Regularization of B-spline objects

摘要

By a d-dimensional B-spline object (denoted as O~d). we mean a B-spline curve (d = 1), a B-spline surface (d = 2) or a B-spline volume (d = 3). By regularization of a B-spline object O~d we mean the process of relocating the control points of O~d such that it approximates an isometric map of its definition domain in certain directions and is shape preserving. In this paper we develop an efficient regularization method for O~d, d = 1,2,3, based on solving weak form L~2-gradient flows constructed from the minimization of certain regularizing energy functionals. These flows are integrated via the finite element method using B-spline basis functions. Our experimental results demonstrate that our new regularization methods are very effective.