Regularization of B-spline objects

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. (C) 2010 Elsevier B.V. All rights reserved.