Constrained implicit function fitting

Abstract

We describe techniques for stabilizing the implicit function fitting process. The key drawback of implicit function fitting methods described in literature thus far has been the stability with respect to outliers in the data. In this paper, we briefly describe methods for stabilizing the implicit function fitting using additional constraints in the form of surface (curve) normals. These constraints eliminate the problem of sensitivity of the implicit function fitting method to outliers in the data. We demonstrate that in certain cases the fitting process can be reduced to a generalized eigenvalue problem that can be efficiently solved by standard numerical procedures. Preliminary experimental results with 2D curves consisting of point location and curve normal constraints as data are encouraging. Our future research efforts will focus on experimenting with 3D data and incorporating both surface normal and surface curvature constraints.