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

TL;DR

This paper introduces a method for modeling cracks in 3D images using minimum-weight surfaces within bounded Voronoi diagrams, extending shortest path concepts to three dimensions for improved image segmentation and structural analysis.

Contribution

The paper presents a novel approach that applies minimum-weight surfaces in 3D Voronoi diagrams to generate synthetic crack images, advancing geometric modeling techniques.

Findings

Effective in generating realistic 3D crack images

Demonstrates the applicability of minimum-weight surfaces in complex structures

Provides a new tool for image segmentation and structural analysis

Abstract

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.