Learning on 3D Meshes With Laplacian Encoding and Pooling

Qiao, Yi-Ling; Gao, Lin; Yang, Jie; Rosin, Paul L.; Lai, Yuekun; Chen, Xilin

doi:10.1109/tvcg.2020.3014449

Cited by 21 publications

(10 citation statements)

References 49 publications

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“…Bruna et al [43] define the spectral networks that project the per-vertex features onto a spectral basis by a learned linear model. Qiao et al [44] define the Laplacian pooling layers using Laplacian spectral clustering. Despite graph Laplacians being favored for their simplicity, the drawbacks of failing to converge to a continuous operator that captures the geometry of the surface can lead to undesirable behavior in practical applications.…”

Section: Laplacian-based Approachesmentioning

confidence: 99%

Laplacian2Mesh: Laplacian-Based Mesh Understanding

Qian¹,

Wang²,

Gao³

et al. 2022

Preprint

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Geometric deep learning has sparked a rising interest in computer graphics to perform shape understanding tasks, such as shape classification and semantic segmentation on three-dimensional (3D) geometric surfaces. Previous works explored the significant direction by defining the operations of convolution and pooling on triangle meshes, but most methods explicitly utilized the graph connection structure of the mesh. Motivated by the geometric spectral surface reconstruction theory, we introduce a novel and flexible convolutional neural network (CNN) model, called Laplacian2Mesh, for 3D triangle mesh, which maps the features of mesh in the Euclidean space to the multi-dimensional Laplacian-Beltrami space, which is similar to the multi-resolution input in 2D CNN. Mesh pooling is applied to expand the receptive field of the network by the multi-space transformation of Laplacian which retains the surface topology, and channel self-attention convolutions are applied in the new space. Since implicitly using the intrinsic geodesic connections of the mesh through the adjacency matrix, we do not consider the number of the neighbors of the vertices, thereby mesh data with different numbers of vertices can be input. Experiments on various learning tasks applied to 3D meshes demonstrate the effectiveness and efficiency of Laplacian2Mesh.

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Section: Laplacian-based Approachesmentioning

confidence: 99%

Laplacian2Mesh: Laplacian-Based Mesh Understanding

Qian¹,

Wang²,

Gao³

et al. 2022

Preprint

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show abstract

“…Yi et al [2017] define kernels in Laplacian eigenbases, including spectral parameterizations of dilated convolutional kernels and transformer networks. Qiao et al [2020] use Laplacian spectral clustering to define neighborhoods for pooling.…”

Section: Neural Network On Meshesmentioning

confidence: 99%

HodgeNet

Smirnov

Solomon

2021

ACM Trans. Graph.

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Fig. 1. Mesh segmentation results on the full-resolution MIT animation dataset. Each mesh in the dataset contains 20,000 faces (10,000 vertices). We show an example ground truth segmentation in the bottom-left. In contrast to previous works, which downsample each mesh by more than 10×, we efficiently process dense meshes both at train and test time.Constrained by the limitations of learning toolkits engineered for other applications, such as those in image processing, many mesh-based learning algorithms employ data flows that would be atypical from the perspective of conventional geometry processing. As an alternative, we present a technique for learning from meshes built from standard geometry processing modules and operations. We show that low-order eigenvalue/eigenvector computation from operators parameterized using discrete exterior calculus is amenable to efficient approximate backpropagation, yielding spectral per-element or per-mesh features with similar formulas to classical descriptors like the heat/wave kernel signatures. Our model uses few parameters, generalizes to high-resolution meshes, and exhibits performance and time complexity on par with past work.

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“…proposed LaplacianNet [13] in 2020, which performs multi-scale pooling on the basis of Laplacian spectral clustering, and uses grid pooling blocks to utilize global information after pooling, and introduces a The correlation network is used to calculate the correlation matrix, which aggregates global features by multiplying with the matrix of clustering features, and achieves good results on the ShapeNet and COSEG data sets. Litany et al proposed a learning-based method to complete the three-dimensional graph generation and completion [14].…”

Section: Problem Description and Existing Workmentioning

confidence: 99%

3D Mesh Model Classification with a Capsule Network

Zheng

Zhao

et al. 2021

Algorithms

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With the widespread success of deep learning in the two-dimensional field, how to apply deep learning methods from two-dimensional to three-dimensional field has become a current research hotspot. Among them, the polygon mesh structure in the three-dimensional representation as a complex data structure provides an effective shape approximate representation for the three-dimensional object. Although the traditional method can extract the characteristics of the three-dimensional object through the graphical method, it cannot be applied to more complex objects. However, due to the complexity and irregularity of the mesh data, it is difficult to directly apply convolutional neural networks to 3D mesh data processing. Considering this problem, we propose a deep learning method based on a capsule network to effectively classify mesh data. We first design a polynomial convolution template. Through a sliding operation similar to a two-dimensional image convolution window, we directly sample on the grid surface, and use the window sampling surface as the minimum unit of calculation. Because a high-order polynomial can effectively represent a surface, we fit the approximate shape of the surface through the polynomial, use the polynomial parameter as the shape feature of the surface, and add the center point coordinates and normal vector of the surface as the pose feature of the surface. The feature is used as the feature vector of the surface. At the same time, to solve the problem of the introduction of a large number of pooling layers in traditional convolutional neural networks, the capsule network is introduced. For the problem of nonuniform size of the input grid model, the capsule network attitude parameter learning method is improved by sharing the weight of the attitude matrix. The amount of model parameters is reduced, and the training efficiency of the 3D mesh model is further improved. The experiment is compared with the traditional method and the latest two methods on the SHREC15 data set. Compared with the MeshNet and MeshCNN, the average recognition accuracy in the original test set is improved by 3.4% and 2.1%, and the average after fusion of features the accuracy reaches 93.8%. At the same time, under the premise of short training time, this method can also achieve considerable recognition results through experimental verification. The three-dimensional mesh classification method proposed in this paper combines the advantages of graphics and deep learning methods, and effectively improves the classification effect of 3D mesh model.

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Learning on 3D Meshes With Laplacian Encoding and Pooling

Cited by 21 publications

References 49 publications

Laplacian2Mesh: Laplacian-Based Mesh Understanding

Laplacian2Mesh: Laplacian-Based Mesh Understanding

HodgeNet

3D Mesh Model Classification with a Capsule Network

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