Journal articles: 'Laplacian smoothing'

1

Field, David A. "Laplacian smoothing and Delaunay triangulations." Communications in Applied Numerical Methods 4, no. 6 (November 1988): 709–12. http://dx.doi.org/10.1002/cnm.1630040603.

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Wang, Xiao Ling, and Hui Zhao. "Virtual Mechanical Equipment Model Smoothing." Advanced Materials Research 156-157 (October 2010): 355–59. http://dx.doi.org/10.4028/www.scientific.net/amr.156-157.355.

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We present a system to remove noise or smooth three dimensional (3D) virtual mechanical equipment models. Our system works not in well-known Euclidean space, but in Laplacian space [1, 2]. We transform the model from its global representation into the local representation. Then we manipulate the local property with the Laplacian Coordinates [1]. Our whole system can be modeled as a huge sparse linear system which can be solved very fast by state-of-art numerical solver [3].

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O'sullivan, Finbarr. "Discretized Laplacian Smoothing by Fourier Methods." Journal of the American Statistical Association 86, no. 415 (September 1991): 634–42. http://dx.doi.org/10.1080/01621459.1991.10475089.

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Hansbo, Peter. "Generalized Laplacian smoothing of unstructured grids." Communications in Numerical Methods in Engineering 11, no. 5 (May 1995): 455–64. http://dx.doi.org/10.1002/cnm.1640110510.

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Gu, SuiCheng, Ying Tan, and XinGui He. "Laplacian smoothing transform for face recognition." Science China Information Sciences 53, no. 12 (November 26, 2010): 2415–28. http://dx.doi.org/10.1007/s11432-010-4099-1.

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Xiao, Lei, Guoxiang Yang, Kunyang Zhao, and Gang Mei. "Efficient Parallel Algorithms for 3D Laplacian Smoothing on the GPU." Applied Sciences 9, no. 24 (December 11, 2019): 5437. http://dx.doi.org/10.3390/app9245437.

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In numerical modeling, mesh quality is one of the decisive factors that strongly affects the accuracy of calculations and the convergence of iterations. To improve mesh quality, the Laplacian mesh smoothing method, which repositions nodes to the barycenter of adjacent nodes without changing the mesh topology, has been widely used. However, smoothing a large-scale three dimensional mesh is quite computationally expensive, and few studies have focused on accelerating the Laplacian mesh smoothing method by utilizing the graphics processing unit (GPU). This paper presents a GPU-accelerated parallel algorithm for Laplacian smoothing in three dimensions by considering the influence of different data layouts and iteration forms. To evaluate the efficiency of the GPU implementation, the parallel solution is compared with the original serial solution. Experimental results show that our parallel implementation is up to 46 times faster than the serial version.

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Xi, Ning, Yinjie Sun, Lei Xiao, and Gang Mei. "Designing Parallel Adaptive Laplacian Smoothing for Improving Tetrahedral Mesh Quality on the GPU." Applied Sciences 11, no. 12 (June 15, 2021): 5543. http://dx.doi.org/10.3390/app11125543.

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Mesh quality is a critical issue in numerical computing because it directly impacts both computational efficiency and accuracy. Tetrahedral meshes are widely used in various engineering and science applications. However, in large-scale and complicated application scenarios, there are a large number of tetrahedrons, and in this case, the improvement of mesh quality is computationally expensive. Laplacian mesh smoothing is a simple mesh optimization method that improves mesh quality by changing the locations of nodes. In this paper, by exploiting the parallelism features of the modern graphics processing unit (GPU), we specifically designed a parallel adaptive Laplacian smoothing algorithm for improving the quality of large-scale tetrahedral meshes. In the proposed adaptive algorithm, we defined the aspect ratio as a metric to judge the mesh quality after each iteration to ensure that every smoothing improves the mesh quality. The adaptive algorithm avoids the shortcoming of the ordinary Laplacian algorithm to create potential invalid elements in the concave area. We conducted 5 groups of comparative experimental tests to evaluate the performance of the proposed parallel algorithm. The results demonstrated that the proposed adaptive algorithm is up to 23 times faster than the serial algorithms; and the accuracy of the tetrahedral mesh is satisfactorily improved after adaptive Laplacian mesh smoothing. Compared with the ordinary Laplacian algorithm, the proposed adaptive Laplacian algorithm is more applicable, and can effectively deal with those tetrahedrons with extremely poor quality. This indicates that the proposed parallel algorithm can be applied to improve the mesh quality in large-scale and complicated application scenarios.

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Griffin, M. P., F. Chen, K. L. McMahon, G. Campbell, S. J. Wilson, S. E. Rose, M. Veidt, C. J. Bennett, M. Wegner, and D. M. Doddrell. "Measuring cardiac strain using Laplacian smoothing splines." ANZIAM Journal 44 (April 1, 2003): 249. http://dx.doi.org/10.21914/anziamj.v44i0.681.

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Vollmer, J., R. Mencl, and H. Muller. "Improved Laplacian Smoothing of Noisy Surface Meshes." Computer Graphics Forum 18, no. 3 (September 1999): 131–38. http://dx.doi.org/10.1111/1467-8659.00334.

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Zhan, Yi. "The Nonlocalp-Laplacian Evolution for Image Interpolation." Mathematical Problems in Engineering 2011 (2011): 1–11. http://dx.doi.org/10.1155/2011/837426.

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This paper presents an image interpolation model with nonlocalp-Laplacian regularization. The nonlocalp-Laplacian regularization overcomes the drawback of the partial differential equation (PDE) proposed by Belahmidi and Guichard (2004) that image density diffuses in the directions pointed bylocalgradient. The grey values of images diffuse along image feature direction not gradient direction under the control of the proposed model, that is, minimal smoothing in the directions across the image features and maximal smoothing in the directions along the image features. The total regularizer combines the advantages of nonlocalp-Laplacian regularization and total variation (TV) regularization (preserving discontinuities and 1D image structures). The derived model efficiently reconstructs the real image, leading to a natural interpolation, with reduced blurring and staircase artifacts. We present experimental results that prove the potential and efficacy of the method.

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Gong, Weikang, Renbo Zhao, and Stefan Grünewald. "Structured sparse K-means clustering via Laplacian smoothing." Pattern Recognition Letters 112 (September 2018): 63–69. http://dx.doi.org/10.1016/j.patrec.2018.06.006.

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Wang, Bao, Difan Zou, Quanquan Gu, and Stanley J. Osher. "Laplacian Smoothing Stochastic Gradient Markov Chain Monte Carlo." SIAM Journal on Scientific Computing 43, no. 1 (January 2021): A26—A53. http://dx.doi.org/10.1137/19m1294356.

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Pan, Wei, Xuequan Lu, Yuanhao Gong, Wenming Tang, Jun Liu, Ying He, and Guoping Qiu. "HLO: Half-kernel Laplacian operator for surface smoothing." Computer-Aided Design 121 (April 2020): 102807. http://dx.doi.org/10.1016/j.cad.2019.102807.

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Huang, Zhuo-ju, Jie-min Ding, and Sheng-yi Xiang. "Suspension Footbridge Form-Finding with Laplacian Smoothing Algorithm." International Journal of Steel Structures 20, no. 6 (September 18, 2020): 1989–95. http://dx.doi.org/10.1007/s13296-020-00396-4.

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Listiowarni, Indah. "Implementasi Naïve Bayessian dengan Laplacian Smoothing untuk Peminatan dan Lintas Minat Siswa SMAN 5 Pamekasan." Jurnal Sisfokom (Sistem Informasi dan Komputer) 8, no. 2 (August 13, 2019): 124. http://dx.doi.org/10.32736/sisfokom.v8i2.652.

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Kurikulum 2013 memiliki beberapa perubahan dasar dari kurikulum sebelumnya, salah satunya adalah penyaluran dan penempatan siswa pada program peminatan. Setelah dilakukan klasifikasi peminatan, siswa akan diklasifikasikan lagi menggunakan nilai tes, yang disebut sebagai Lintas Minat Siswa. Penelitian ini berkonsentrasi untuk menerapkan metode Naive Bayessian pada sebuah sistem untuk menanggulangi permasalahan rumitnya proses klasifikasi dua tingkatan dan banyaknya data setiap tahunnya.Naive Bayes merupakan salah satu metode machine learning yang menggunakan perhitungan probabilitas, dan memggunakan laplacian smoothing untuk menghindari hasil akhir bernilai 0. Nilai perhitungan accuracy dan error rate pada 720 data training dengan pengambilan 5 kali jumlah data testing yang berbeda menggunakan naive bayessian dan laplacian smoothing, didapat nilai accuracy : 92,11% dan nilai error rate : 7,02%

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WU, Zouqi, Irina SEMENOVA, Ichiro HAGIWARA, and Junichi SHINODA. "541 A NEW ERROR-MEASURE FOR COMPARISON BETWEEN LAPLACIAN SMOOTHING AND TRAPEZIUM DRAWING ALGORITHM." Proceedings of the JSME annual meeting 2005.1 (2005): 51–52. http://dx.doi.org/10.1299/jsmemecjo.2005.1.0_51.

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Ma, Tian, and Yurong Li. "Improved Tooth Crown Edge Smoothing Method Based on Noise Classification and Fitting." Journal of Medical Imaging and Health Informatics 10, no. 11 (November 1, 2020): 2609–19. http://dx.doi.org/10.1166/jmihi.2020.3261.

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Because three-dimensional (3D) models of teeth are currently obtained via oral scanning, there are only the tooth crown and gingival surface part, lack of data on the roots of teeth, which is not conducive to the 3D reconstruction of teeth. In order to help doctors to carry out virtual tooth correction, this paper studies the edge characteristics of the tooth crown model, removes the edge noise, which can better carry out the 3D reconstruction of teeth. Therefore, this paper proposes an improved method of tooth crown edge smoothing based on noise classification and fitting. First, according to the characteristics of the tooth crown edge, the method of noise classification is proposed after fitting analysis. The noise can be divided into two types: the noise in the boundary line and the noise in the fitting curve. Then, the noise can be identified according to the Gaussian curvature. Finally, the improved Laplacian smoothing and least squares fitting methods are used to remove the two types of noise, and the denoised tooth crown model is the output. The smoothing effect of the method is verified in terms of the noise removal rate, the patch filling rate, and the patch deletion rate. Compared with the traditional Laplacian smoothig, the new method exhibited a noise removal rate increase of 86.0%, a probability of patch filling that approximately doubled, and a probability of patch deletion that basically remained the same. Compared with the least squares fitting method, the new method exhibited a noise removal rate increase of 75.9%, a patch filling reduction of 22.61%, and a patch deletion reduction of 22.14%.

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Ma, Tian, and Yurong Li. "Improved Tooth Crown Edge Smoothing Method Based on Noise Classification and Fitting." Journal of Medical Imaging and Health Informatics 10, no. 11 (November 1, 2020): 2609–19. http://dx.doi.org/10.1166/jmihi.2020.32612609.

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Because three-dimensional (3D) models of teeth are currently obtained via oral scanning, there are only the tooth crown and gingival surface part, lack of data on the roots of teeth, which is not conducive to the 3D reconstruction of teeth. In order to help doctors to carry out virtual tooth correction, this paper studies the edge characteristics of the tooth crown model, removes the edge noise, which can better carry out the 3D reconstruction of teeth. Therefore, this paper proposes an improved method of tooth crown edge smoothing based on noise classification and fitting. First, according to the characteristics of the tooth crown edge, the method of noise classification is proposed after fitting analysis. The noise can be divided into two types: the noise in the boundary line and the noise in the fitting curve. Then, the noise can be identified according to the Gaussian curvature. Finally, the improved Laplacian smoothing and least squares fitting methods are used to remove the two types of noise, and the denoised tooth crown model is the output. The smoothing effect of the method is verified in terms of the noise removal rate, the patch filling rate, and the patch deletion rate. Compared with the traditional Laplacian smoothig, the new method exhibited a noise removal rate increase of 86.0%, a probability of patch filling that approximately doubled, and a probability of patch deletion that basically remained the same. Compared with the least squares fitting method, the new method exhibited a noise removal rate increase of 75.9%, a patch filling reduction of 22.61%, and a patch deletion reduction of 22.14%.

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Wang, Ying Hui, and Wei Yong Wu. "A Graph Spectral Smoothing Approach for Point-Based Surface on GPU." Applied Mechanics and Materials 201-202 (October 2012): 753–57. http://dx.doi.org/10.4028/www.scientific.net/amm.201-202.753.

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In order to smooth point-based surface with noise, Bezier surface fitting method was applied to compute principal curvature and normal vector at each point. We construct an undirected weighted graph from scattered points, and a heat diffusion partial differential equation was defined on this graph. Considering principal curvature as heat power, the smoothing process is realized by diffusing principal curvature along graph structure. We adapt the position of each point along normal direction according to the difference of curvature. Computing heat diffusion equation can be boiled down to the spectral decomposition of Laplacian matrix. We use parallel computing method to solve the spectral decomposition of Laplacian Matrix on GPU to improve the efficiency. Some examples show that our method works well on complex models with large scale point sets.

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Yan, Bencheng, Chaokun Wang, and Gaoyang Guo. "Graph Dilated Network with Rejection Mechanism." Applied Sciences 10, no. 7 (April 2, 2020): 2421. http://dx.doi.org/10.3390/app10072421.

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Recently, graph neural networks (GNNs) have achieved great success in dealing with graph-based data. The basic idea of GNNs is iteratively aggregating the information from neighbors, which is a special form of Laplacian smoothing. However, most of GNNs fall into the over-smoothing problem, i.e., when the model goes deeper, the learned representations become indistinguishable. This reflects the inability of the current GNNs to explore the global graph structure. In this paper, we propose a novel graph neural network to address this problem. A rejection mechanism is designed to address the over-smoothing problem, and a dilated graph convolution kernel is presented to capture the high-level graph structure. A number of experimental results demonstrate that the proposed model outperforms the state-of-the-art GNNs, and can effectively overcome the over-smoothing problem.

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Guitton, Antoine, Gboyega Ayeni, and Esteban Díaz. "Constrained full-waveform inversion by model reparameterization." GEOPHYSICS 77, no. 2 (March 2012): R117—R127. http://dx.doi.org/10.1190/geo2011-0196.1.

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The waveform inversion problem is inherently ill-posed. Traditionally, regularization schemes are used to address this issue. For waveform inversion, where the model is expected to have many details reflecting the physical properties of the Earth, regularization and data fitting can work in opposite directions: the former smoothing and the latter adding details to the model. We propose constraining estimated velocity fields by reparameterizing the model. This technique, also called model-space preconditioning, is based on directional Laplacian filters: It preserves most of the details of the velocity model while smoothing the solution along known geological dips. Preconditioning also yields faster convergence at early iterations. The Laplacian filters have the property to smooth or kill local planar events according to a local dip field. By construction, these filters can be inverted and used in a preconditioned waveform inversion strategy to yield geologically meaningful models. We illustrate with 2D synthetic and field data examples how preconditioning with nonstationary directional Laplacian filters outperforms traditional waveform inversion when sparse data are inverted and when sharp velocity contrasts are present. Adding geological information with preconditioning could benefit full-waveform inversion of real data whenever irregular geometry, coherent noise and lack of low frequencies are present.

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Tai, C. H., D. C. Chiang, and Y. P. Su. "Three-dimensional hyperbolic grid generation with inherent dissipation and Laplacian smoothing." AIAA Journal 34, no. 9 (September 1996): 1801–6. http://dx.doi.org/10.2514/3.13310.

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O'Sullivan, Finbarr. "An Iterative Approach to Two-Dimensional Laplacian Smoothing with Application Image Restoration." Journal of the American Statistical Association 85, no. 409 (March 1990): 213. http://dx.doi.org/10.2307/2289547.

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Zhao, Kunyang. "On the Accelerating of Two-dimensional Smart Laplacian Smoothing on the GPU." Journal of Information and Computational Science 12, no. 13 (September 1, 2015): 5133–43. http://dx.doi.org/10.12733/jics20106587.

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Mei, Gang, John C. Tipper, and Nengxiong Xu. "A Generic Paradigm for Accelerating Laplacian-Based Mesh Smoothing on the GPU." Arabian Journal for Science and Engineering 39, no. 11 (October 12, 2014): 7907–21. http://dx.doi.org/10.1007/s13369-014-1406-y.

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Liao, Zhiwu, Shaoxiang Hu, Dan Sun, and Wufan Chen. "Enclosed Laplacian Operator of Nonlinear Anisotropic Diffusion to Preserve Singularities and Delete Isolated Points in Image Smoothing." Mathematical Problems in Engineering 2011 (2011): 1–15. http://dx.doi.org/10.1155/2011/749456.

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Existing Nonlinear Anisotropic Diffusion (NAD) methods in image smoothing cannot obtain satisfied results near singularities and isolated points because of the discretization errors. In this paper, we propose a new scheme, named Enclosed Laplacian Operator of Nonlinear Anisotropic Diffusion (ELONAD), which allows us to provide a unified framework for points in flat regions, edge points and corners, even can delete isolated points and spurs. ELONAD extends two diffusion directions of classical NAD to eight or more enclosed directions. Thus it not only performs NAD according to modules of enclosed directions which can reduce the influence of traction errors greatly, but also distinguishes isolated points and small spurs from corners which must be preserved. Smoothing results for test patterns and real images using different discretization schemes are also given to test and verify our discussions.

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Hwang, Yao-Hsin, K. C. Ng, and Tony W. H. Sheu. "An improved particle smoothing procedure for Laplacian operator in a randomly scattered cloud." Numerical Heat Transfer, Part B: Fundamentals 70, no. 2 (June 23, 2016): 111–35. http://dx.doi.org/10.1080/10407790.2016.1177403.

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O'sullivan, Finbarr. "An Iterative Approach to Two-Dimensional Laplacian Smoothing with Application to Image Restoration." Journal of the American Statistical Association 85, no. 409 (March 1990): 213–19. http://dx.doi.org/10.1080/01621459.1990.10475328.

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Muntasa, Arif. "Features Fusion based on the Fisherface and Simplification of the Laplacian Smoothing Transform." International Journal on Electrical Engineering and Informatics 9, no. 4 (December 30, 2017): 716–31. http://dx.doi.org/10.15676/ijeei.2017.9.4.6.

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Xu, Dongqing, Dong Zhang, and Xinyi Zhuang. "Investigation of the Coarse Aggregate Texture Property Using an Improved Laplacian Smoothing Algorithm." Journal of Testing and Evaluation 49, no. 3 (July 2, 2019): 20180626. http://dx.doi.org/10.1520/jte20180626.

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Bonforte, Matteo, Razvan Gabriel Iagar, and Juan Luis Vázquez. "Local smoothing effects, positivity, and Harnack inequalities for the fast p-Laplacian equation." Advances in Mathematics 224, no. 5 (August 2010): 2151–215. http://dx.doi.org/10.1016/j.aim.2010.01.023.

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Chen, Eryang, Ruichun Chang, Ke Guo, Fang Miao, Kaibo Shi, Ansheng Ye, and Jianghong Yuan. "Hyperspectral image spectral-spatial classification via weighted Laplacian smoothing constraint-based sparse representation." PLOS ONE 16, no. 7 (July 13, 2021): e0254362. http://dx.doi.org/10.1371/journal.pone.0254362.

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As a powerful tool in hyperspectral image (HSI) classification, sparse representation has gained much attention in recent years owing to its detailed representation of features. In particular, the results of the joint use of spatial and spectral information has been widely applied to HSI classification. However, dealing with the spatial relationship between pixels is a nontrivial task. This paper proposes a new spatial-spectral combined classification method that considers the boundaries of adjacent features in the HSI. Based on the proposed method, a smoothing-constraint Laplacian vector is constructed, which consists of the interest pixel and its four nearest neighbors through their weighting factor. Then, a novel large-block sparse dictionary is developed for simultaneous orthogonal matching pursuit. Our proposed method can obtain a better accuracy of HSI classification on three real HSI datasets than the existing spectral-spatial HSI classifiers. Finally, the experimental results are presented to verify the effectiveness and superiority of the proposed method.

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Park, Jung-Ho, Sanghun Park, and Seung-Hyun Yoon. "Parametric Blending of Hole Patches Based on Shape Difference." Symmetry 12, no. 11 (October 23, 2020): 1759. http://dx.doi.org/10.3390/sym12111759.

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A triangular mesh obtained by scanning 3D models typically contains holes. We present an effective technique for filling a hole in a triangular mesh in geometric modeling. Simple triangulation of a hole is refined and remeshed iteratively to generate an initial patch. The generated patch is then enhanced to become a target patch by minimizing the variation of principal curvatures. In discrete approximation, this produces a third-order Laplacian system of sparse symmetric positive definite matrix, and the symmetry can efficiently be used to find the robust solutions to the given Laplacian system. Laplacian smoothing of the target patch is defined as a source patch. The shape difference between two corresponding vertices of the source and the target patches is measured in terms of Euclidean distance and curvature variation. On the basis of the shape difference and a user-specified control parameter, different blending weights are determined for each vertex, and the final patch is generated by blending two patches. We demonstrate the effectiveness of our technique by discussing several examples. The experimental results show that our technique can effectively restore salient geometric features of the original shape.

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Hu, Ruiqi, Shirui Pan, Guodong Long, Qinghua Lu, Liming Zhu, and Jing Jiang. "Going Deep: Graph Convolutional Ladder-Shape Networks." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 03 (April 3, 2020): 2838–45. http://dx.doi.org/10.1609/aaai.v34i03.5673.

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Neighborhood aggregation algorithms like spectral graph convolutional networks (GCNs) formulate graph convolutions as a symmetric Laplacian smoothing operation to aggregate the feature information of one node with that of its neighbors. While they have achieved great success in semi-supervised node classification on graphs, current approaches suffer from the over-smoothing problem when the depth of the neural networks increases, which always leads to a noticeable degradation of performance. To solve this problem, we present graph convolutional ladder-shape networks (GCLN), a novel graph neural network architecture that transmits messages from shallow layers to deeper layers to overcome the over-smoothing problem and dramatically extend the scale of the neural networks with improved performance. We have validated the effectiveness of proposed GCLN at a node-wise level with a semi-supervised task (node classification) and an unsupervised task (node clustering), and at a graph-wise level with graph classification by applying a differentiable pooling operation. The proposed GCLN outperforms original GCNs, deep GCNs and other state-of-the-art GCN-based models for all three tasks, which were designed from various perspectives on six real-world benchmark data sets.

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Muntasa, Arif. "Enhancement of the Eigen-Laplacian Smoothing Transform Modeling Based on the Neuman Sparse Spectral." International Review on Computers and Software (IRECOS) 11, no. 9 (September 30, 2016): 794. http://dx.doi.org/10.15866/irecos.v11i9.9945.

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Wei, Mingqiang, Wuyao Shen, Jing Qin, Jianhuang Wu, Tien-Tsin Wong, and Pheng-Ann Heng. "Feature-preserving optimization for noisy mesh using joint bilateral filter and constrained Laplacian smoothing." Optics and Lasers in Engineering 51, no. 11 (November 2013): 1223–34. http://dx.doi.org/10.1016/j.optlaseng.2013.04.018.

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Hutchinson, M. F. "A Stochastic Estimator of the Trace of the Influence Matrix for Laplacian Smoothing Splines." Communications in Statistics - Simulation and Computation 18, no. 3 (January 1989): 1059–76. http://dx.doi.org/10.1080/03610918908812806.

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Hutchinson, M. F. "A stochastic estimator of the trace of the influence matrix for laplacian smoothing splines." Communications in Statistics - Simulation and Computation 19, no. 2 (January 1990): 433–50. http://dx.doi.org/10.1080/03610919008812866.

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Liu, Tiantian, Minxin Chen, Yu Song, Hongliang Li, and Benzhuo Lu. "Quality improvement of surface triangular mesh using a modified Laplacian smoothing approach avoiding intersection." PLOS ONE 12, no. 9 (September 8, 2017): e0184206. http://dx.doi.org/10.1371/journal.pone.0184206.

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Okazawa, Noboru, and Tomomi Yokota. "Global Existence and Smoothing Effect for the Complex Ginzburg–Landau Equation with p-Laplacian." Journal of Differential Equations 182, no. 2 (July 2002): 541–76. http://dx.doi.org/10.1006/jdeq.2001.4097.

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Nguyen, Nha, Heng Huang, Soontorn Oraintara, and An Vo. "Stationary Wavelet Packet Transform and Dependent Laplacian Bivariate Shrinkage Estimator for Array-CGH Data Smoothing." Journal of Computational Biology 17, no. 2 (February 2010): 139–52. http://dx.doi.org/10.1089/cmb.2009.0013.

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KREJČIŘÍK, DAVID, and HELENA ŠEDIVÁKOVÁ. "THE EFFECTIVE HAMILTONIAN IN CURVED QUANTUM WAVEGUIDES UNDER MILD REGULARITY ASSUMPTIONS." Reviews in Mathematical Physics 24, no. 07 (July 20, 2012): 1250018. http://dx.doi.org/10.1142/s0129055x12500183.

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The Dirichlet Laplacian in a curved three-dimensional tube built along a spatial (bounded or unbounded) curve is investigated in the limit when the uniform cross-section of the tube diminishes. Both deformations due to bending and twisting of the tube are considered. We show that the Laplacian converges in a norm-resolvent sense to the well-known one-dimensional Schrödinger operator whose potential is expressed in terms of the curvature of the reference curve, the twisting angle and a constant measuring the asymmetry of the cross-section. Contrary to previous results, we allow the reference curves to have non-continuous and possibly vanishing curvature. For such curves, the distinguished Frenet frame standardly used to define the tube need not exist and, moreover, the known approaches to prove the result for unbounded tubes do not work. To establish the norm-resolvent convergence under the minimal regularity assumptions, we use an alternative frame defined by a parallel transport along the curve and a refined smoothing of the curvature via the Steklov approximation.

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Klein, Joshua, Luis Carvalho, and Joseph Zaia. "Application of network smoothing to glycan LC-MS profiling." Bioinformatics 34, no. 20 (May 22, 2018): 3511–18. http://dx.doi.org/10.1093/bioinformatics/bty397.

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Abstract Motivation Glycosylation is one of the most heterogeneous and complex protein post-translational modifications. Liquid chromatography coupled mass spectrometry (LC-MS) is a common high throughput method for analyzing complex biological samples. Accurate study of glycans require high resolution mass spectrometry. Mass spectrometry data contains intricate sub-structures that encode mass and abundance, requiring several transformations before it can be used to identify biological molecules, requiring automated tools to analyze samples in a high throughput setting. Existing tools for interpreting the resulting data do not take into account related glycans when evaluating individual observations, limiting their sensitivity. Results We developed an algorithm for assigning glycan compositions from LC-MS data by exploring biosynthetic network relationships among glycans. Our algorithm optimizes a set of likelihood scoring functions based on glycan chemical properties but uses network Laplacian regularization and optionally prior information about expected glycan families to smooth the likelihood and thus achieve a consistent and more representative solution. Our method was able to identify as many, or more glycan compositions compared to previous approaches, and demonstrated greater sensitivity with regularization. Our network definition was tailored to N-glycans but the method may be applied to glycomics data from other glycan families like O-glycans or heparan sulfate where the relationships between compositions can be expressed as a graph. Availability and implementation Built Executable http://www.bumc.bu.edu/msr/glycresoft/ and Source Code: https://github.com/BostonUniversityCBMS/glycresoft. Supplementary information Supplementary data are available at Bioinformatics online.

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Abdallah, Emad E., Ibrahim Al-Oqily, Alaa E. Abdallah, Ahmed F. Otoom, and Ayoub Alsarhan. "Spectral Graph and Minimal Spanning Tree for 3D Polygonal Meshes Fingerprinting." International Journal of Information Technology and Web Engineering 9, no. 4 (October 2014): 40–53. http://dx.doi.org/10.4018/ijitwe.2014100104.

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In this paper, the authors present a robust three-dimensional fingerprint algorithm for verification, indexing, and identification. The core idea behind our technique is to apply the eigen-decomposition to the mesh Laplacian matrix, and then compute minimum spanning trees (MST) of several concentrations of the mesh shape structure. The fixed size hash vector of a 3D mesh is defined in terms of the MST values and number of the initial patches. The extensive experimental results on several 3D meshes prove the uniqueness of the extracted hash vectors and the robustness of the proposed technique against the most common attacks including distortion-less attacks, compression, noise, smoothing, scaling, rotation as well as mixtures of these attacks.

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Li, Shihu, Wei Liu, and Yingchao Xie. "Ergodicity of 3D Leray-α model with fractional dissipation and degenerate stochastic forcing." Infinite Dimensional Analysis, Quantum Probability and Related Topics 22, no. 01 (March 2019): 1950002. http://dx.doi.org/10.1142/s0219025719500024.

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By using the asymptotic coupling method, the asymptotic log-Harnack inequality is established for the transition semigroup associated to the 3D Leray-[Formula: see text] model with fractional dissipation driven by highly degenerate noise. As applications, we derive the asymptotic strong Feller property and ergodicity for the stochastic 3D Leray-[Formula: see text] model with fractional dissipation, which is the stochastic 3D Navier–Stokes equation regularized through a smoothing kernel of order [Formula: see text] in the nonlinear term and a [Formula: see text]-fractional Laplacian. The main results can be applied to the classical stochastic 3D Leray-[Formula: see text] model ([Formula: see text]), stochastic 3D hyperviscous Navier–Stokes equation ([Formula: see text]) and stochastic 3D critical Leray-[Formula: see text] model ([Formula: see text]).

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Muntasa, Arif, and Indah Agustien Siradjuddin. "Contradictory of the Laplacian Smoothing Transform and Linear Discriminant Analysis Modeling to Extract the Face Image Features." TELKOMNIKA (Telecommunication Computing Electronics and Control) 15, no. 4 (December 1, 2017): 1794. http://dx.doi.org/10.12928/telkomnika.v15i4.6576.

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Kim, Jbium. "The Effect of Mesh Reordering on Laplacian Smoothing for Nonuniform Memory Access Architecture-based High Performance Computing Systems." Journal of the Institute of Electronics and Information Engineers 51, no. 3 (March 25, 2014): 82–88. http://dx.doi.org/10.5573/ieie.2014.51.3.082.

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Yu, Houqiang, Mingyue Ding, and Xuming Zhang. "Laplacian Eigenmaps Network-Based Nonlocal Means Method for MR Image Denoising." Sensors 19, no. 13 (July 1, 2019): 2918. http://dx.doi.org/10.3390/s19132918.

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Magnetic resonance (MR) images are often corrupted by Rician noise which degrades the accuracy of image-based diagnosis tasks. The nonlocal means (NLM) method is a representative filter in denoising MR images due to its competitive denoising performance. However, the existing NLM methods usually exploit the gray-level information or hand-crafted features to evaluate the similarity between image patches, which is disadvantageous for preserving the image details while smoothing out noise. In this paper, an improved nonlocal means method is proposed for removing Rician noise in MR images by using the refined similarity measures. The proposed method firstly extracts the intrinsic features from the pre-denoised image using a shallow convolutional neural network named Laplacian eigenmaps network (LEPNet). Then, the extracted features are used for computing the similarity in the NLM method to produce the denoised image. Finally, the method noise of the denoised image is utilized to further improve the denoising performance. Specifically, the LEPNet model is composed of two cascaded convolutional layers and a nonlinear output layer, in which the Laplacian eigenmaps are employed to learn the filter bank in the convolutional layers and the Leaky Rectified Linear Unit activation function is used in the final output layer to output the nonlinear features. Due to the advantage of LEPNet in recovering the geometric structure of the manifold in the low-dimension space, the features extracted by this network can facilitate characterizing the self-similarity better than the existing NLM methods. Experiments have been performed on the BrainWeb phantom and the real images. Experimental results demonstrate that among several compared denoising methods, the proposed method can provide more effective noise removal and better details preservation in terms of human vision and such objective indexes as peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM).

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Crouzeix, Michel, and Vidar Thomée. "Resolvent Estimates in l_p for Discrete Laplacians on Irregular Meshes and Maximum-norm Stability of Parabolic Finite Difference Schemes." Computational Methods in Applied Mathematics 1, no. 1 (2001): 3–17. http://dx.doi.org/10.2478/cmam-2001-0001.

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AbstractIn an attempt to show maximum-norm stability and smoothing estimates for finite element discretizations of parabolic problems on nonquasi-uniform triangulations we consider the lumped mass method with piecewise linear finite elements in one and two space dimensions. By an energy argument we derive resolvent estimate for the associated discrete Laplacian, which is then a finite difference operator on an irregular mesh, which show that this generates an analytic semigroup in l_p for p‹∞ uniformly in the mesh, assuming in the two-dimensional case that the triangulations are of Delaunay type, and with a logarithmic bound for p=∞. By a different argument based on a weighted norm estimate for a discrete Green's function this is improved to hold without a logarithmic factor for p=∞ in one dimension under a weak mesh-ratio condition. Our estimates are applied to show stability also for time stepping methods.

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Bobkov, Vladimir V. "Spectrally Consistent Approximations to the Matrix Exponent and Their Applications to Boundary Layer Problem." Computational Methods in Applied Mathematics 2, no. 4 (2002): 354–77. http://dx.doi.org/10.2478/cmam-2002-0020.

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AbstractIn an attempt to show maximum-norm stability and smoothing estimates for finite element discretizations of parabolic problems on nonquasi-uniform triangulations we consider the lumped mass method with piecewise linear finite elements in one and two space dimensions. By an energy argument we derive resolvent estimate for the associated discrete Laplacian, which is then a finite difference operator on an irregular mesh, which show that this generates an analytic semigroup in l_p for p‹∞ uniformly in the mesh, assuming in the two-dimensional case that the triangulations are of Delaunay type, and with a logarithmic bound for p=∞. By a different argument based on a weighted norm estimate for a discrete Green's function this is improved to hold without a logarithmic factor for p=∞ in one dimension under a weak mesh-ratio condition. Our estimates are applied to show stability also for time stepping methods.

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Journal articles on the topic 'Laplacian smoothing'

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