A Gaussian mixture model for combining single threshold and adaptive threshold segmentation of bone microstructure

Segmentation of high-resolution CT enables the assessment of bone microstructure and provides relevant information in determining bone quality and fracture risk. Segmentation is typically performed with a global threshold value, expressed in bone mineral density (BMD). While consistent, a global threshold can lead to a poor representation of bone microstructure; amongst others, caused by altered bone physiology, image noise, image inhomogeneities, and partial volume effects. Adaptive threshold segmentations can preserve fine features, yet, it does not retain any quantitative information on BMD. We propose a new method for bone microstructure segmentation based on a Gaussian mixture model (GMM). This technique models the normalized image histogram as a bi-modal Gaussian distribution, reflecting bone and non-bone voxels, and gives an analytical description of the intensity threshold where probability of belonging to either class is equal. Next, the technique calculates a range of intensities around this threshold, where the tissue class is uncertain; only intensities within this range are adaptively segmented; others with a single threshold. Verification n was performed using simulated images with<i>a priori</i>known distributions. The GMM subsequentially reconstructed the input models. Next, high-resolution peripheral quantitative CT (HR-pQCT) and photon-counting CT (PCCT) images of cadaveric wrists were segmented, and segmentations were scored against reference segmentations from micro-CT. GMM segmentation accuracy was compared to adaptive and global thresholding. The optimal threshold from simulated images could accurately be determined, provided the bi-modal components did not accumulate into a single Gaussian. For HR-pQCT, full adaptive segmentation achieved the highest segmentation accuracy in this specific dataset (86.2 ± 3.7%), although the GMM led to comparable results (83.0 ± 2.3%). For PCCT, the GMM led to a slightly higher segmentation accuracy (77.9 ± 2.3%) than adaptive segmentation did (76.4 ± 2.4%). We conclude that this new method can segment bone microstructure with comparable accuracy as conventional techniques. Through the definition of uncertain intensities, the GMM method has the benefit that it provides the opportunity to tune the segmentation towards higher sensitivity or specificity, depending on the objective.