基于改进稀疏场算法的水平集形状过渡

Morphing Based on Mended Sparse-Field Algorithm of Level-Set Method

水平集进化是基于体模型进行三维形状过渡的常用方法,窄带算法和稀疏场算法能高效实现水平集进化,窄带算法的结果较为平滑,稀疏场算法速度更快.一方面通过改进稀疏场算法应用于欧氏距离模型提高速度,另一方面运用窄带算法弥补稀疏场算法的误差.提出用拓扑关系代替距离值范围定义各层体素集,并通过单侧活动集定义使算法更为高效和鲁棒.稀疏场算法因为欧氏距离的近似计算引起误差,在过渡的中后期走样明显,为此,提出了均值平移和窄带回退两种反走样方法对过渡模型进行平滑,前者简单、快速,后者失真度低.

Level-Set method is a good way to do metamorphosis. Narrowband and sparse-field algorithms improve its performance. Results of narrowband morphing are smoother when the sparse-field algorithm is faster. Sparse-field algorithm is mended to fit Euclidean distance model and the narrowband algorithm is used to make up the error of the sparse-field morphing. Topological relationship replaces distance band to define layer sets, and a single side active set is proposed to improve efficiency and robustness. To make up the error of the sparse-field algorithm, which causes obvious alias at the last half stage, two remedy methods are proposed. Averaging and translation method is simpler and more efficient. Narrowband evolution and back method is better for reserving the sharp shape.