[NS][Lab_Seminar_240708]RIMeshGNN: A Rotation-Invariant Graph Neural Network for Mesh Classification.pptx

RIMeshGNN: A Rotation-Invariant Graph Neural Network for Mesh Classification

1. RIMeshGNN: A Rotation-Invariant Graph Neural Network for Mesh Classification Tien-Bach-Thanh Do Network Science Lab Dept. of Artificial Intelligence The Catholic University of Korea E-mail: os fa19730 @catholic.ac.kr 202 4/07/08 Bahareh Shakibajahromi et al. WACV 2024

2. Introduction Rotation Invariance Shape analysis tasks demonstrate symmetries in Euclidean space and should be invariant to geometric transformations such as rotation and translation

3. Introduction Rotation Invariance All shapes in 3D shape datasets are aligned In practical scenarios, 3D meshes can undergo arbitrary rotations and may not have such canonical pose

4. Previous Work Most point clouds and mesh analysis techniques are affected by rotation

5. Previous Work We can mitigate this issue by extensive data augmentation

6. Previous Work Some techniques utilize handcrafted features that are rotation-invariant, derived from the intrinsic geometries of objects Another group of work focuses on canonical pose normalization Utilize Principal Component Analysis (PCA) to determine three orthogonal bases, transforming point clouds into standardized poses Introduce Pose Selector modules, designed to disambiguate PCA-based canonical poses Limitation: decreased accuracy when classifying datasets with non-symmetrical objects, where intra-class shapes do not share similar structures

7. Method E(3)-Equivariant GNN A 3D shape is a mesh comprised of vertices, edges, and faces, also represented as graph G = (V, E), where V is set of N vertices in mesh, E is set of edges, with feature vectors fi, hij, hG Vertex features include Rotation equivariant Rotation invariant

8. Method Rotation Equivariant GNN The proposed rotation equivariant layer utilizes the nodes, edges, and graph features as input and generates corresponding output features by gathering information from the neighboring nodes in the mesh graph Update edge features: feed-forward neural network edge embedding embedding of rotation invariant portion distance between incident vertices’ coordinates cosine of angles between incident vertices normal graph embedding

9. Method Rotation Equivariant GNN Update node features: Rotation equivariant Rotation invariant MLP

10. Method Rotation Invariant Aggregation Function Calculate the aggregation of node features => design a aggregation function for combining node features Input 3D shapes have been scaled to fit within a unit sphere centered at the origin Divide the range of distances from 0 to 1 into equal intervals, creating spherical bins Bucketize nodes into spherical bins and assign an index k i to each node based on their initial positions and their distances to the center Compute the mean of node embedding h i l+1 within each bin to form m k l+1 Construct a complete graph, each node represents a spherical bin and has a feature vector

11. Method Rotation Equivariant GNN

12. Method Local Pooling Layer Influenced by Garland and Heckbert’s surface simplification algorithm and MeshCNN The local pooling layer performs mesh coarsening at various scales, thus allowing for mesh analysis at multiple resolutions Identify the most appropriate edges for collapsing using a scoring function Rank all edges according to their scores Starting with highest, perform edge collapse only if it preserves manifold faces

13. Method RIMESHGNN for Mesh Classification Concatenate graph features from all layers, fusing all information from intermediate layers

14. Experiments Classification Results - ModelNet40 RIMESHGNN classification network is robust to (seen and unseen) rotations

15. Experiments Classification Results - SHREC11 RIMESHGNN classification network is robust to (seen and unseen) rotations and outperforms others

16. Conclusion Present a novel representation learning model to address challenge of rotation invariance in shape analysis tasks Approach consists of E(3) equivariant GNN layer, aggregation function and local pooling layer Maintain accuracy even when test samples experience arbitrary rotations, without requiring extensive training on rotation-augmented dataset Can be adapted for other mesh analysis tasks: mesh segmentation and retrieval