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Graph neural networks for 3D shape analysis
Dissertation   Open access

Graph neural networks for 3D shape analysis

Bahareh Shakibajahromi
Doctor of Philosophy (Ph.D.), Drexel University
Jun 2024
DOI:
https://doi.org/10.17918/00010594
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Abstract

Deep learning (Machine learning) Graph neural networks Machine Learning
Deep learning on 3D meshes presents significant challenges due to their intricate and non-uniform structure. Traditional deep learning methods, which are optimized for structured data such as time series, images, or voxel grids, struggle to effectively handle the complexity of mesh data. Additionally, achieving consistent performance in mesh analysis tasks across various mesh orientations is both crucial and challenging with conventional approaches. Graph Neural Networks (GNNs) offer an effective solution to these challenges by naturally adapting to the irregular, graph-like structure of 3D meshes. This dissertation details three major contributions to the field of 3D shape analysis based on GNNs. Firstly, in mesh segmentation, we introduce a deterministic process for transforming meshes into hybrid graphs. This is complemented by our Node-Edge-Face (NEF) embedding layer within the HyNet architecture, which excels in capturing complex geometric interactions for detailed and context-rich segmentation, as evidenced by superior performance in benchmark tests. Secondly, for mesh classification our novel representation learning model, RIMeshGNN, utilizes E(3) equivariant layers, aggregation functions, and pooling techniques to ensure rotation invariance, achieving exceptional accuracy without the need for rotation-augmented training. Lastly, in the area of mesh retrieval, we extend our classification model to encode objects into a discriminative embedding space using a contrastive loss function. This facilitates effective 3D object retrieval based on shape similarities. Due to the absence of a suitable 3D object dataset with ranked similarities for query objects, we created our own ground truth using an image-based retrieval method from Azure AI Vision Studio. Our comprehensive experiments across various datasets demonstrate that our methods achieve state-of-the-art performance, significantly enhancing the practicality and reliability of 3D shape analysis.

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