The Euclidean distance geometry (EDG) problem is a crucial machine learning task that appears in many applications. Utilizing the pairwise Euclidean distance information of a given point set, EDG reconstructs the configuration of the point system. When only partial distance information is available, matrix completion techniques can be incorporated to fill in the missing pairwise distances. In this paper, we propose a novel dual basis Riemannian gradient descent algorithm, coined RieEDG, for the EDG completion problem. The numerical experiments verify the effectiveness of the proposed algorithm. In particular, we show that RieEDG can precisely reconstruct various datasets consisting of 2- and 3-dimensional points by accessing a small fraction of pairwise distance information.
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Orthogonal Dictionary Guided Shape Completion Network for Point Cloud
Point cloud shape completion, which aims to reconstruct the missing regions of the incomplete point clouds with plausible shapes, is an ill-posed and challenging task that benefits many downstream 3D applications. Prior approaches achieve this goal by employing a two-stage completion framework, generating a coarse yet complete seed point cloud through an encoder-decoder network, followed by refinement and upsampling. However, the encoded features suffer from information loss of the missing portion, leading to an inability of the decoder to reconstruct seed points with detailed geometric clues. To tackle this issue, we propose a novel Orthogonal Dictionary Guided Shape Completion Network (ODGNet). The proposed ODGNet consists of a Seed Generation U-Net, which leverages multi-level feature extraction and concatenation to significantly enhance the representation capability of seed points, and Orthogonal Dictionaries that can learn shape priors from training samples and thus compensate for the information loss of the missing portions during inference. Our design is simple but to the point, extensive experiment results indicate that the proposed method can reconstruct point clouds with more details and outperform previous state-of-the-art counterparts. The implementation code is available at https://github.com/corecai163/ODGNet.
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- Award ID(s):
- 2018966
- PAR ID:
- 10557762
- Publisher / Repository:
- AAAI
- Date Published:
- Journal Name:
- Proceedings of the AAAI Conference on Artificial Intelligence
- Volume:
- 38
- Issue:
- 2
- ISSN:
- 2159-5399
- Page Range / eLocation ID:
- 864 to 872
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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