# Cube-Cut: Vertebral Body Segmentation in MRI-Data through Cubic-Shaped Divergences

arXiv: https://arxiv.org/abs/1404.4467 · HTML: https://mlsanity.com/paper/1404.4467/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Apr 2014.

## Built on by (most cited first, 1 of 1)

- [Weakly Supervised Segmentation of Vertebral Bodies with Iterative Slice-propagation](https://mlsanity.com/paper/2402.08892/) (2024)

## Abstract (arXiv)

In this article, we present a graph-based method using a cubic template for volumetric segmentation of vertebrae in magnetic resonance imaging (MRI) acquisitions. The user can define the degree of deviation from a regular cube via a smoothness value Delta. The Cube-Cut algorithm generates a directed graph with two terminal nodes (s-t-network), where the nodes of the graph correspond to a cubic-shaped subset of the image's voxels. The weightings of the graph's terminal edges, which connect every node with a virtual source s or a virtual sink t, represent the affinity of a voxel to the vertebra (source) and to the background (sink). Furthermore, a set of infinite weighted and non-terminal edges implements the smoothness term. After graph construction, a minimal s-t-cut is calculated within polynomial computation time, which splits the nodes into two disjoint units. Subsequently, the segmentation result is determined out of the source-set. A quantitative evaluation of a C++ implementation of the algorithm resulted in an average Dice Similarity Coefficient (DSC) of 81.33% and a running time of less than a minute.