善于捕捉空间信息的条件随机场模型虽然已被应用于高光谱遥感图像分类，但条件随机场的性能受到了标注训练样本数量的制约。为解决上述问题，本文提出了一种半监督条件随机场模型用于高光谱遥感图像分类。在该模型中，首先，利用空间-光谱拉普拉斯支持向量机定义关联势函数，以利用未标注样本中包含的信息获取样本类别概率；然后，在交互势函数中嵌入未标注的空间邻域样本，以充分利用空间信息实现对样本类别概率的修正；最后，采用分布式学习策略和平均场完成半监督条件随机场的训练和推断。本文在两个公开的高光谱数据集（Indian Pines数据集，Pavia University数据集）上进行了实验。实验结果表明Kappa系数提升3.94%。

Hyperspectral remote sensing image classification is one of the enormous challenges in the field of applied remote sensing.Traditionally,supervised methods,such as Support Vector Machine (SVM),dominate this area.Especially,Conditional Random Field (CRF) excels in solving this kind of problem in most cases,due to its prominent ability in formulating the spatial relationship.However,CRF suffers from the availability of large amount of labeled samples,which is labor-and time-consuming to obtain in practice.The accuracy tends to decrease dramatically once labeled samples are not adequate or informative enough.To solve the above problem,a semi-supervised CRF model is proposed in this paper.
In the semi-supervised CRF model,the association potential is defined as the spatio-spectral Laplacian Support Vector Machine (ssLapSVM),to exploit the information contained in the unlabeled samples.And the multi-class probability for each sample is obtained by the ssLapSVM with the one-versus-one scheme.In addition,the interaction potential is newly designed by introducing a weight into the Potts model.Note that,in the classification of hyperspectral remote sensing with limited labeled samples,unlabeled neighbors of one labeled samples may often exist.Thus,the labels of these unlabeled neighbors are assigned based on maximum probability acquired by the ssLapSVM,and use the maximum probability as a weight.In the training phrase,the optimal parameters in the association potential,i.e.ssLapSVM,is firstly trained,and then the whole semi-supervised CRF model is trained to get the optimal parameters in the interaction potential.In the inference phrase,mean-field is adopted to find the optimal label configuration over the testing set.
The performance of the proposed semi-supervised CRF model is evaluated on two well-known benchmarks,i.e.Indian Pines scene and Pavia University scene.The objective comparison experiments are carried out among some state-of-the-art methods in terms of kappa statistic.On both Indian Pines (IP) scene and Pavia University (PU) scene,the proposed method can exhibits completely better performance,improve by 4.94%@IP and 3.28%@PU,respectively.In addition,the kappa of the proposed method rises with the increase of the number of labeled training samples.And in most cases,the proposed method shows better performance than other contrast methods under the case of the same training labeled samples.With the increase of trade-off coefficient,kappa statistic rise first and tend to steady,and then degrades dramatically.The proposed method also shows better performance when the larger scope of samples participating in the construction of the interaction potential.
In this paper,we have developed a semi-supervised CRF to address the problem of hyperspectral image classification.Our method can effectively improve the kappa statistic under limited labeled-training set by newly designed association and interaction potential.Experiments conducted on two well-known hyperspectral datasets demonstrate the effectiveness of the proposed method.And when compared to related semi-supervised algorithms,the proposed method shows its superiority.