We present a two-stage variational approach for segmenting 3D bone CT data that performs robustly with respect to thin cartilage interfaces. In the first stage, we minimize a flux-augmented Chan–Vese model that accurately segments well-separated regions. In the second stage, we apply a new phase-field fracture inspired model that reliably eliminates spurious bridges across thin cartilage interfaces, resulting in an accurate segmentation topology, from which each bone object can be identified. Its mathematical formulation is based on the phase-field approach to variational fracture, which naturally blends with the variational approach to segmentation. We successfully test and validate our methodology for the segmentation of 3D femur and vertebra bones, which feature thin cartilage regions in the hip joint, the intervertebral disks, and synovial joints of the spinous processes. The major strength of the new methodology is its potential for full automation and seamless integration with downstream predictive bone simulation in a common finite element framework.
Bibliographical noteFunding Information:
T. Gangwar is partially supported by a Sommerfeld Fellowship awarded by the Department of Civil, Environmental, and Geo- Engineering at the University of Minnesota, which is gratefully acknowledged. D. Schillinger gratefully acknowledges support from the National Science Foundation through the research grant CISE-1565997 and the NSF CAREER Award No. 1651577 . We acknowledge the Academic Health Center (AHC) and the Institutional Review Board (IRB) of the University of Minnesota for providing clinical data and supporting its use in this study. The Minnesota Supercomputing Institute (MSI) of the University of Minnesota has provided computing resources that have contributed to the research results reported within this paper ( https://www.msi.umn.edu/ ), which is also gratefully acknowledged.
- 3D bone CT data
- Femur extraction
- Flux-augmented Chan–Vese model
- Phase-field fracture mechanics
- Thin cartilage interfaces
- Variational segmentation
- Vertebra extraction
- Voxel finite elements