# Crack Modeling via Minimum-Weight Surfaces in 3d Voronoi Diagrams

arXiv: https://arxiv.org/abs/2210.05093 · HTML: https://mlsanity.com/paper/2210.05093/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Oct 2022.

## Built on by (most cited first, 5 of 5)

- [Riesz networks: scale invariant neural networks in a single forward pass](https://mlsanity.com/paper/2305.04665/) (2023)
- [Stochastic Geometry Models for Texture Synthesis of Machined Metallic Surfaces: Sandblasting and Milling](https://mlsanity.com/paper/2403.13439/) (2024)
- [A statistical method for crack pre-detection in 3D concrete images](https://mlsanity.com/paper/2402.16126/) (2024)
- [A Novel Distance-Based Metric for Quality Assessment in Image Segmentation](https://mlsanity.com/paper/2504.00023/) (2025)
- [Synthetic Defect Geometries of Cast Metal Objects Modeled via 2d Voronoi Tessellations](https://mlsanity.com/paper/2602.05440/) (2026)

## Abstract (arXiv)

Shortest paths play an important role in mathematical modeling and image processing. Usually, shortest path problems are formulated on planar graphs that consist of vertices and weighted arcs. In this context, one is interested in finding a path of minimum weight from a start vertex to an end vertex. The concept of minimum-weight surfaces extends shortest paths to 3d. The minimum-weight surface problem is formulated on a cellular complex with weighted facets. A cycle on the arcs of the complex serves as input and one is interested in finding a surface of minimum weight bounded by that cycle. In practice, minimum-weight surfaces can be used to segment 3d images. Vice versa, it is possible to use them as a modeling tool for geometric structures such as cracks. In this work, we present an approach for using minimum-weight surfaces in bounded Voronoi diagrams to generate synthetic 3d images of cracks.