Because curvature information is of high order differential nature, initial estimates from above method are sensitive to noise, and local neighborhood consistency is poor. We propose to alleviate these problems by associating confidence measures, similar to , from the initial curvature estimation to get local smooth curvature maps. Currently, our smoothing scheme consists of two terms. One tries to adhere to the initial curvature estimates, and is weighted by the confidence measures. The other one is the local smoothness constraint, which can be easily achieved through the neighboring relationship defined by local finite element grid generated from the Delaunay tessellation process. The optimization functional is constructed as follows:
Here, is the entire surface domain, is the optimal smoothed curvature, is the initial curvature estimate, and is a confidence measure matrix from the initial estimation which consists of two components. One is simply inversely proportional to the surface fitting residual error, another component is a function of the eigenvalues , and of the scatter matrix , which indicate the goodness of the local surface patch tangent-normal direction estimation. It favors large , , small , large differences between , and , and small difference between and .
The discrete version of the optimization functional can be conveniently posed as a series of linear equations, and can be solved using iterative methods, such as simultaneous over-relaxation(SOR) approach.