RelEdgePool: Relational Edge-Aware Pooling for n-gonal manifold and non-manifold 3D meshes

3D computer vision has become an important topic in research and engineering applications. Various methods and algorithms have been introduced to make it possible to train neural networks on 3D mesh data. However, the complexity and size of mesh data make it difficult to perform batch processing and hierarchical feature extraction on it. An efficient pooling operation is needed to reduce meshes of higher vertex density to lower vertex density, while maintaining geometric resemblance between the input and pooled meshes. In this paper, I propose a novel algorithm for pooling mesh datasets. My algorithm utilizes edge-based vertex averaging for pooling and a novel approach, “Vertex Relational Clustering,” to re-establish connectivity in pooled meshes. The proposed algorithm is deterministic in nature, improving training stability and reducing variability in gradient flow, contributing to more efficient optimization. The edge-based vertex averaging component is fully differentiable, allowing gradient flow during training, while the vertex relational clustering component for edge re-establishment is treated as a non-differentiable structural operation that does not require backpropagation. The algorithm supports n-gonal manifold and non-manifold meshes directly, without any need for triangulation or remeshing, making it broadly applicable and versatile.