Mosella-Montoro A. Graph Convolutional Neural Networks for 3D Data Analysis. Ruiz-Hidalgo J. Signal Theory and Communications. [Barcelona]: Universitat Polit├Ęcnica de Catalunya; 2023.


Deep Learning allows the extraction of complex features directly from raw input data, eliminating the need for hand-crafted features from the classical Machine Learning pipeline. This new paradigm brought a boost in the performance across several domains, including computer vision, natural language processing and audio processing. However, there are still challenges when dealing with unorganized structures. This thesis addresses this challenge using Graph Convolutional Neural Networks, a new set of techniques capable of managing graph structures that can be used for processing 3D data.  

The first part of the thesis focuses on the Graph Analysis task, in which we study the capabilities of Graph Convolutional Neural Networks to capture the intrinsic geometric information of 3D data. We propose the Attention Graph Convolution layer that learns to infer the kernel used during the convolution, taking into account the particularities of each neighbourhood of the graph. We explore two variants of the Attention Graph Convolution layer, one that explores a residual approach and another one that allows the convolution to combine different neighbourhood domains. Furthermore, we propose a set of 3D pooling layers that mimics the behaviour of the pooling layers found in common 2D Convolutional Neural Networks architectures. Finally, we present a 2D-3D Fusion block capable of merging the 3D geometric information that we get from a Graph Convolutional Neural Network with the texture information obtained by a 2D Convolutional Neural Network. We evaluate the presented contributions on the RGB-D Scene Classification task. 

The second part of this thesis focuses on the Node Analysis task, which consists of extracting features on a node level, taking into account the neighbourhood structure. We present the Multi-Aggregator Graph Convolution layer that uses a multiple aggregator approach to better generalize for unseen topologies and learn better local representations. In addition, it reduces the memory footprint with respect to the Attention Graph Convolution layer. Finally, we analyze the capabilities of our proposed Graph Convolution layers to deal with heterogeneous graphs where the nodes of the graph may belong to different modalities. We evaluate the presented contributions with the Computer Graphics process of skinning a character mesh. Specifically, we propose a Two-Stream Graph Neural Network capable of predicting the skinning weights of a 3D character.