Star Convex Cuts with Encoding Swaps for Fast Whole-Spine Vertebrae Segmentation in MRI

Abstract

We propose an automatic approach for fast vertebral body segmentation in three-dimensional magnetic resonance images of the whole spine. Previous works are limited to the lower thoracolumbar section and often take minutes to compute, which can be problematic in clinical routine or for data sets with numerous subjects. We address these limitations by a graph cut formulation. Our formulation involves appearance and shape information as well as star-convexity constraints to ensure a topologically correct segmentation for each vertebra. For close targets such as adjacent vertebrae, implementing star-convexity without fusing targets (naive binary formulations) or increasing run time/loosing optimality guarantees (multi-label formulations) is challenging. We provide a solution based on encoding swaps, which preserve optimality and ensure topological correctness between vertebrae. We validated our approach on two data sets. The first contains T1- and T2-weighted whole-spine images of 64 subjects. The second comprises 23 T2-weighted thoracolumbar images and is publicly available. Our results are competitive to previous works (or better) at a fraction of the run time. We yielded Dice coefficients of 85:1 +/- 4:4% and 89:7 +/- 2:3% with run times of 1:65 +/- 0:28 s and 2:73 +/- 0:36 s per vertebra on consumer hardware.