基于马尔可夫随机场的曲面光顺算法

利用最小均方（LMS）线性预测方法检测曲面型值点，对误差较大的坏点采用预测值进行修正，从而有效地避免了坏点对曲面光顺效果的影响。基于马尔可夫随机场（MRF）的局部特性，采用二阶邻域内数据点的线性组合代替原型值点，选择适当的加权系数，依次对各型值点进行修改，即可在保证曲面精度的前提下实现曲面光顺。计算结果证明，此算法结构简单，运算速度快，修改能力强，对不同形式的参数曲面都可以取得良好的光顺效果。

Surface Fairing Algorithm Based on Markov Random Fields

The least mean square (LMS) linear prediction method was introduced to detect data points of a surface. To avoid bad points affecting the surface fairing performance, all of them were replaced by their predicted values. Based on the local characteristic of the Markov random fields (MRF), every data point of the surface was replaced by the linear combination of the neighboring data points up to the second order. Choosing proper weight coefficient, all the data points in turn can be adjusted and the surface can be faired with fine precision. Numerical results show that the proposed algorithm is simple, effective and can be used for different kinds of parametric surfaces.