基于有向距离场的代数B-样条曲线重建

提出了一种以代数B-样条曲线为表达形式、基于有向距离场的隐式曲线重建方法.首先给定一个表示封闭曲线、可能带有噪音且分布不均匀的平面点云,采用移动最小平方(moving least square,简称MLS)方法对点云去噪、重采样,得到一个低噪音、分布均匀的"线状"点云,再通过Level Set方法建立该"线状"点云的离散几何距离场,最后用一个代数B-样条函数光顺拟合该离散距离场,代数函数的零点集即为重建曲线.曲线重建过程可以归结为求解线性方程组问题.这种重建方法不仅可以得到高质量的重建曲线,还可以得到曲线周围的距离场信息.同时,避免了隐式曲线重建中经常出现的多余分支问题.

Algebraic B-Spline Curve Reconstruction Based on Signed Distance Field

An algebraic B-spline curve fitting algorithm based on the signed distance field is proposed in this paper.Given a planar point set,the moving least square(MLS)method is adopted to denoise and resample it so that the resulting point set is with low noise and uniform sampling density.Then the reliable signed distance field of the preprocessed point set is constructed by using the Level Set method.Finally,an algebraic B-spline function is adopted to fit the signed distance field by solving a linear equation system.As a result,an algebraic curve is obtained which is the zero level set of the algebraic function.By using the proposed method,not only the high quality curve is obtained,but also geometric information around the curve.Furthermore,the unwanted branches in implicit curve fitting could be avoided.