an evaluation system of voxels for high-precision reconstruction.In contrast to existing approaches,it allows us to reconstruct the thin structure of the diamond inclusion.Based on this,we obtain a significant improvement in reconstruction precision,especially for thin inclusion.

关键词： 3D reconstruction Voxel model CUDA

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Preface

Communications in Mathematics and Statistics 2023年第1期11卷 1-2页

作者： Weinan E Princeton falai chen Zaiwen Wen University&Peking University University of Science and Technology of China Peking University

In the past several centuries,there have been two major different paradigms for doing scientific research:the Keplerian paradigm and the Newtonian paradigm.In the Keplerian paradigm,natural laws are discovered through the analysis of data while in the Newtonian paradigm,one focuses on pursuing fundamental principles that govern Nature.

关键词： Newtonian principles fundamental

Computing μ-Bases of Univariate Polynomial Matrices Using Polynomial Matrix Factorization

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Journal of Systems Science & Complexity 2021年第3期34卷 1189-1206页

作者： HUANG Bingru chen falai Department of Mathematics University of Science and Technology of ChinaHefei 230000China

This paper extends the notion of μ-bases to arbitrary univariate polynomial matrices and present an efficient algorithm to compute a μ-basis for a univariate polynomial matrix based on polynomial matrix factorization. Particularly, when applied to polynomial vectors, the algorithm computes a μ-basis of a rational space curve in arbitrary dimension. The authors perform theoretical complexity analysis in this situation and show that the computational complexity of the algorithm is O(dn4+d2 n3),where n is the dimension of the polynomial vector and d is the maximum degree of the polynomials in the vector. In general, the algorithm is n times faster than Song and Goldman’s method, and is more efficient than Hoon Hong’s method when d is relatively large with respect to n. Especially, for computing μ-bases of planar rational curves, the algorithm is among the two fastest algorithms.

关键词： Computational complexity matrix factorization μ-bases