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Graph representations of 3D data for machine learning

Tomasz Prytuła

TL;DR

The paper argues that non-Euclidean representations (graphs, meshes, point clouds) offer scalable, informative ways to analyze 3D data with machine learning, addressing the computational burden of volumetric methods. It surveys data representations, the 2-step graph-analysis pipeline, and skeletonization-based graph generation, highlighting Graph Neural Networks as a central tool and comparing to 3D CNNs. Two concrete applications—mitochondrial networks in muscle cells and AI-assisted 3D CAD design—demonstrate practical pipelines and the potential for explainability and efficient analysis, while also noting limitations and the need for more data. The work emphasizes a pragmatic, application-driven view of geometric machine learning and provides a path toward guidelines for 3D data analysis using combinatorial representations.

Abstract

We give an overview of combinatorial methods to represent 3D data, such as graphs and meshes, from the viewpoint of their amenability to analysis using machine learning algorithms. We highlight pros and cons of various representations and we discuss some methods of generating/switching between the representations. We finally present two concrete applications in life science and industry. Despite its theoretical nature, our discussion is in general motivated by, and biased towards real-world challenges.

Graph representations of 3D data for machine learning

TL;DR

The paper argues that non-Euclidean representations (graphs, meshes, point clouds) offer scalable, informative ways to analyze 3D data with machine learning, addressing the computational burden of volumetric methods. It surveys data representations, the 2-step graph-analysis pipeline, and skeletonization-based graph generation, highlighting Graph Neural Networks as a central tool and comparing to 3D CNNs. Two concrete applications—mitochondrial networks in muscle cells and AI-assisted 3D CAD design—demonstrate practical pipelines and the potential for explainability and efficient analysis, while also noting limitations and the need for more data. The work emphasizes a pragmatic, application-driven view of geometric machine learning and provides a path toward guidelines for 3D data analysis using combinatorial representations.

Abstract

We give an overview of combinatorial methods to represent 3D data, such as graphs and meshes, from the viewpoint of their amenability to analysis using machine learning algorithms. We highlight pros and cons of various representations and we discuss some methods of generating/switching between the representations. We finally present two concrete applications in life science and industry. Despite its theoretical nature, our discussion is in general motivated by, and biased towards real-world challenges.
Paper Structure (6 sections, 11 figures)

This paper contains 6 sections, 11 figures.

Table of Contents

  1. Introduction
  2. 3D data
  3. The ‘2-step process’ in graph analysis
  4. Applications in concrete cases
  5. Mitochondrial networks in muscle cells
  6. AI for 3D design generation and analysis

Figures (11)

  • Figure 1: Example of various data representations of a 3D object. Source:rabbit_fig.
  • Figure 2: A 3D image of a neuron cell. The actual cell occupies relatively little of the encompassing 3D volume. Source: Bioneer (https://bioneer.dk).
  • Figure 3: The skeletonization algorithm choses nodes based on the size of the sphere one can inscribe in the object. Source:sn_graph.
  • Figure 4: Graph skeleton (right) is considerably lighter than raw voxels (center) or dense point cloud (left). Source:sn_graph.
  • Figure 5: A slice of an image of a mitochondrial network.
  • ...and 6 more figures