中文摘要：

Grouplet变换是一种崭新的方向性小波，可以在任意时间和空间上进行变换，拥有根据图像纹理结构自适应的改变基的能力，从而具有好的稀疏表示能力。基于此，将Grouplet变换引入到金属断口图像处理中，并结合核主成分分析（KPCA），提出了一种基于Grouplet-KPCA的金属断13图像识别方法，同时，提出的方法与基于小波-KPCA方法进行对比。实验结果表明，提出的方法克服了小波-KPCA识别方法只能获取图像有限的方向信息，取得了更高的识别率。Grouplet峭度相比于Grouplet熵，Grouplet峭度对断口图像的纹理变化更敏感，特别适于金属断口的特征提取，因而，基于Grouplet峭度-KPCA的金属断口特征提取取得了比基于Grouplet熵-KPCA的金属断口特征提取更高的识别效果。

英文摘要：

Grouplet transform is a new directional wavelet. This wavelet can be transformed at any time and space, and adaptively change the basis according to image texture. Therefore Grouplet transform has a good ability of sparse representation. Here, Grouplet transform is introduced into the metal fracture images, and combined with the Kernel Principal Component Analysis （KPCA）, a new recognition method of metal fracture images based on Grouplet-KPCA is proposed. At the same time, the proposed method is compared with the wavelet-KPCA recognition method. The experimental results show that the proposed method can overcome the information of finite directions only obtained by the wavelet-KPCA recognition method, and can have a satisfactory recognition rate. Compared with Grouplet entropy, Grouplet kurtosis is more sensitive to the texture change of metal fracture and suitable for feature extraction of metal fracture. Therefore the recognition method based on Grouplet kurtosis-KPCA have better recognition rate than the recognition method based on Grouplet entropy-KPCA.