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Feature-based morphological analysis of shape graph data

Murad Hossen, Demetrio Labate, Nicolas Charon

TL;DR

This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces, designed to satisfy key invariance properties.

Abstract

This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to retrieve and distinguish variations in the connectivity structure of the data but also geometric differences of the network branches. Our proposed approach relies on the extraction of a specifically curated and explicit set of topological, geometric and directional features, designed to satisfy key invariance properties. We leverage the resulting feature representation for tasks such as group comparison, clustering and classification on cohorts of shape graphs. The effectiveness of this representation is evaluated on several real-world datasets including urban road/street networks, neuronal traces and astrocyte imaging. These results are benchmarked against several alternative methods, both feature-based and not.

Feature-based morphological analysis of shape graph data

TL;DR

This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces, designed to satisfy key invariance properties.

Abstract

This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to retrieve and distinguish variations in the connectivity structure of the data but also geometric differences of the network branches. Our proposed approach relies on the extraction of a specifically curated and explicit set of topological, geometric and directional features, designed to satisfy key invariance properties. We leverage the resulting feature representation for tasks such as group comparison, clustering and classification on cohorts of shape graphs. The effectiveness of this representation is evaluated on several real-world datasets including urban road/street networks, neuronal traces and astrocyte imaging. These results are benchmarked against several alternative methods, both feature-based and not.
Paper Structure (28 sections, 29 equations, 12 figures, 3 tables)

This paper contains 28 sections, 29 equations, 12 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Shape Graph
  3. Invariant features on shape graphs
  4. Topological Features
  5. Geometric Features
  6. Directional Statistics Features
  7. Directional histogram of a shape graph
  8. Directional features
  9. Feature-based statistical analysis
  10. Group Comparison
  11. Automatic Clustering
  12. Classification
  13. Experimental validation
  14. City road networks
  15. Data description
  16. ...and 13 more sections

Figures (12)

  • Figure 1: Proposed general data analysis pipeline.
  • Figure 2: Visualization of Shape Graph
  • Figure 3: Fractal dimension calculation using neuronal reconstruction images. The input image is first processed to extract the shape graph (including the extraction of the graph branches), next the box-counting log-log plots is computed, finally the fractal dimension is obtained from the slope of the box-counting plot.
  • Figure 4: Visualization of directional histograms of 2D (left) and 3D (right) shape graphs. The original sum of Dirac distributions are plotted as markers (with size proportional to the weight) on the half circle and half sphere, respectively.
  • Figure 5: Street networks for Downtown Houston (Grid), Trastevere district in Rome (Organic) and Canberra (Hybrid). Nodes and branches are plotted in red and green, respectively.
  • ...and 7 more figures