1,119 research outputs found
Difference of Normals as a Multi-Scale Operator in Unorganized Point Clouds
A novel multi-scale operator for unorganized 3D point clouds is introduced.
The Difference of Normals (DoN) provides a computationally efficient,
multi-scale approach to processing large unorganized 3D point clouds. The
application of DoN in the multi-scale filtering of two different real-world
outdoor urban LIDAR scene datasets is quantitatively and qualitatively
demonstrated. In both datasets the DoN operator is shown to segment large 3D
point clouds into scale-salient clusters, such as cars, people, and lamp posts
towards applications in semi-automatic annotation, and as a pre-processing step
in automatic object recognition. The application of the operator to
segmentation is evaluated on a large public dataset of outdoor LIDAR scenes
with ground truth annotations.Comment: To be published in proceedings of 3DIMPVT 201
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μ£Ό.In this dissertation, we present a theoretical analysis of spectral-based graph neural networks and their practical performance. We analyze how the spectra of a graph Laplacian relates to the convolution operation of a graph neural network, and we discuss how expressive a graph convolutional model can be and how competent expressiveness can be achieved by implementing various convolutions on a graph based on this spectra. The results show that spectral-based graph neural networks can perform well on graph-based tasks, and we discuss what improvements can be made in the future to improve their performance in practice. As an extension, we apply it to traditional computer vision tasks in addition to graph-based tasks and show that it is comparably expressive.
In addition, we present several results of its applications utilizing graphs. Specifically, we conducted experiments on the task of salient object detection using directed acyclic graphs. We also show experimental results of applying the simple model based on the theory of Fourier analysis to practical applications such as the rain removal task. These experiments empirically demonstrate that incorporating the knowledge of graph theory and Fourier analysis into the model helps improve performance.λ³Έ λλ¬Έμμλ μ€ννΈλΌ κΈ°λ° κ·Έλν μΈκ³΅μ κ²½λ§μ μ΄λ‘ μ λΆμκ³Ό κ·Έ μ€μ©μ μ±λ₯μ λν΄ λ€λ£¬λ€. κ·Έλν μ κ²½λ§μμμ 컨볼루μ
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1 Introduction 1
2 Preliminaries 4
2.1 Graph Neural Networks 4
2.1.1 Mathematical Terminologies 4
2.1.2 Graph Message Passing 5
2.1.3 Spatial-based Graph Neural Networks 6
2.1.4 Spectral-based Graph Neural Networks 8
2.2 Collaborative Filtering 8
2.3 Directed Acyclic Graphs Learning 10
3 Related Works 12
3.1 Spectral-based Graph Neural Networks 12
3.1.1 Spectral Network 12
3.1.2 ChebNet 12
3.1.3 Graph Convolutional Networks 13
3.2 Collaborative Filtering 13
3.3 Salient Object Detection 15
3.4 Rain Removal Tasks 17
4 Spectral Analysis of Graph Neural Networks 20
4.1 Schwartz space S (Rd) and Ring graph Rn 20
4.2 Convolution on General Graphs 25
5 Proposed Method 30
5.1 Proposal Background 30
5.2 Spectral GNNs to Computational Fluid Dynamics 31
5.3 Collaborative Filtering 33
5.4 Salient Object Detection 34
5.5 Rain Removal Task 36
6 Experiments 39
6.1 Spectral GNNs to Computational Fluid Dynamics 39
6.1.1 Datasets 39
6.1.2 Experimental Results 40
6.2 Collaborative Filtering 45
6.2.1 Datasets 45
6.2.2 Evaluation Metric 46
6.2.3 Bayesian Personalized Ranking 47
6.2.4 Experimental Results 49
6.3 Salient Object Detection 50
6.3.1 Datasets 50
6.3.2 Evaluation metrics 51
6.3.3 Experimental Results 52
6.4 Rain Removal Task 57
6.4.1 Datasets 57
6.4.2 Experimental Results 57
7 Conclusion 63
References 65
Abstract (in Korean) 73λ°
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