A Dimension Splitting-Interpolating Moving Least Squares (DS-IMLS) Method with Nonsingular Weight Functions

Wang, Jufeng; Sun, Fengxin; Cheng, Rongjun

doi:10.3390/math9192424

Cited by 7 publications

(4 citation statements)

References 63 publications

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“…Firstly, in order to enquire more useful point cloud information, the up-sampling algorithm was applied to increase the point clouds density ( Figure 3 d), in which each grain point was sampled with uniform random distribution to maintain a constant point density. Secondly, since the difference between filled/unfilled rice grains was the curvature of the cavity in the belly of the grain, the normal vector was acquired based on the MLS method ( Figure 3 e) [ 27 ], which was an important feature for filled/unfilled rice grain identification. And the principle of MLS method to calculate a normal vector was as follows: finding any point

{

} in a certain field; obtaining a plane α:

, in which the sum

of the squares of the distances from

to the plane was minimized by the Formula (3).…”

Section: Methodsmentioning

confidence: 99%

A Novel Method for Filled/Unfilled Grain Classification Based on Structured Light Imaging and Improved PointNet++

Huang

Lü

Shi

et al. 2023

Sensors

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China is the largest producer and consumer of rice, and the classification of filled/unfilled rice grains is of great significance for rice breeding and genetic analysis. The traditional method for filled/unfilled rice grain identification was generally manual, which had the disadvantages of low efficiency, poor repeatability, and low precision. In this study, we have proposed a novel method for filled/unfilled grain classification based on structured light imaging and Improved PointNet++. Firstly, the 3D point cloud data of rice grains were obtained by structured light imaging. And then the specified processing algorithms were developed for the single grain segmentation, and data enhancement with normal vector. Finally, the PointNet++ network was improved by adding an additional Set Abstraction layer and combining the maximum pooling of normal vectors to realize filled/unfilled rice grain point cloud classification. To verify the model performance, the Improved PointNet++ was compared with six machine learning methods, PointNet and PointConv. The results showed that the optimal machine learning model is XGboost, with a classification accuracy of 91.99%, while the classification accuracy of Improved PointNet++ was 98.50% outperforming the PointNet 93.75% and PointConv 92.25%. In conclusion, this study has demonstrated a novel and effective method for filled/unfilled grain recognition.

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{

} in a certain field; obtaining a plane α:

, in which the sum

of the squares of the distances from

to the plane was minimized by the Formula (3).…”

Section: Methodsmentioning

confidence: 99%

A Novel Method for Filled/Unfilled Grain Classification Based on Structured Light Imaging and Improved PointNet++

Huang

Lü

Shi

et al. 2023

Sensors

View full text Add to dashboard Cite

show abstract

“…This method first combines the target shape, then divides it into eight equal parts and performs convolutional neural network extraction of voxel features within each octant; based on O-CNN, adaptive O-CNN [14] proposed a planar fitting method for three-dimensional surfaces, in addition to using the pre-set depth of the octree and whether the number of point clouds within the octree reaches a threshold as the partition conditions for the octree, and using the ability to fit the current shape within the octree as an additional partition condition; based on O-CNN, DeepMLS proposed to perform convolutional neural network feature extraction in each smallest octant, and output MLS point cloud through MLP. The moving least-square function is used to approximate the signed distance function, which is used as an implicit function to extract three-dimensional surfaces; dual graph neural networks (GNN) [15] utilized graph convolution to combine voxel features of different scales and transmit octahedral feature information of different depths; Neural-IMLS [16] proposed different weight functions based on DeepMLS and learns SDF directly from the original point cloud in a self-supervised manner. Towards implicit text-guided 3D-shape generation (TISG) [17] generated 3D shapes from text based on an octree; dynamic code cloud-deep implicit functions (DCC-DIF) [18] discretized the space into regular 3D meshes (or octree) and store local codes in grid points (or octant nodes) to calculate local features by interpolating their adjacent local codes and their positions.…”

Section: Related Workmentioning

confidence: 99%

3D Reconstruction Based on Iterative Optimization of Moving Least-Squares Function

Li,

Su,

Jiang

et al. 2024

Algorithms

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Three-dimensional reconstruction from point clouds is an important research topic in computer vision and computer graphics. However, the discrete nature, sparsity, and noise of the original point cloud contribute to the results of 3D surface generation based on global features often appearing jagged and lacking details, making it difficult to describe shape details accurately. We address the challenge of generating smooth and detailed 3D surfaces from point clouds. We propose an adaptive octree partitioning method to divide the global shape into local regions of different scales. An iterative loop method based on GRU is then used to extract features from local voxels and learn local smoothness and global shape priors. Finally, a moving least-squares approach is employed to generate the 3D surface. Experiments demonstrate that our method outperforms existing methods on benchmark datasets (ShapeNet dataset, ABC dataset, and Famous dataset). Ablation studies confirm the effectiveness of the adaptive octree partitioning and GRU modules.

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“…To improve the computational efficiency of the EFG method, by introducing the dimension splitting method [43], Cheng et al proposed the dimension splitting element-free Galerkin (DS-EFG) method [44] and dimension splitting interpolating element-free Galerkin (DS-IEFG) method [45]. The dimension splitting meshless method greatly improves the computational efficiency of the EFG method, and shows high computational efficiency and accuracy for 3D advection-diffusion problems [46], 3D transient heat conduction problems [47][48][49], 3D elasticity problems [50], 3D wave equations [51,52], etc.…”

Section: Introductionmentioning

confidence: 99%

A Dimension-Splitting Variational Multiscale Element-Free Galerkin Method for Three-Dimensional Singularly Perturbed Convection-Diffusion Problems

Wang¹,

Wu²,

Xu³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

Self Cite

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By introducing the dimensional splitting (DS) method into the multiscale interpolating element-free Galerkin (VMIEFG) method, a dimension-splitting multiscale interpolating element-free Galerkin (DS-VMIEFG) method is proposed for three-dimensional (3D) singular perturbed convection-diffusion (SPCD) problems. In the DS-VMIEFG method, the 3D problem is decomposed into a series of 2D problems by the DS method, and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method. The improved interpolation-type moving least squares (IIMLS) method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system of discrete equations for the three-dimensional SPCD problems. The solved numerical example verifies the effectiveness of the method in this paper for the 3D SPCD problems. The numerical solution will gradually converge to the analytical solution with the increase in the number of nodes. For extremely small singular diffusion coefficients, the numerical solution will avoid numerical oscillation and has high computational stability. KEYWORDSDimension-splitting multiscale interpolating element-free Galerkin (DS-VMIEFG) method; interpolating variational multiscale element-free Galerkin (VMIEFG) method; dimension splitting method; singularly perturbed convection-diffusion problems

show abstract

A Dimension Splitting-Interpolating Moving Least Squares (DS-IMLS) Method with Nonsingular Weight Functions

Cited by 7 publications

References 63 publications

A Novel Method for Filled/Unfilled Grain Classification Based on Structured Light Imaging and Improved PointNet++

A Novel Method for Filled/Unfilled Grain Classification Based on Structured Light Imaging and Improved PointNet++

3D Reconstruction Based on Iterative Optimization of Moving Least-Squares Function

A Dimension-Splitting Variational Multiscale Element-Free Galerkin Method for Three-Dimensional Singularly Perturbed Convection-Diffusion Problems

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