基于L_0范数最小化的噪声数据可展曲面重建

Developable surface reconstruction from noisy data with L_0-norm minimization

提出噪声数据的可展曲面重建方法.基于L_0范数定义法向量场的优化目标函数,其极小化得到反映曲面可展几何特征的法向量场.基于优化后的法向量场利用变分逼近算法对模型进行区域分割,得到平面区域的序列.通过对拟合分割区域的简单B样条曲面进行合并得到覆盖目标模型整体区域的初始近似可展曲面,最后通过可展曲面的拟合优化得到重建的B样条可展曲面.该方法对恢复带噪声模型的可展几何信息效果较好,能重建出高质量的可展曲面.文中通过几个例子展现了该方法的有效性.

A novel method is proposed for developable surface reconstruction from noisy model.An optimization approach is employed to smooth normal vector field of given model via L_0-norm minimization.This optimization method has the capability of preserving geometric information concerning developability.Based on the optimized normal vector field,a variational shape approximation procedure is utilized to divide the target model into a sequence of planar segments.After each segment is assigned with an initial B-spline surface,a patch merging procedure is used to obtain a B-spline ruled surface which is nearly developable and covers the whole target model.Finally,a developable surface fitting process is used to improve the quality of fitting surface both in approximation error and developability.The presented method shows pleasing performance in recovering developable information in noisy model and consequently is capable of reconstructing high quality developable surfaces.Some experiments are included to demonstrate the performance of the presented method.