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

Abstract

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.