由于离群点会降低支撑向量回归机的性能，因此为了提高支撑向量回归机的图像处理性能，提出了一种具有抗离群点性能的模糊稳健支撑向量回归机（FRSVR），并首先给出了在任意代价函数下支撑向量回归机的求解方法；然后讨论了构建稳健支撑向量机的代价函数所需的性质，并在此基础上，引入了损失代价函数族；接着根据支撑向量回归机的训练误差，用模糊C均值聚类（FCM）查找离群点；最后通过迭代的方法实现了模糊稳健支撑向量回归机。为了对火焰图像进行有效处理，还将FRSVR算法应用于乳化油燃烧火焰图像处理，以去除火焰图像上的离群点。实验结果表明，FRSVR算法处理图像的性能优于ε-SVR算法和自适应SVR滤镜（ASBF），不仅能有效地查找离群点，而且可去除较大的离群点区域，还能显著的降低离群点的影响，并具有良好的泛化性能。

A novel support vector regression method—FRSVR(fuzzy robust support vector regression) based on traditional ε-SVR is proposed in this paper. First, a solution for support vector regression with arbitrary cost function is given. Second the properties which a cost function should have in order to construct a robust support vector regression are discussed. Then a family of cost functions is introduced. In the training procedure of FRSVR, outliers can also be detected in terms of different training error ranges between normal examples and outliers using fuzzy c-means algorithm (FCM). Through iteration, FRSVR is obtained. Since it is based on ε-SVR, various optimization methods for epsilon support vector regression can be used to solve FRSVR. In the experimental part of the paper, FRSVR is applied to process emulsified oil combustion flame images such that outliers therein can be detected and removed, then flame shapes are accordingly segmented. Experimental results show that FRSVR performs better than ε-SVR and ASBF filter in the sense of removing outliers and enhancing the generalization ability.