To exploit the advantageous properties of isogeometric analysis (IGA) in a scan-based setting, it is important to extract a smooth geometric domain from the scan data (e.g., voxel data). IGA-suitable domains can be constructed by convoluting the grayscale data using B-splines. A negative side-effect of this convolution technique is, however, that it can induce topological changes in the process of smoothing when features with a size similar to that of the voxels are encountered. This manuscript presents an enhanced B-spline-based segmentation procedure using a refinement strategy based on truncated hierarchical (TH)B-splines. A Fourier analysis is presented to explain the effectiveness of local grayscale function refinement in repairing topological anomalies. A moving-window-based topological anomaly detection algorithm is proposed to identify regions in which the grayscale function refinements must be performed. The criterion to identify topological anomalies is based on the Euler characteristic, giving it the capability to distinguish between topological and shape changes. The proposed topology-preserving THB-spline image segmentation strategy is studied using a range of test cases. These tests pertain to both the segmentation procedure itself, and its application in an immersed IGA setting.
翻译:为了利用扫描环境中等离子分析(IGA)的有利特性,必须从扫描数据(例如 voxel 数据)中提取一个平滑的几何域(例如, voxel 数据) 。 可以通过使用 B- spline 将灰度数据混在一起来构建IGA 直观的域。 但是,这种卷发技术的负面副作用是,当遇到与 voxel 相类似的大小特征时,它可以在平滑过程中产生地形变化。 该手稿提供了一种基于B- spline 的强化分解程序,使用了基于脱轨等级( TH) B- spline 的精细化战略。 提出了四重分析, 解释局部灰度功能在修补表层异常方面的效果。 一种基于移动风的表层异常检测算法, 目的是确定必须进行灰度功能改进的区域。 确定表层异常的标准以 Eul 特征为基础, 使其有能力区分表层和形状的变化。 拟议的THHB- 保留 THB- Spline 样图象断段战略的测试范围。 正在测试 I 测试 。