颅骨点云曲面重建的Euler’s Elastica模型

Skull Surface Reconstruction with Euler’s Elastica Model from Point Cloud Data

为从具有复杂拓扑关系的颅骨点云数据中重建精确、光滑的隐式曲面,提出了基于Euler’s Elastica的变分水平集方法.首先,将Euler’s Elastica作为正则化约束引入变分能量泛函,采用增广拉格朗日方法将变分能量泛函最小化问题转化为一系列子问题;其次,分别采用广义软阈值公式、解析公式和快速傅里叶变换求解;最后,在计算过程中采用投影算法,有效地避免了水平集函数的重新初始化过程.实验结果表明,相较于现有方法,所提基于Euler’s Elastica的变分水平集方法具有更好的收敛性和有效性,能够提高重建的精确性,避免曲面边缘的缺失.

In order to reconstruct accurate smooth implicit surfaces from skull point cloud data with complex topological relations,a variational level set method based on Euler’s Elastica model is proposed.Firstly,Euler’s Elastica is introduced into the variational energy functional as a regularization constraint,and the variational energy functional minimization problem is transformed into a series of subproblems by the augmented Lagrange method.Secondly,each subproblem is solved by generalized soft threshold formula,analytical formula and fast Fourier transform respectively.Finally,the projection algorithm is used during the computation to avoid the re-initialization of the level set function effectively.The experimental results show that the proposed variational level set method based on Euler’s Elastica has better convergence and effectiveness than the existing methods,which can improve the reconstruction accuracy and avoid missing surface edges.