Tetrahedral meshes are being extensively used in finite element methods (FEM). This paper proposes an algorithm to generate feature-sensitive and high-quality tetrahedral meshes from an arbitrary surface mesh model. A top-down octree subdivision is conducted on the surface mesh and a set of tetrahedra are constructed using adaptive body-centered cubic (BCC) lattices. Special treatments are given to the tetrahedra near the surface such that the quality of the resulting tetrahedral mesh is provably guaranteed: the smallest dihedral angle is always greater than 5.71°. The meshes generated by our method are not only adaptive from the interior to the boundary, but also feature-sensitive on the surface with denser elements in high-curvature regions where geometric feature most likely reside. A variety of experimental results are presented to demonstrate the effectiveness and robustness of this algorithm.
Intervertebral discs (IVDs), as small joints lying between adjacent vertebrae, have played an important role in pressure buffering and tissue protection. The fully-automatic localization and segmentation of IVDs have been discussed in the literature for many years since they are crucial to spine disease diagnosis and provide quantitative parameters in the treatment. Traditionally hand-crafted features are derived based on image intensities and shape priors to localize and segment IVDs. With the advance of deep learning, various neural network models have gained great success in image analysis including the recognition of intervertebral discs. Particularly, U-Net stands out among other approaches due to its outstanding performance on biomedical images with a relatively small set of training data. This paper proposes a novel convolutional framework based on 3D U-Net to segment IVDs from multi-modality MRI images. We first localize the centers of intervertebral discs in each spine sample and then train the network based on the cropped small volumes centered at the localized intervertebral discs. A detailed comprehensive analysis of the results using various combinations of multi-modalities is presented. Furthermore, experiments conducted on 2D and 3D U-Nets with augmented and nonaugmented datasets are demonstrated and compared in terms of Dice coefficient and Hausdorff distance. Our method has proved to be effective with a mean segmentation Dice coefficient of 89.0% and a standard deviation of 1.4%.
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