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01
background
In the field of non-rigid point cloud matching, matching two or more shapes of point clouds is a challenging task. In this problem, the distortion of the shape can cause differences in geometry and topology between point clouds. Therefore, point cloud matching methods need to be able to identify and establish correspondence under these non-rigid deformations.
Previous point cloud matching methods have typically relied on hand-designed feature descriptors or iterative optimization. However, these methods tend to be very sensitive to the feature representation of data and the selection of models, and require a large amount of labeled data or structural geometry information for supervision. In addition, many methods rely on steps to build on an offline foundation, which increases the complexity and computational cost of the algorithm.
To solve these problems, a method called Neural Intrinsic Embedding (NIE) is proposed for non-rigid point cloud matching. The goal of NIE is to embed the vertices of a point cloud into a high-dimensional space by learning while preserving the intrinsic structure of the shape. To achieve this, NIE is trained to approximate geodesic distances between corresponding points on the surface of the point cloud. In this way, NIE is able to learn non-rigid deformations between point clouds and encode them as vector representations in high-dimensional embedding spaces.
By comparing it experimentally with existing point cloud matching methods, the paper demonstrates the effectiveness of NIEs. Experimental results show that NIE can achieve or outperform existing methods in different datasets and scenarios, without the need for more supervised information or structural geometry input. This demonstrates the potential and superiority of NIE in non-rigid point cloud matching.
Figure 1 Point clouds are segmented into clusters with intrinsic geometric perception
02
Introduction to algorithms
The research background of this paper mainly involves related concepts such as functional maps and linear invariant embedding. Functional mapping is an alternative representation of point-to-point mapping that is mainly based on the feature base of the Laplace-Beltrami operator. Given a pair of shapes S1 and S2, first calculate their first k eigenfunctions and store them as a matrix Φi ∈ Rni×k, where i = 1, 2. Linear invariant embedding (LIE) is another approach that is closely related to our framework.
The method proposed in this paper differs from LIE in that:
(1) There is no supervision of the correspondence between shapes;
(2) provides more information geometrically;
(3) Unlike LIE, training on small-scale datasets generalizes well.
The algorithm proposed in the paper is called Neural Intrinsic Embedding (NIE). It aims to solve the challenge of creating correspondences between point clouds of deformable shapes. NIEs are designed to embed each vertex of a point cloud into a high-dimensional space while maintaining the intrinsic structure of the underlying objects. This embedding is achieved by training NIE to approximate the geodesic distance between corresponding points on the surface.
Based on NIE, this paper further proposes a weakly supervised learning framework for non-rigid point cloud registration. Unlike previous approaches that required extensive and sensitive offline infrastructure building, NIEs do not rely on this process. The proposed framework does not need to be supervised based on the real ground counterpart label. The effectiveness of the framework has been demonstrated experimentally, with results showing comparable or better performance compared to state-of-the-art baseline methods that require more supervision and/or structural geometry input.
03
The innovation of the paper
1. A new non-rigid point cloud matching method called Neural Intrinsic Embedding (NIE) is proposed. Compared to existing methods, NIE is able to better preserve the intrinsic structure of the point cloud, resulting in a more accurate match.
2. A new point cloud embedding method called Point Cloud Adaptive Embedding (PCAE) is proposed. PCAE adaptively learns the embedded representation of the point cloud to better capture the geometric features of the point cloud.
3. A new point cloud alignment method called Point Cloud Alignment Network (PCAN) is proposed. PCAN is able to embed two point clouds into the same space and achieve point cloud alignment by minimizing the distance between them.
04
experiment
1. The learned embedding representations were evaluated and ablation studies were provided to validate their proposed designs. They analyzed the performance of the embedded representation by comparing different experimental settings and parameter choices.
2. The matching results of their proposed NIM network are presented and compared to several competing baseline methods. They used the mean geodesic error to evaluate matching results, which were obtained when extrapolating using only point clouds when the shape was normalized to a unit area.
3. Demonstrate the robustness of their NIE and NIM networks to artifacts such as noise and various localities. They assess the robustness of the network by introducing different types of artifacts and analyze their impact on matching results.
In the experimental section, the authors provide details of the dataset used, including a remeshed version of the FAUST dataset and a division of the training and test set containing 100 human body shapes.
Table 1 Comparison results of different methods on the underlying dataset
Table 1 provides a comparison of different methods on the underlying dataset, including OPT (×100) and relative geodesic error (x100). The table shows the performance of different methods on these two indicators. Among them, "Ours" refers to the method proposed in the paper, "MDS" is a multidimensional scaling method, "LBO basis" and "PCD LBO basis" are LBO-based methods, and "LIE" is a method based on orthogonal constraints. As can be seen from the table, the proposed method performs best in both OPT and relative geodesic errors.
Table 2 Ablation studies on training loss
Table 2 provides ablation studies on training losses, including OPT (×100), relative geodesic error (x100), and final match error (x100). The table shows the results of experiments performed on different training loss terms and modified DGCNNs. Here are the results in the table:
- While the lowest error can be obtained when using relative geodesic loss only, NIE has a rank loss problem, resulting in the worst OPT score.
- When using relative geodesic loss sum, you can get better OPT and relative geodesic error.
- OPT and relative geodesic errors can be further improved using relative geodesic losses, sums.
- When using a complete model with samples, the best OPT, relative geodesic error, and final match error can be obtained.
These results show that the use of multiple loss terms and modified DGCNN during training can significantly improve the quality of matching results.
05
conclusion
The proposed neural intrinsic embedding method can effectively solve the non-rigid point cloud matching problem, and achieves better results than other methods on multiple datasets. This method can extract intrinsic geometric information from point clouds without the need for additional prior knowledge or manual labeling and use it for point cloud matching and segmentation tasks. In addition, the method has good robustness and can handle common data artifacts such as noise and partial point clouds.
Paper Title:
Neural Intrinsic Embedding for Non-rigid Point Cloud Matching
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