Computed tomography (CT) has been a powerful diagnostic tool since its emergence in the 1970s. Using CT data, three-dimensional (3D) structures of human internal organs and tissues, such as blood vessels, can be reconstructed using professional software. This 3D reconstruction is crucial for surgical operations and can serve as a vivid medical teaching example. However, traditional 3D reconstruction heavily relies on manual operations, which are time-consuming, subjective, and require substantial experience. To address this problem, we develop a novel semiparametric Gaussian mixture model tailored for the 3D reconstruction of blood vessels. This model extends the classical Gaussian mixture model by enabling nonparametric variations in the component-wise parameters of interest according to voxel positions. We develop a kernel-based expectation-maximization algorithm for estimating the model parameters, accompanied by a supporting asymptotic theory. Furthermore, we propose a novel regression method for optimal bandwidth selection. Compared to the conventional cross-validation-based (CV) method, the regression method outperforms the CV method in terms of computational and statistical efficiency. In application, this methodology facilitates the fully automated reconstruction of 3D blood vessel structures with remarkable accuracy.

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