Ji Chengcheng, Li Jianzhang, Praster Maximilian, Rath Björn, Hildebrand Frank, Eschweiler Jörg
Department of Orthopaedics, Trauma and Reconstructive Surgery, RWTH Aachen University Hospital, 52074 Aachen, Germany.
Department of Orthopaedic Surgery, Klinikum Wels-Grieskirchen, 4600 Wels, Austria.
Life (Basel). 2022 May 23;12(5):770. doi: 10.3390/life12050770.
The carpal bones are eight small bones with irregularities and high curvature on their surfaces. The 3D model of the carpal bone serves as the foundation of further clinical applications, e.g., wrist kinematic behavior. However, due to the limitation of the Magnetic Resonance Imaging (MRI) technique, reconstructed carpal bone models are discretely undersampled, which has dramatic stair-step effects and leads to abnormal meshes on edges or surfaces, etc. Our study focuses on determining the viability of various smoothing techniques for a carpal model reconstructed by in vivo gathered MR images. Five algorithms, namely the Laplacian smoothing algorithm, the Laplacian smoothing algorithm with pre-dilation, the scale-dependent Laplacian algorithm, the curvature flow algorithm, and the inverse distance algorithm, were chosen for evaluation. The assessment took into account the Relative Volume Difference and the Hausdorff Distance as well as the surface quality and the preservation of morphological and morphometric properties. For the five algorithms, we analyzed the Relative Volume Difference and the Hausdorff Distance for all eight carpal bones. Among all the algorithms, the scale-dependent Laplacian method processed the best result regarding surface quality and the preservation of morphological and morphometric properties. Based on our extensive examinations, the scale-dependent Laplacian algorithm is suitable for the undersampled carpal bone model with small volume and large curvature.
腕骨是八块表面不规则且曲率高的小骨头。腕骨的三维模型是进一步临床应用（如手腕运动行为）的基础。然而，由于磁共振成像（MRI）技术的局限性，重建的腕骨模型存在离散欠采样问题，这会产生明显的阶梯效应，并导致边缘或表面出现异常网格等情况。我们的研究重点是确定各种平滑技术对通过体内采集的MR图像重建的腕骨模型的可行性。选择了五种算法进行评估，即拉普拉斯平滑算法、带预扩张的拉普拉斯平滑算法、尺度相关拉普拉斯算法、曲率流算法和反距离算法。评估考虑了相对体积差异、豪斯多夫距离以及表面质量和形态学与形态测量学特性的保留情况。对于这五种算法，我们分析了所有八块腕骨的相对体积差异和豪斯多夫距离。在所有算法中，尺度相关拉普拉斯方法在表面质量以及形态学与形态测量学特性的保留方面处理效果最佳。基于我们的广泛研究，尺度相关拉普拉斯算法适用于体积小且曲率大的欠采样腕骨模型。
