Many implicit surface reconstruction methods mainly focus on coping with noisy point cloud

but hardly with outliers. Implicit surface reconstruction methods generally require that a point cloud normal is accurate and oriented. However

normal estimation itself is a complex problem for a point cloud with defects laden

such as noises

outliers

low sampling

or registration errors. Hence

a new implicit surface reconstruction algorithm using Voronoi covariance matrix is proposed Poisson surface reconstruction with an indicator function (defined as 1 at points inside the model and 0 at points outside)is used to represent the reconstructed surface. The oriented point samples can be viewed as samples of the gradient of the indicator function of the model. The problem of computing the indicator function is reduced to finding the scalar function

whose gradient best approximates a vector field defined by the samples. Poisson surface reconstruction is robust to noises

even with a few outliers. However

it requires point cloud with oriented normal. The Voronoi covariance matrix can be computed by integrating the domain of its Voronoi cell. The eigenvector of the largest eigenvalues of the Voronoi covariance matrix adequately approximates a normal surface. The anisotropy of the Voronoi cell

which represents the confidence of normal estimation

is the ratio between the largest and the smallest eigenvalues. TheVoronoi covariance matrix is used in this study instead of point cloud normal to avoid the difficulty of normal estimation based on Poisson surface reconstruction. The differential equation of implicit function is also formulated

which satisfies the requirement that the function gradient must be aligned with the principal axes of the Voronoi covariance tensor field. The differential equation is solved in a discrete exterior form. As a result

the surface reconstruction problem is reduced to a generalized eigenvalue problem. Cholesky factorization of TAUCS library and Arnoldi iteration of ARPACK++ library are employed to solve the generalized eigenvalue problem of sparse and symmetrical matrices. When dividing point cloud space

the length of the shortest tetrahedral edge is limited to avoid local space excessive division. The thin shell around the point cloud

which is defined by probability measure theory

is further divided to increase surface reconstruction accuracy. Delaunay refinement is used to extract isosurface. Compared with the traditional marching cube method

Delaunay refinement guarantees that reconstructed surface is homotopic to implicit surface and is more flexible in terms of resolution. Experiments show that our algorithm can reconstruct the surface well from point cloud even with noises and outliers. Triangle mesh of different resolutions can be generated by adjusting the Delaunay refinement parameter. The fitness between reconstructed surface and point cloud is related to the fitness parameter

and different parts of the surface can be distinguished by adjusting the fitness parameter. However

the bottleneck of the algorithm lies in the high memory requirement and time-consuming Cholesky factor for large models. A new implicit surface reconstruction method using Voronoi covariance matrix is presented. Results show that the algorithm is practical and can robustly reconstruct surfaces with good aspect ratioand without point cloud normal.