在處理資料時，特徵粹取主要應用於移除多餘的特徵，並且增進處理效果。當類別間的邊界為非線性時，線性降維方法功效不如非線性降維方法，可在低維度空間分離出類別資訊。基於核函數之非線性降維法是以一正定函數點積方式，投影資料到高維度並結合線性降維方法，來模擬實現非線性降維法。在核函數方法中，輻射基底函數是常見拿來應用的核函數，然而對於特徵粹取方法而言，基於輻射基底函數之核函數方法只考慮歐式距離，因此，此函數並不適用於分類的問題中。
　　在本論文中分別應用影像上資料的紋理以及類別資訊加以改進輻射基底函數。若資料屬於同類別或者其影像上的結構相似，我們將適時增強其在核函數中的相似度，這使得應用核函數之非線性降維法時，能增加其類別間的鑑別度。
　　我們以合成及實際影像來測試效能好壞。實驗證實所提出之基於馬可夫隨基場核函數比輻射基底函數和線性降維法有較好的分類正確率，而且所提出的基於馬可夫隨基場核函數特徵粹取能以單點分類器模式勝過基於馬可夫隨機場之分類器。

　　Feature extraction has been intensively used in pattern recognition for removing redundant features and accelerating data processing. When classes are separated by a nonlinear boundary, the linear feature reduction methods may not as efficiently as nonlinear methods separate classes in a low dimensional feature space. By replacing the inner product with an appropriate positive definite function, the kernel-based nonlinear feature extraction methods implicitly perform a nonlinear mapping of the input data into a high-dimensional feature space and then compute a linear feature extraction method. The radial basis kernel function (RBF) is a commonly seen kernel trick. However, the RBF kernel method may not fulfill feature extraction perfectly in classification problem since its similarity measure is based merely on the Euclidean distance.
　　This study incorporates contextualand class information into the RBF kernel function to improve the performance of kernel-based feature extraction. Samples are considered closer in case of the same class labels or in case that their neighbors are alike in the MRF sense. This leads to an increased discrimination between samples when using kernel function implicitly for a nonlinear mapping of data into a higher-dimensional space. 　　
　　Experiments have been tested on three synthesized dataset and real images. In our experiments, the proposed MRF-based kernel method yielded comparatively higher classification accuracy than the traditional RBF-based kernel method and other linear feature extraction methods. Also, the MRF-based kernel feature extraction, followed by a pixel-wise classifier, out performed the MRF-based contextual classifier.

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