RelEdgePool

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

---

Overview

RelEdgePool is a novel, deterministic, and efficient mesh pooling algorithm designed specifically for deep learning and geometric processing on 3D meshes of arbitrary topology—including n-gonal, manifold, and non-manifold meshes. Unlike conventional approaches that are limited to triangular meshes or require extensive pre-processing (triangulation or remeshing), RelEdgePool operates natively on diverse mesh structures, preserving geometric resemblance while efficiently reducing mesh complexity.

Key Features

• Edge-Based Vertex Averaging: Differentiable pooling via local edge-based vertex aggregation.
• Vertex Relational Clustering: A novel, non-differentiable structural step for edge re-establishment and mesh connectivity reconstruction.
• Broad Applicability: Direct support for n-gonal (triangular, quadrilateral, etc.), manifold, and non-manifold meshes—even those with irregular connectivity.
• Determinism: Consistent results for identical inputs, reducing variability in gradient flow and improving training stability.
• Efficient Vertex Reduction: Removes approximately ~72% of vertices per pooling iteration for triangular meshes, and 50% for quadrilateral meshes.
• PyTorch Implementation: Optimized for GPU acceleration and easy integration into deep learning pipelines.

---

Algorithmic Highlights

The RelEdgePool workflow is comprised of two main stages:

1. Edge-Based Vertex Averaging: Clusters vertices based on edge connectivity and computes their centroids, thus reducing the vertex set while maintaining local geometry.
2. Vertex Relational Clustering: Reconstructs the mesh's edge structure by analyzing direct and indirect relationships between clusters, ensuring valid and consistent connectivity in the pooled mesh.

The algorithm is highly generalizable, capable of processing a wide range of mesh topologies, including those that are highly irregular or non-manifold. It enables hierarchical feature extraction and can pool meshes down to a single vertex for applications such as shape classification or segmentation.

---

Experimental Results

• Generalizability: Successfully pools both manifold and non-manifold, triangular, quadrilateral, and higher n-gonal meshes.
• Performance: Outperforms existing mesh pooling algorithms in terms of determinism, generalizability, and vertex reduction, while maintaining highly competitive performance in geometric preservation.
• Robustness: Handles challenging scenarios such as meshes with regions of no thickness, shared edges among multiple faces, interior faces, and inconsistent normals.

Please refer to the paper for detailed results, ablation studies, and benchmarks.

---

Getting Started

Prerequisites

The implementation is based on Python and PyTorch. The following packages are required for the totality of this repository:

• torch
• numpy
• matplotlib
• scipy
• pytorch3d
• point_cloud_utils

---

Usage

The core algorithm is implemented in two main Python files:

• code_implementation/edge_based_vertex_averaging.py: Implements the edge-based vertex averaging pooling step.
• code_implementation/vertex_relational_clustering.py: Implements the vertex relational clustering algorithm for edge re-establishment.

You may use these modules directly in your mesh processing or neural network pipeline. Refer to the notebook for an in-depth integration guideline.

---

Citation

If you use this code or ideas from RelEdgePool in your research, please cite:

@online{rashid2025reledgepool,
  author       = {Haroon Rashid},
  title        = {RelEdgePool: Relational Edge-Aware Pooling for n-gonal manifold and non-manifold 3D meshes},
  date         = {2025-09-22},
  doi          = {10.22541/au.175856984.48726132/v1},
  url          = {https://doi.org/10.22541/au.175856984.48726132/v1},
  publisher    = {Authorea},
  note         = {Preprint}
}

---

Contact

For questions or collaboration:

• Author: Haroon Rashid
• Email: haroonrashidmcvd@proton.me
• ORCID: 0009-0002-1150-3829

---

License

See LICENSE file for details.

---

Acknowledgements

This repository accompanies the paper RelEdgePool: Relational Edge-Aware Pooling for n-gonal manifold and non-manifold 3D meshes.
For more details, algorithmic explanations, and experimental results, please refer to the paper.